Single droplet drying of proteins and protein formulations

SINGLE DROPLET DRYING OF
PROTEINS AND PROTEIN FORMULATIONS
VIA ACOUSTIC LEVITATION
Den naturwissenschaftlichen Fakultäten
der Friedrich-Alexander Universität Erlangen-Nürnberg
zur
Erlangung des Doktorgrades
vorgelegt von
Heiko Alexander Schiffter
aus Heilbronn-Neckargartach

Als Dissertation genehmigt von den
naturwissenschaftlichen Fakultäten der Universität Erlangen-Nürnberg
Tag der mündlichen Prüfung:
Vorsitzender der Promotionskommision: Prof. Dr. D.-P. Häder
Erstberichterstatter: Prof. Dr. Geoffrey Lee
Zweitberichterstatter: Prof. Dr. Anker Jensen

To my family
in love and gratitude
Schreib in den Sand, die dich betrüben,
Vergiß dann schnell, und schlafe drüber ein,
Denn was du in den Sand geschrieben,
Das wird schon morgen nicht mehr sein.
Schreib in den Stein, was du erfahren
An Liebe, Seligkeit und Glück.
Es gibt der Stein dir auch nach Jahren
Dies als Erinnerung zurück.

ACKNOWLEDGEMENTS
The present thesis has been acquired between August 2002 and December 2005 at the Department
of Pharmaceutical Technology, Friedrich-Alexander-University Nuremberg-Erlangen, Germany.
First of all, Professor Dr. Geoffrey Lee is gratefully acknowledged for offering me the opportunity
to work in this very interesting field of research, for many constructive discussions and support
during this period, for promoting additional research projects, for the opportunity to develop a
complete lecture in pharmacokinetics and for the friendly atmosphere within the department.
Professor Dr. Anker Jensen, Department of Chemical Engineering, Technical University of
Denmark, is thanked for kindly being co-referee for this thesis.
Many thanks to Professor Dr. Günther Brenn, Department of Chemical Engineering, Technical,
University of Graz, Austria and Dr. Dirk Rensink, Adam Opel AG, Germany, for their help and
support with the acoustic levitation system and the knowledge they shared with me. They always
found time to answer all of my questions in detail.
Christian Schwartzbach and Sune Klint Anderson, Niro A/S, Denmark is thanked for gratefully
supporting this project and for giving me new inspirations by discussing many critical details of the
evaporation process. Also thank you very much for the invitation and the visit in Copenhagen.
Thank you very much to Dr. Rudolf Tuckermann for helping me with the acoustic levitator,
providing me with his thesis and giving me new inspirations when visiting my laboratory in
Erlangen.
Dr. Gerhard Simon and Dr. Stefan Seyferth is thanked for their support in problems with computer
hardware and software.
Innerhalb des Instituts für pharmazeutische Technologie in Erlangen möchte ich mich zuerst bei
Dr. Michael Maury für seine langjährige Freundschaft während des gemeinsamen Studiums in
Heidelberg und der Promotion in Erlangen, für die vielen Diskussionen über Wissenschaft und
Studentenpraktika, die Zeit im „Heidelberger Labor“ und die lustigen Abende Downtown
bedanken. Vielen Dank an Dr. Henning Gieseler für die gemeinsame Zeit in Erlangen, die Hilfe und
Ratschläge bei wissenschaftlichen Fragen, die kulinarischen Abende in Nürnberg und Umgebung
und eine unvergesslich Woche auf dem AAPS-Kongress in Nashville. Danke auch an Alexander
Mauerer für die Hilfe bei jeder Art von Soft- und Hardwareproblemen, aber vor allem für die vielen

Stunden innerhalb und außerhalb der Universität, wie auch für die immer exakten
Wegbeschreibungen zu den besten Locations der Region. Vielen Dank an Andreas Ziegler und
Peter Lassner, dem selbsternannten „Labor Harmonie“, für die vielen oft lustigen, manchmal auch
ernsthaften Gespräche während den diversen Erholungspausen und die Möglichkeit immer eine
Anlaufstelle zu haben. Vielen Dank auch an Jürgen Bögelein und Henning Wegner für die vielen
Next-door-Events während und außerhalb des Semesters und natürlich auch für die gemeinsame
Solida-Betreuung. Danke an Dr. Stefan Seyferth, Dr. Christian Führling und Dr. Christian Rochelle
für die gemeinsame Zeit im Institut, beim Tisch-Fußball oder bei diversen anderen Veranstaltungen.
Bei Harald Pudritz möchte ich mich für die gemeinsame Zeit im Labor bedanken und natürlich für
die vielen netten Geschichten und Sprüche.
Euch allen: Ihr seid mir in der gemeinsamen Zeit in Erlangen sehr ans Herz gewachsen. Ich hoffe
sehr wir bleiben ein Leben lang Freunde und werden uns noch oft wieder sehen.
Danke auch an meine weiteren Kolleginnen und Kollegen Joanna Sawiec, Eva Meister,
Silja von Graberg, Eva Schmidt, Anke Czerwinski, Dr. Doris Köpper und Dr. Marc Fitzner für die
gemeinsamen Stunden im Praktikum und manche nette Unterhaltung.
Ein ganz großes Dankeschön geht an Winfried Bauer und Josef Hubert, ohne deren handwerkliches
Geschick die praktische Umsetzung des Levitationssystem nicht möglich gewesen wäre, an Luise
Schedl für die Unmengen rasterelektonenmikroskopischer Bilder einzelner Partikel, an Petra
Neubarth und Waltraut Klenk für alle administrativen Tätigkeiten und an Petra speziell für die
Mithilfe beim Erstellen von Praktikumsplänen und der Pharmakokinetik-Klausur, an Christiane
Blaha für die Bestellungen von Chemikalien, Glasgeräten und unzähligen Mikroliterspritzen und an
Eberhardt Nürnberg für interessante Einblicke in die Erlangener Pharmazie lange vor unserer Zeit.
Außerhalb der Universität möchte ich vor allem meiner Freundin Martina für ihre Liebe und für
ihre Unterstützung meiner Arbeit in den letzten drei Jahren sowie natürlich auch für das
Korrekturlesen danken.
Zu guter letzt gilt mein größter Dank aber meiner Familie, meiner Mutter Gerlinde, meinem Bruder
Jens, meiner Oma Erika, Werner, meinem Opa Hans und meiner Uroma Emsel. Den beiden letzten
ist es leider nicht vergönnt dem Tag meiner Promotion auf Erden beizuwohnen. Ihr habt mich zu
jeder Zeit meines Lebens unterstützt, gefördert und mir alle Türen und Tore geöffnet. Ohne Euch
wäre all das hier nicht möglich gewesen. Keine Worte dieser Welt können ausdrücken wie sehr ich
Euch für Eure Liebe und all Eure Unterstützung in meinem Leben dankbar bin.

PARTS OF THIS THESIS HAVE ALREADY BEEN PRESENTED OR PUBLISHED
I. Heiko A. Schiffter, Geoffrey Lee (2004). „Protein spray-drying: single droplet drying kinetics
via acoustical levitation.” 5 th World Meeting on Pharmaceutics, Biopharmaceutics and
Pharmaceutical Technology. Nuremberg (Germany).
II. Heiko A. Schiffter, Geoffrey Lee (2005). „Protein spray-drying: influence of trehalose on the
single droplet drying kinetics of solutions of bovine serum albumin in an acoustic levitator.”
1 st European Congress of Life Science Technology. Nuremberg (Germany).
III. Heiko A. Schiffter, Geoffrey Lee (2005). „Determination of single droplet drying kinetics of
protein solutions via acoustic levitation.” AAPS Annual Meeting. Nashville (USA)
IV. Jacob Sloth, Soren Z. Kiil, Anker D. Jensen, Sune K. Anderson, Heiko A. Schiffter,
Geoffrey Lee (2006). „Model based analysis of the drying of a single droplet in an ultrasonic
levitator.” Chemical Engineering Science. Accepted and in press.

CONTENTS I
Table of contents
1. General introduction ..........................................................................................1
2. Single droplet drying ..........................................................................................9
2.1 General heat transfer considerations......................................................................................... 9
2.1.1 Heat transfer by conduction ...................................................................................................... 9
Heat transfer through dry porous solid material ..................................................................... 10
Heat transfer through humid porous solid material ................................................................ 11
2.1.2 Convective heat transfer.......................................................................................................... 12
2.1.3 Heat transfer by radiation........................................................................................................ 14
2.2 Diffusion and mass transfer .................................................................................................... 16
2.2.1 Diffusion ................................................................................................................................. 16
Stefan-Maxwell Equation ....................................................................................................... 16
Fick’s law of molecular diffusion ........................................................................................... 18
Diffusion coefficient for gases................................................................................................ 18
2.2.2 Convective mass transfer considerations ................................................................................ 19
Equimolar diffusion in gases................................................................................................... 19
General case for diffusion of gases plus convection............................................................... 20
Unimolar diffusion.................................................................................................................. 21
2.2.3 Film theory.............................................................................................................................. 22
2.2.4 Boundary layer theory............................................................................................................. 24
2.2.5 Penetration theory ................................................................................................................... 25
2.2.6 Surface renewal theory............................................................................................................ 26
2.3 Heat and mass transfer considerations for pure solvents ........................................................ 26
2.3.1 The D 2 -law .............................................................................................................................. 26
2.3.2 Abramzon and Sirignano’s model........................................................................................... 31
2.3.3 Diffusion controlled evaporation of a single droplet .............................................................. 33
2.3.4 Evaporation of single droplets containing solvent mixtures................................................... 34
2.3.4 Droplet-gas interactions .......................................................................................................... 35

II CONTENTS
2.4 Evaporation of liquid droplets containing dissolved solids .................................................... 36
2.4.1 The drying stages of droplets containing dissolved or suspended solids................................ 36
The first drying stage .............................................................................................................. 37
The critical moisture content................................................................................................... 38
The second drying stage.......................................................................................................... 38
2.4.2 The movement of moisture in solids....................................................................................... 41
2.4.3 Modelling of drying of single droplets containing dissolved or suspended solids ................. 42
Droplets with dissolved solids ................................................................................................ 42
Droplets with suspended inert solids ...................................................................................... 43
2.5 Particle formation, size and morphology ................................................................................ 44
2.5.1 Spray-dried particles ............................................................................................................... 44
2.5.2 Single droplet drying experiments .......................................................................................... 46
3. Acoustic levitation.............................................................................................49
3.1 Basic principles of levitation................................................................................................... 49
3.1.1 Application of acoustic levitation ........................................................................................... 49
3.1.2 Fundamentals of acoustics ...................................................................................................... 51
3.1.3 Forces of a standing acoustic wave......................................................................................... 53
3.2. Influences on droplets inside an acoustic levitator ................................................................. 61
3.2.1 Interactions with the acoustic field ......................................................................................... 61
3.2.2 Acoustic streaming.................................................................................................................. 61
Influence of the inner acoustic streaming on mass transfer.................................................... 63
Influence of the outer acoustic streaming on mass transfer.................................................... 65
3.2.3 Influence of droplet volume.................................................................................................... 67
3.2.4 Vertical position of levitated droplet ...................................................................................... 68
3.2.5 Influences of the ultrasonic transducer ................................................................................... 69
3.3 Single droplet drying in an acoustic levitator ......................................................................... 70
3.3.1 Pure solvent droplets............................................................................................................... 70
3.3.2 Droplets of binary liquid mixtures.......................................................................................... 71
3.3.3 Solution and suspension droplets............................................................................................ 72

CONTENTS III
4. Materials and Methods ....................................................................................75
4.1 Materials.................................................................................................................................. 75
4.1.1 Proteins ................................................................................................................................... 75
Bovine serum albumin ............................................................................................................ 75
Catalase from bovine liver ...................................................................................................... 76
4.1.2 Excipients and reagents........................................................................................................... 78
4.1.3 Acoustic levitation system ...................................................................................................... 79
Acoustic levitator .................................................................................................................... 79
Controlled evaporation mixer ................................................................................................. 82
CCD-camera and imaging software........................................................................................ 84
4.2 Methods................................................................................................................................... 86
4.2.1 Acoustic levitation .................................................................................................................. 86
Camera system and imaging software .................................................................................... 86
Acoustic levitator .................................................................................................................... 86
Controlled evaporation mixer ................................................................................................. 86
Levitation procedure ............................................................................................................... 87
4.2.2 Maximum bubble pressure tensiometry.................................................................................. 87
4.2.3 Ring tensiometry..................................................................................................................... 89
4.2.4 Spray-drying............................................................................................................................ 90
4.2.5 Karl-Fischer titration............................................................................................................... 92
4.2.6 Enzyme activity assay of catalase........................................................................................... 92
4.2.7 Kinetic viscosity...................................................................................................................... 93
4.2.8 Liquid density ......................................................................................................................... 94
4.2.9 Scanning electron microscopy ................................................................................................ 94
5. Results and discussions ....................................................................................95
5.1 Pre-liminary levitation tests .................................................................................................... 95
5.1.1 Size measurement ................................................................................................................... 95
5.1.2 Injectable volume.................................................................................................................... 97
5.1.3 Heating of process chamber.................................................................................................... 99
5.1.4 Parametric studies ................................................................................................................. 101

IV CONTENTS
5.2 Evaporation of pure solvent droplets .................................................................................... 103
5.2.1 Data analysis ......................................................................................................................... 103
Different initial droplet size .................................................................................................. 103
Different droplet liquids........................................................................................................ 106
Multicomponent droplets ...................................................................................................... 107
5.2.2 Evaporation of pure water droplets....................................................................................... 109
Calculation of limits of levitation range for water droplets.................................................. 110
Levitation of water droplets .................................................................................................. 111
5.2.3 Evaporation of pure ethanol droplets.................................................................................... 124
Calculation of limits of levitation range for ethanol droplets ............................................... 124
Levitation of pure ethanol droplets ....................................................................................... 124
5.2.4 Evaporation of ethanol-water mixtures................................................................................. 136
5.3 Evaporation of solution droplets........................................................................................... 138
5.3.1 Evaporation of maltodextrin solution droplets...................................................................... 138
Properties of maltodextrin..................................................................................................... 138
Data analysis of maltodextrin experiments........................................................................... 138
5.3.2 Evaporation of trehalose solution droplets............................................................................ 147
Properties of trehalose........................................................................................................... 147
Data analysis of trehalose experiments................................................................................. 149
5.3.3 Evaporation of mannitol solution droplets............................................................................ 159
Properties of mannitol........................................................................................................... 159
Data analysis of trehalose experiments................................................................................. 160
5.3.4 Evaporation of bSA solution droplets................................................................................... 170
Properties of bSA.................................................................................................................. 170
Data analysis of bSA solution experiments .......................................................................... 171
Interfacial behaviour and surface excess of bSA.................................................................. 186
Interfacial behaviour and surface excess of Pluronic F127 .................................................. 193
Influence of trehalose on the interfacial behaviour of bSA .................................................. 195
Determination of bSA monolayer......................................................................................... 199
5.3.4 Evaporation of catalase solution droplets ............................................................................. 202
Properties of catalase ............................................................................................................ 202
Data analysis of catalase solution experiments..................................................................... 204
Interfacial behaviour and surface excess of catalase ............................................................ 213

CONTENTS V
Influence of trehalose on the interfacial behaviour of catalase............................................. 216
Comparison of surface tension and surface excess of bSA and catalase.............................. 218
Enzyme activity of levitated catalase solution droplets........................................................ 219
6. Conclusions......................................................................................................222
7. Zusammenfassung ..........................................................................................230
8. Annex ...............................................................................................................239
9. References........................................................................................................241

VI ABBREVIATIONS
Capital letters
List of abbreviations
A 0
amplitude of the acoustic field
A0 e
effective amplitude of the acoustic field
A0 em
effective amplitude of the acoustic field at drop-out point
A surface area
B gas particle velocity
C D
drag coefficient
D diffusion coefficient
D AB
binary diffusion coefficient
E BM
bulk modulus of elasticity
F correction factor
F L
axial acoustic levitation force
F r
radial acoustic levitation force
HC kinetic energy correction in viscometry
I acoustic intensity
J molar flux through a reference plane
K acoustic
constant of standing acoustic wave
K SPL
constant of acoustic field
K viscometer
constant of viscometer
L dw, Lwd
specific coefficients for a binary liquid mixture
L I
sound intensity level
L p
sound pressure level
L R
distance transducer and reflector
L ν
sound velocity level
L W
sound power level
M molecular weigh
N i
flux of a component i
Q heat flow/quantity

T temperature
T M
midpoint of thermal denaturation
T S
surface temperature
T WB
wet bulb temperature
T ∞
temperature of drying air
R gas constant
U 0
driving voltage of ultrasonic transducer
ABBREVIATIONS VII
U 0 m
driving voltage of ultrasonic transducer at drop-out point
V volume
W acoustic power
X moisture content
Y i
mass fraction of component i
Z i
mole fraction of component i
Small letters
a fraction of vertically arranged plates
c concentration
c m
molar heat capacity
c P
heat capacity at constant pressure
c s
specific heat capacity, specific heat
d diameter
df dilution factor
f frequency
g gravitational acceleration
h heat transfer coefficient
h ci
averaged heat transfer coefficient of the whole droplet surface of the liquid
component i
h v
latent heat of vaporization
k mass transfer coefficient
k′ modified mass transfer coefficient

VIII ABBREVIATIONS
k 0
wave number
k r
radial wave number
k z
axial wave number
l length
m mass
m& vap
mass flux of vapour per time
n natural number
p pressure
p BM
logarithmic mean value of partial pressures
p′ i
pressure perturbation of the incident acoustic wave
p S
saturation vapour pressure
p′ S
pressure perturbation of the scattered acoustic wave
p ∞
vapour pressure in drying air
q& heat flux = transferred heat per time and area
r radial coordinate
r S
droplet radius
s fraction rate of surface renewal
t time
u velocity
u acoustic
averaged velocity of the inner acoustic streaming
w weight
x fraction
x D
distance form centre of droplet mass to adjacent pressure node
y mass fraction
z length, horizontal coordinate
Big Greek letters
Γ surface excess concentration
Π surface pressure
Ω D
collision integral

Small Greek letters
α adiabatic index
β coefficient of expansion
ABBREVIATIONS IX
β d
evaporation coefficient calculated from the droplet diameter
β r
evaporation coefficient calculated from the droplet radius
γ interfacial / surface tension
δ thickness of wall or layer
δ IAS
thickness of acoustic boundary layer
δ diff
thickness of diffusion boundary layer
ε porosity
θ perimeter angle
ϕ relative humidity
λ thermal conductivity (chapter 2)
λ 0
wavelength
μ dynamic viscosity
ν velocity
ν 0
velocity of sound
ϑ temperature in °C
κ gas
diffusivity of drying gas
ρ density
σ surface tension
σ Stefan-Boltzmann constant = 5,
67 ⋅10
SB
σ AB
effective collision diameter
υ relaxation time in tensiometry
ψ activity coefficient for binary mixtures
ω emissivity (chapter 2)
angular frequency (chapter 3)
−8
W⋅
m
ω SW
angular frequency of standing acoustic wave
ς friction coefficient between two components
1,
2
ξ dimensionless radial coordinate
−2
⋅ K
−4

X ABBREVIATIONS
Mathematical sign
∈ Lennard-Jones force
Subscripts
A , B components
Expressions
bSA bovine serum albumin
CAT catalase from bovine liver
CCD charged coupled device
CD circular dichroism
CEM controlled evaporation mixer
ESCA electron spectroscopy for chemical analysis
FTIR Fourier transformed infrared spectroscopy
HFA hydrofluoroalkane
LDH lactate dehydrogenase
pMDI pressurized metered dose inhaler
SD spray-drying
SDD single droplet drying
SEM scanning electron microscopy
SIL sound intensity level
SPL sound pressure level
SPL effective
effective sound pressure level
SVL sound velocity level
SWL sound power level

CHAPTER 1 GENERAL INTRODUCTION 1
1 General Introduction
Many manufacturing processes require one or more stages in which the unit operation “Drying” is
carried out. Due to its influence in specifying the quality of a product, drying is one of the most
important unit operations and has probably the widest application in industry. The drying is a
cutting-off process where liquid is removed from a solid in form of a solution, suspension, slurry,
paste or a solid matrix. This usually involves the evaporation of the liquid and its subsequent
diffusion away from the surface of the product. The evaporation can either result as a transfer of
heat to the liquid at temperatures ≥ than the boiling point of the liquid, or at room temperature
which takes a much longer time for the drying process. In conductive drying the wet solid is, for
example, put into a vessel and heated from the outside by placing onto a heated surface. For a heat
supply by radiation the energy of infra-red irradiation is used. Convective drying uses the transfer of
heat from a bulk gas to the liquid. A large advantage of the latter is that the bulk gas can also be
used for removal of the evaporated liquid. Using conductive or radiative heating a vent is installed
additionally to the heat source to remove the vapour. Commercially a large number of dryer types is
available using either conductive, radiative or convective heating. Table 1.1 gives an overview of
the different principles, characteristics and types of dryers. For the rate of evaporation not only the
temperature and the way the heat is transferred to the liquid are important, but also the mechanism
by which the liquid is bound in the solid matrix.
Table 1.1: Overview of different methods of heat transfer, the drying principles and a sample of the corresponding
commercial equipment.
Nature of heat transfer Principle of heat transfer Apparatus (e.g.)
Conductive
Contact of the heating source and the
product. Directly or via other
materials
Radiative Infra-red or microwave Irradiation
Convective
Heated bulk gas effacing the surface
of the product
- Plate dryer
- Mixer dryer
- Nutsche filter dryer
- Infra-red tunnel dryer
- Microwave vacuum dryer
- Spray dryer
- Fluidized bed dryer
Spray-drying, as an example of drying using convective drying principles is the most widely
used industrial process involving particle formation and drying [Niro 2005]. It is embedded in the
techniques of suspended particle processing (SPP) that use liquid atomization to create droplets
which are dried to individual particles in the gaseous drying medium. Other SPP systems for

2 GENERAL INTRODUCTION
example are spray-agglomeration, spray-granulation or spray-cooling. Spray-drying is a technique
involving liquid spraying, droplet drying, particle formation, powder collection and handling
[Masters 2002]. Figure 1.1 shows the flow diagram of a modern spray-drying plant. The first step is
atomization by centrifugal, pressure or sonic nozzles, where the liquid feed is broken up into many
of small individual droplets forming a spray. This leads to an enormous increase in the specific
surface area of the liquid resulting in very fast rates of heat and mass transfer in the subsequent
drying process. During the second stage, hot air contact, moisture evaporates and particles are
formed. In the third and last stage, an efficient particle collection is necessary, for example by a gassolid
cyclone. As a continuous production method spray-drying is ideal to produce powders,
granulates or agglomerate forms from a liquid feed. With relatively low device-related effort and
optimized energy consumption, high production rates of an end-product with specified requirements
like particle size distribution, bulk and particle density, residual moisture content, dispersibility and
even flavour and aroma retention of volatile substances can be achieved.
Figure 1.1: Basis flow diagram of a spray-dryer [Masters 2002].
The popularity of spray-drying is shown in various application areas in different branches of
industry listed in Table 1.2 [Niro 2005]. The ability to control the above mentioned product
characteristics by the drying procedure and to keep the drying temperature as low as possible, is the
major advantage of the spray-drying technique over other drying methods. This is very important if
the formulation to be dried contains a heat sensitive ingredient. In the food and dairy industry, for
example, a large loss of a volatile flavour or aroma during the drying process would reduce the
quality of the end-product.

CHAPTER 1 GENERAL INTRODUCTION 3
Table 1.2: Industrial applications of spray-drying according to the application brochure published by GEA Niro A/S,
Denmark in 2005
Branch of Industry Industrial Application
Pharmaceutical Industry
Food and Dairy Industry
Chemical Industry
Polymer Industry
Ceramic Industry
- Analgesics
- Antibiotics
- Enzymes
- Plasma and plasma substitutes
- Baby food
- Cheese and whey products
- Coconut milk
- Coffee and coffee substitutes
- Coffee whitener
- Eggs
- Flavours
- Maltodextrines
- Catalysts
- Detergents
- Dyestuffs
- Fine (in)organic chemicals
- Tannins
- ABS
- E-PVC
- PMMA
- UF/MF resins
- Advanced ceramic formulations
- Carbides
- Ferrites
- Nitrides
- Vaccines
- Vitamins
- Yeasts
- Milk
- Soup mixes
- Soy-based food
- Spices/herb extracts
- Sugar-based food
- Tea
- Tomato
- Vegetable protein
- Chelates
- Fungicides
- Herbicides
- Insecticides
- Oxides
- Silicates
- Steatites
- Titanates
In the pharmaceutical industry the application of proteins and peptides as active ingredients
has been rapidly increasing since the middle of the 1990s facilitated by improvements in modern
biotechnology. Many are already available for therapy [Banga 1995]. The worldwide sale of
recombinant protein and peptide substances was 41.3 billion US$ in 2002 according to Frost &
Sullivan, Banc Boston [ISB 2005]. The five top-selling products on the market are listed in
Table 1.3. These peptides and proteins are delivered by injection due to their poor bioavailability.
Unfortunately, parenteral production is time- and cost-intensive and the injection itself needs skilled
personal and is viewed sceptically by patients [Patton 1997]. Therefore, alternative ways of protein
delivery have been increasingly discussed and examined within the last decade. Possible and
favoured routes of administration can be pulmonary, transdermal and nasal delivery systems
[Banga 1995].

4 GENERAL INTRODUCTION
Table 1.3: Sales of the five top-selling recombinant drugs in 2004 according to the publication by the Information
Secretary of Biotechnology 2005 [ISB 2005].
Product Protein Effect / Therapeutic Use Marketed by
Procrit /
Eprex
Rituxan
(Mabthera)
Remicade
Enbrel
Erythropoietin alpha
Rituximab
(Humanised MAb)
Infliximab
(Chimaeric MAb)
Etanercept
(Fusion protein of
antibody-Fc and p75-
TNF receptor protein)
Epogen Erythropoietin
Stimulation of the production of
erythrocytes
Worldwide sales 2004
[US$m]
J&J, Ortho Biotech 3589
Leukaemia and Lymphoma Genentech, Roche 2989
Rheumatoid arthritis,
Morbus Crohn
J&J 2891
Rheumatoid arthritis Amgen 2580
Stimulation of the production of
erythrocytes
Amgen 2601
Karil © is an example for nasal application containing salmon-calcitonin used in therapy to limit the
risk of a vertebral fracture of women with post menopausal osteoporosis [Novartis 2005]. The
bioavailability of the calcitonin compared with a parenteral injection is between 2 to 15% according
to specific information supplied by Novartis Pharma. Possible reasons for the poor absorption of the
protein via the nasal mucous membrane are inactivation by enzymes at the application area and an
epithelial layer that acts as a permeation barrier [Banga 1995]. Considering these facts, the lungs
where some 300 million alveoli constitute a capillarized area of approximately 100 m 2 are a
promising alternative [Almer et al. 2002]. Already at the beginning of the 1990s the pulmonary
absorption of leuprolide acetate, a nonapeptide with potent luteinising hormone releasing activity,
was tested. Lung administration of a dose of 1.0mg to beagle dogs showed an absolute
bioavailability of 40% [Adjei 1994]. Granulocyte colony stimulating factor (G-CSF) after
intratracheal instillation formulated as an aerosol was also investigated. The bioavailability
compared to parenteral application was 45.9% of the administered dose and 62.0% of the dose
reaching the lung lobes [Niven et al. 1993]. Further proteins of interest, not only for systemic
delivery but also for the lungs as a local target are alpha-1 antitrypsin (therapy of emphysema),
interleukin-1 receptor (therapy of asthma), cyclosporine (therapy of immunsuppression after
transplantation), anti-cytomegalovirus antibody (therapy of cytomegalovirus) or the already
approved and marketed recombinant human desoxyribonuclease (rhDNase) with the product name
Pulmozyme © [Roche 2005].

CHAPTER 1 GENERAL INTRODUCTION 5
A major challenge in the development of stable peptide and protein formulations and dosage
forms is to ensure their shelf life stability. Instability of peptides and proteins can broadly be
classified into two sections: physical and chemical instability. Physical instability refers to a change
in secondary, tertiary or quaternary structure of the protein and includes denaturation, aggregation,
precipitation and adsorption to surfaces [Banga 1995]. Due to the primary structure of the proteins
consisting of various amino acids, there are multiple reactive sites for chemical reactions. Chemical
instability involves covalent modification of the protein via bond formation or cleavage, including
deamination, hydrolysis, oxidation, disulfide exchange, racemisation, β-elimination and Maillard-
reaction [Banga 1995; Goolcharran et al. 2000].
The challenge of deep lung delivery of costly proteins and peptides has led to the development
of dry powder formulations of proteins and peptides to overcome the limitations of conventional
aerosol delivery systems. These dry powder formulations have several advantages, including
product and formulation stability, low susceptibility to microbiological growth and applicability to
both soluble and insoluble drugs [Patton 1997]. The inhalable insulin Exubera © is marketed by
Pfizer and developed in cooperation with Nektar [Nektar 2005]. To achieve an optimal deep lung
delivery it is important to use the correct particle size of 1 to 5µm in diameter for best deposition
efficiency and to ensure the stability of the peptide and proteins in the production process of the
microparticles as well as during their shelf life. To meet these requirements, spray-drying is an
effective and efficient method to produce peptide or protein loaded powders suitable for pulmonary
delivery. If the correct formulation and spray-drying conditions can be identified, a product with a
high yield and the above mentioned required characteristics can be achieved [Maa et al. 1997] [Lee
2002]. Since the drying time of the atomized liquid droplets is < 1 s depending on their initial
diameter [Stahl 1980] [Nürnberg 1980], spray-drying is considered as a gentle process for
microparticle production out of peptide or protein solutions. Unfortunately, the spray-drying of
aqueous solutions of pure proteins without any excipients can lead to unfolding, aggregation or
inactivation. Therefore the protein must be stabilized by formulation with one or more substances,
for example glassy carriers such as sucrose to improve the process as well as the storage stability.
Proteins such as recombinant human granulocyte-colony stimulating factor (rhG-CSF) [Niven et al.
1994], recombinant human growth hormone rhGH [Maa et al. 1998 a], trypsinogen [Tzannis 1999],
lactic dehydrogenase (LDH) [Adler 1999], recombinant humanized anti-IgE monoclonal antibody
[Andya et al. 1999] and human immunoglobulin G (IgG) [Maury et al. 2005 a] have been
successfully stabilized in this way. Unfortunately, these kinds of proteins are usually very expensive
and available only in small quantities for formulation studies. 500mg lyophilized powder of a

6 GENERAL INTRODUCTION
human IgG with a protein content of approximately 80% in reagent grade cost almost 1300 €
[Sigma 2004]. The currently favoured equipment in both industrial and university research is
therefore a small laboratory-scale spray dryer such as the Büchi Mini Spray-Dryer B-290 TM
[Büchi 2005] or the Niro Lab Spray Dryer SD Micro TM [Niro 2005]. Newer developments in
cyclone technology for powder collection can maximize the yield during the drying process and
reduce the utilized peptide or protein amount [Maury et al. 2005 b].
Research on the formulation of peptide or protein solutions for spray drying is not only
concerned with the stabilisation and yield optimisation, but also with prediction of particle
morphology and drying kinetics. Though some investigations of variables has already been done
[Maa et al. 1997] [Adler et al. 2000] [Elverson et al. 2003] it is still a challenge to examine drying
kinetics and predict particle morphology from formulations.
The application and properties of a dry powder containing a pharmaceutical peptide or protein
are determined by market forces. A fast and cost-efficient adaptation of the spray-drying process is
therefore one of the main components to success. This leads to search for a technique to investigate
and to optimize spray-drying processes taking the targeted product properties into account. Because
of difficulties associated with investigating spray drying in situ, research has tended to be divided
into four main areas:
1. Atomizing studies (Correlation of droplet size distribution with feed characteristics, atomizer
design, pressure or rotational speed, throughput or shearing stress for peptides and proteins);
2. Studies of gas flow patterns and residence time;
3. Single droplet drying studies;
4. Mathematical models, with data from point 1 to 3, to simulate dryer performance and to predict
droplet drying rates and drying behaviour.
The main interests have been studies of atomization and gas flow patterns. However, within the last
decade the investigation of single droplet drying has increased rapidly. To understand more about
the behaviour of a protein during the spray-drying process, its stability or instability, its particle
formation and particle morphology, precise knowledge of the heat and mass transfer processes
during the drying period is necessary. The drying period is one of the most important sub-processes,
because residual water content, protein activity and particle morphology are determined herein.
Inside the spray-drying tower precise examinations are not possible. All these considerations show
the need for a tool and a method for single droplet drying to investigate the drying behaviour and
kinetics of peptide and proteins formulations during spray-drying.

CHAPTER 1 GENERAL INTRODUCTION 7
In the literature different setups for single droplet drying experiments are described. They can
be divided into techniques with contact [Walton 1994] and techniques without contact to the
evaporating droplet. The former have the disadvantage of interferences in heat transfer, change in
surface and volume of the droplet and influence on particle formation. In contrast, the contact-less
techniques, also termed as levitation techniques or containerless-processing, cause less interference
to the sample droplet. Table 1.4 shows an overview over some levitation techniques, their
underlying physical principle and their characteristics [Lierke 1995]. Acoustic ultrasonic levitation
has the large advantage that liquid droplets of pure solvents, suspensions or solutions with a size
range from 50µm to 4000µm can be levitated very easily [Kastner 2001]. In combination with
embedded air flow or with aerodynamic principles in a hybrid levitator, experiments under different
flow velocities are possible for comparison with spray-drying procedure.
Table 1.4: Summary of the different levitation principles for containerless processing [Lierke 1995]
Levitator Principle of levitation Characteristics
Aerodynamic levitator
Electrostatic levitator
Acoustic levitator
Acoustic-aerodynamic
hybrid levitator
Acoustic-electrostatic
hybrid levitator
Levitation in a upwards air-flow of a
wind tunnel low in turbulence or in a
upwards spreading air-flow
Levitation of electrically charged
droplets in an electric field
(“Millican”-experiment)
Levitation in the pressure nodes of a
standing ultrasonic wave between a
transducer and a reflector
Levitation as a combination of
acoustic and aerodynamic principles
Levitation as a combination of
acoustic and electrostatic principles
- Precise adjustments necessary due to
unstable balance of forces determining flow
velocity and droplet deformation
- Similar to the aerodynamic levitator, precise
adjustments for every droplet size necessary
- Levitation without air flow
- for every droplet diameter is a large range
for stable levitation adjustment
- Levitation in still air or with air flow
possible
- Utilization of stable levitation area and the
possibilities of high flow velocity
- Unique variation possibilities of engineering
operation.
The aim of this work in this thesis was to set up an acoustic levitation system to examine
pharmaceutical spray-drying formulations of peptides and proteins. The work can be divided into
three different sections:
1. Set up the acoustic levitation system for single droplet drying experiments under varying drying
conditions;
2. Investigation of the evaporation behaviour of single droplets with pure solvents or mixtures of
solvent, and verification of the results obtained with simple gas-phase models and data from the
literature;

8 GENERAL INTRODUCTION
3. Investigation of the evaporation behaviour of single solution droplets containing sugars,
peptides or proteins and complex protein formulations. Comparison and verification of the
results with data form spray-drying experiments and the literature.
The first part of this work presents the theoretical background of drying and acoustic levitation.
At the beginning the basic physical and thermodynamic principles of single droplet drying are
discussed. Also a brief summary of published models for the evaporation of single droplets is given.
Then the historical background and the fundamentals of acoustic levitation as a containerlessprocessing
technique are focused on. Existing techniques for the determination of single droplet
drying kinetics of suspension droplets [Kastner et al. 2001] [Groenewold et al. 2002] inside an
acoustic tube levitator are discussed.
The second part of this work deals with the evaporation of single droplets of pure solvents and
mixtures of solvents. The influences of temperature, humidity, air flow and sound pressure level
(SPL) on the evaporation kinetics inside the levitation system are examined. The part concludes
with the set-up of a simple model describing the evaporation process of solvent droplets inside the
acoustic levitator.
In the third part the drying of single solution droplets in the ultrasonic levitator is shown. Again,
the influence of process parameters on the drying kinetics and on the formation of solid particles
and their morphology is dealt with. Different sugar and protein solutions are considered and the
influence of the ingredients on the drying kinetics and particle morphology is discussed. Additional
these results are compared to experimental data of laboratory spray-dryers and from the literature.

CHAPTER 2 SINGLE DROPLET DRYING 9
2 SINGLE DROPLET DRYING
2.1 General heat transfer considerations
2.1.1 Heat transfer by conduction
Where there exists a temperature gradient within a body, heat energy, Q , will flow from the region
of high temperature, T1, to the region of low temperature, T2. If the temperatures on both sides of a
flat homogeneous isotropic barrier with the surface area, A, and the thickness, δ, are constant with
time, the heat transfer is described by Fourier’s Law.
T1
− T2
Equation 2.1 Q = λ ⋅ A⋅
⋅ t
δ
Using the expressions Q & = Q / t and q & = Q&
/ A for the heat flux, Equation 2.1 becomes
Equation 2.2
T1
− T2
∂T
q&
= −λ
⋅ = -λ
⋅
δ ∂z
The coefficient λ in the above equations is called heat conductivity and is specific for the wall
material. The negative algebraic sign in Equation 2.2 includes the heat transfer with decreasing heat
gradient ∂ T / ∂z
[Bosnjakovic 1997].
If a material or substance is inhomogeneous and anisotropic, for example a porous solid,
heat transfer by conduction has to be discussed differently by using a segment model (Figure 2.1).
The segments consist of different parallel plates that are arranged vertically and horizontally to the
direction of heat flow. The distance between the plates can be varied to set the porosity, ε , to a
certain value [Kneule 1975].

10 SINGLE DROPLET DRYING
Figure 2.1: (a-c) Different segment models to describe the heat conduction inside a porous solid material; (I) Segment
model with lengthwise plates, parallel to the heat flow; (II) Segment model with plates vertical to the heat flow [Kneule
1975].
Heat transfer through dry porous solid materials
For dry porous solids, whose interstitials are filled with air, two different cases are possible. In
case I with lengthwise plates (Figure 2.1 (I)), parallel to the heat flow, the transferred heat is given
by
Equation 2.3
&
∂T
A⋅
λ ⋅
∂z
Qtot I = I
λ I is the average thermal conductivity including the porous structure of solid
Equation 2.4 λI = ε ⋅ λgas
+ ( 1−
ε ) ⋅ λsolid
Case II (Figure 2.1 (II)) describes the arrangement with a vertical heat flow, which can be treated
similar to a serial connection in electrical engineering
Equation 2.5
&
∂T
A⋅
λ ⋅
∂z
Qtot I = II
With the thermal conductivity λ II
Equation 2.6
λ
II
=
1
ε 1−
ε
+
λ λ
gas
solid

CHAPTER 2 SINGLE DROPLET DRYING 11
To characterize the effective heat conductivity λ eff of porous substances a combination of both
cases is necessary. The parameter a describes the fraction of vertically arranged plates, ( − a)
fraction of lengthwise arrange plates [Bosnjakovic 1997; Kneule 1975].
Equation 2.7
λ
1
=
1−
+
λ λ
eff a a
Heat transfer through humid porous solid materials
I
II
1 the
To calculate the effective thermal conductivity of humid materials or substances two new cases
have to be taken into account. Case A is applied if the pores of the solid substance are totally filled
with water. According to the considerations for dry porous materials, the effective thermal
conductivity is calculated by [Kneule 1975]
Equation 2.8 λA I = ε ⋅ λliquid
+ ( 1−
ε ) ⋅ λsolid
Equation 2.9
λ
A II
=
ε
λ
liquid
1
1−
ε
+
λ
solid
In case B only parts of the pores are filled with a gaseous medium. In contrast, the walls of the
pores are wetted by the liquid. If there are temperature differences within the porous solid, diffusion
of vapour due to a vapour gradient occurs, with evaporation at the warmer spots and condensation
at the colder spots [Kneule 1975; Walton 1994]. The total heat transferred inside an ideal material
with parallel pores can be calculated using the thermal conductivity of the dry gas, λ gas , and the
diffusion related thermal conductivity, λ diff
A
T A T
Equation 2.10 Q& ∂
∂
tot = Q&
gas + Q&
diff = − ⋅ ( λgas
+ λdiff
) ⋅ = − ⋅ λtot
⋅
ε
∂z
ε ∂z
DAB
p ∂pvapour
Equation 2.11 λdiff =
⋅ ⋅ ⋅ Δhv
R ⋅T
p − p ∂T
D
vapour

12 SINGLE DROPLET DRYING
2.1.2 Convective heat transfer
Heat energy transferred between a surface and a moving fluid at different temperatures is known as
convection. It is a combination of diffusion and bulk motion of molecules. Near the surface the fluid
velocity is low and diffusion dominates. Away from the surface, bulk motion increases influence
and therefore dominates. Convective heat transfer may take the form of either
- natural (free) convection
- forced (assisted) convection
The essential ingredients for the analysis of convective heat transfer are given by Newton’s Law of
Cooling (Equation 2.12). The rate of surface cooling of a solid material, immersed in a colder fluid,
is proportional to the difference between temperature of the surface and the temperature of the
cooling fluid [Earle 2004].
Equation 2.12 q& = h ⋅ ( T − T )
A
S
The coefficient h is called the heat transfer coefficient (synonymous film coefficient or film
conductance) and can be regarded as the conductance of a hypothetical surface film of the
thickness, δ , of the fluid
Equation 2.13
λ fluid
h =
δ
Heat transfer by convection is more difficult to analyse than heat transfer by conduction, because no
single property of the heat transfer medium, such as thermal conductivity, can be defined to
describe the mechanism. Heat transfer by convection varies from situation to situation upon the
fluid flow properties and conditions, and it is frequently coupled with the mode of fluid flow. In
practise, analyses of heat transfer and heat transfer coefficients are treated empirically by direct
observation [Engineersedge 2005]. Factors that can affect the heat transfer coefficient are
- fluid velocity;
- fluid properties (e.g. fluid density, fluid viscosity);
- heat flux, q& ;
- surface characteristics (e.g. shape, roughness);
- type of flow (e.g. single-phase, two-phase).
Of particular interest, not only for drying operations, is the heat transfer between a fluid and a
definite surface. For the magnitude of the heat transfer the properties of the fluid layer on the
surface are most important. For this reason L. Prandtl set up the boundary-layer theory in 1904 as a

CHAPTER 2 SINGLE DROPLET DRYING 13
part of fluid dynamics essential for heat and mass transfer calculations. To calculate the heat
transfer coefficient it has to be connected to the temperature gradient. Directly on the surface (z→0)
the gas velocity can be set zero and the heat is only transferred by conduction. Instead of Newton’s
law of cooling, Fourier’s law is valid [Schlichting 2000].
⎛ ∂T
⎞
Equation 2.14 q& = −λ
⋅ ⎜ ⎟
⎝ ∂z
⎠
Here − λ represents the thermal conductivity of the fluid at surface temperature. The heat flux q& is
determined via the slope of the tangent at z = 0 of the temperature gradient in the fluid.
Equation 2.15
⎛ ∂T
⎞
⎜ ⎟
z
h
⎝ ∂
= −λ
⋅
⎠
T − T
F
S
To calculate the heat transfer coefficient, precise knowledge of the temperature gradient inside the
fluid influenced by the flow conditions is necessary. Therefore, not only thermodynamical but also
fluid mechanic principles are important for the survey of the heat transfer coefficient
[Bosnjakovic 1997; Earle 2004].
Natural convection is caused by buoyancy forces due to density differences caused by
temperature variations in the fluid. At heating the density change in the boundary layer will cause
the fluid to rise and be replaced by cooler fluid that also will heat and rise. This continues
phenomena can be seen, for example, in the hot air rising off the surface of a radiator
[EngineeringToolBox 2005]. Natural convection rates depend up on the physical properties of the
fluid, density ρ , dynamic viscosity μ , thermal conductivity λ , specific heat at constant
pressure c P and coefficients of thermal expansion β which for gases is = 1/
T by Charles’ Law.
Other factors that affect the convective heat transfer are some linear dimensions of the system like
diameter d or length, temperature gradient Δ T and the gravitational acceleration g since it is
density differences acted upon by gravity that create circulation [Earle 2004]. It has been shown
experimentally that heat transfer under natural or free convection can be described in terms of these
factors grouped in dimensionless numbers [Baehr 1998, Walton 1994]:
- Nusselt number
h ⋅ d
Nu
=
λ

14 SINGLE DROPLET DRYING
- Prandtl number
cP ⋅ µ
Pr =
λ
3 2
d ⋅ ρ ⋅ g ⋅ β ⋅ ΔT
- Grashof number Gr =
2
µ
If we assume that these ratios can be related by a simple function, we can write the most general
equation for natural convection [Baehr 1998; Earle 2004; Kneule 1975].
Equation 2.16 ( ) n
m
Nu = K ⋅ (Pr) ⋅ Gr
Experimental work has evaluated K, m and n for different technical set-ups under various
conditions. The magnitude of the constants in single droplet drying under natural convection will be
discussed in chapter 2.3.
Forced convection occurs when a fluid flow is induced by an external flow, such as a pump,
fan or mixer [EngineeringToolBox 2005]. The fluid is constantly replaced and the rates of heat
transfer are therefore higher than for natural convection. In case of low fluid flow velocities, where
rates of natural convection are comparable to those of forced convection, the Grashof number is still
significant. But normally the influence of natural circulation due to coefficients of thermal
expansion and gravitational acceleration is replaced by dependence on circulation velocities factors
grouped in another dimensionless number, the Reynolds number [Earle 2004].
- Reynolds number
⋅ ρ ⋅υ
=
μ
d
Re
As for heat transfer for natural convection, a general equation for the heat transfer under forced
convection can be derived [Baehr 1998; Kneule 1975].
Equation 2.17 ( ) n
m
Nu = K ⋅ (Pr) ⋅ Re
The constants K, m and n relevant in single droplet drying under forced convection have to be found
empirically and will be discussed in chapter 2.3.
2.1.3 Heat transfer by radiation
Radiant heat transfer is the transfer of heat by electromagnetic radiation that arises due to the
temperature of a body. The energy is carried by photons of light in the infrared and visible portions

CHAPTER 2 SINGLE DROPLET DRYING 15
of the electromagnetic spectrum in a wavelength range of 0.1 to 100 microns [Engineersedge 2005].
Radiation operates independently of the medium itself through which it occurs and depends upon
the relative temperature, geometric arrangements and surface structures like area, reflectivity and
emissivity of the materials emitting or absorbing heat [Earle 2004]. The basic formula for radiant
heat transfer is described by the Stefan-Boltzmann Law
Equation 2.18
4
q& = σ SB ⋅T
T is the absolute temperature in Kelvin, A the total radiating surface area and σ SB the Stefan-
Boltzmann constant
−8
−2
−4
σ SB = 5,
67 ⋅10
W⋅
m ⋅ K [Tipler 2000]. This law describes the radiation
energy of a perfect radiator, a so-called black body. A black body gives the maximum amount of
emitted radiation possible at its particular temperature. Equation 2.18 overestimates the energy
emitted by real surfaces at a temperature T , but it was found, that many emit a constant fraction of
the radiation from a black body [Earle 2004; Haas 2002]. For these real bodies Equation 2.18 can be
rewritten
Equation 2.19
&
4
q = ω ⋅σ
SB ⋅T
The constant ω is called the emissivity of a particular body and is a number between zero and one.
It depends not only on the properties of the material but also on the composition of the surface area,
for example roughness. Bodies obeying this equation are termed grey bodies. If radiation between
two surfaces occurs the energy transferred depends again upon the above mentioned factors of the
two surfaces. For two parallel surfaces, facing each other and neglecting edge effects, each must
intercept the total energy emitted by the other, either absorbing or reflecting it [Earle 2004]. Then
the net heat transfer is calculated by
4 4
Equation 2.20 q& = Ε ⋅σ
SB ⋅ ( T − T )
with the temperaturesT 1 andT 2 of the two bodies and with
1 1 1
Equation 2.21 = + −1
E
ω ω
1
2
1
2

16 SINGLE DROPLET DRYING
In case of a small body in surroundings that are at uniform temperature, the net heat transfer is
given by
4 4
Equation 2.22 q& = ω ⋅σ
SB ⋅ ( T − T )
1
T 1 is the temperature of the body with emissivity 1 ω and 2
the surroundings [Earle 2004; Engineersedge 2005].
2.2 Diffusion and Mass transfer
2.2.1 Diffusion
1
2
T is the uniform absolute temperature of
Diffusion is the movement under the influence of a physical
stimulus of an individual component through a mixture. The
most common driving force of diffusion is a concentration
gradient of the diffusing component. Molecular diffusion
caused by temperature is called thermal diffusion and in case of
an external field like a pressure gradient, forced diffusion. A
concentration gradient tends to move the diffusing component
into the direction as to equalize the concentrations and to
destroy the gradient. If the gradient is maintained by constantly Figure 2.2: Schematic diagram of
molecular diffusion. A random path that
supplying component at high concentration side and removing molecule A might take in diffusion
through B molecule from point (1) to (2)
it a low concentration side, a steady-state flux is achieved. This is shown [Geankoplis 1993]
is characteristic for many mass transfer operations [McCabe et al. 2005]. In evaporation it is
important to have a look at the diffusion inside a solution or suspension droplet as well as at the
vapour diffusion through the liquid-gas interface into the gas phase. In Figure 2.2 the molecular
diffusion process is shown schematically.
Stefan-Maxwell Equation
A simple experimental setup with two glass bulbs connected by a capillary will help to understand
the diffusion phenomena. The bulb at the left side contains hydrogen and the right side nitrogen.
The two glass bulbs are connected via a capillary. The whole system is at ambient pressure and
temperature. At the beginning a sharp front between the two gases can be seen in the middle of the
capillary. After some hours the mol fraction x of hydrogen and nitrogen inside the left bulb

CHAPTER 2 SINGLE DROPLET DRYING 17
approaches 0.5. Figure 2.3 shows the concentration equalization inside the capillary at the point z
[Geankoplis 1993].
Figure 2.3: Two glass bulbs connected via a capillary to explain the diffusion phenomena. The points z and z + Δz
are the reference points for the derivation of the Maxwell-Stefan equation [Krishna and Wesselingh 2000]
Consider the mixture between two nearby points z and z + Δz
in the capillary. The velocities u A
and u B (average diffusive velocities) with which the two components are moving through each
other cause friction between the two species. If the momentum balance of hydrogen (component A )
in the slice between z and z + Δz
is considered, this contains the following terms [Krishna 2000]:
- a force due to the partial pressure at z : A z A p ⋅
- a force due to the partial pressure at z + dz : A z dz A p − ⋅ +
- the friction force exerted by the two components proportional to their partial pressures:
A
B
( u u )
∝ p ⋅ p ⋅ −
B
A
In steady-state considerations, taking the limit for Δz → 0 and using the ideal gas law
= p / RT , the three remaining terms lead to
cA A
( )
RT dpA
Equation 2.23 − ∝ R ⋅T
⋅ pB
⋅ ( uA
− uB
)
p dz
A
Krishna and Wesselingh [Krishna 2000] describe the left-hand side of Equation 2.23 as the driving
force F 1 on component A , whereas the right hand side stands for the friction force exerted by
component B on component A . Using xB ∝ pB
, Equation 2.23 can be rewritten as
( u u )
ς A,
B xB ⋅ A − B , where A, B
ς is the friction coefficient between species A and B . The complete
equation with driving force, friction force and generalized to any component i surrounded by other
components j is given by

18 SINGLE DROPLET DRYING
F i = ∑ i,
j
i≠
j
Equation 2.24 ς x ⋅ ( u − u )
j
i
j
This equation is called the Maxwell-Stefan Equation and is much more general than the following
Fick’s law of diffusion. It does yield Fick’s equation as a limiting case for simple but important
diffusion problems [Krishna 2000]. Simplifying mathematics the approximated difference form of
the composition driving force of the Maxwell-Stefan equation for the potential gradient can also be
written in the form of [Krishna 2000].
Equation 2.25
RT Δxi
F1
= − ⋅
Δz
x
Fick’s law for molecular diffusion
i
The general Fick’s first law equation for one-dimensional steady-state diffusion for the molar flux
J A of component A through a reference plane in the binary mixture of A and B can be written as
Equation 2.26
J
A
= −D
AB
dc
⋅
dz
A
The diffusion flux J A is assumed to be proportional to the concentration gradient dcA / dz . The
diffusivity of component A in its mixture with component B is denoted by the binary diffusion
coefficient D AB [Geankoplis 1993; McCabe et al. 2005].
In case of unsteady-state diffusion with no chemical reactions, only a two component
system, a constant binary diffusion coefficient and a one-dimensional mass transfer, Fick’s second
law can be taken into account [McCabe et al. 2005]
2
A d c
Equation 2.27 = DAB
⋅ 2
dt dz
Diffusion coefficients for gases
dc A
Diffusivities can be determined by a number of different experimental methods, but often the
desired values are not available for the system of interest [Geankoplis 1993]. A second possibility is
the estimation from published data or correlations. For diffusion in gases a third approach based on
modern kinetic gas theory allows the prediction of binary diffusion coefficients dependent on the
different sizes and velocities of the molecules and the mutual interactions as they approach one

CHAPTER 2 SINGLE DROPLET DRYING 19
another. For a pair of non-polar molecules a reasonable approximation to the forces is the Lennard-
Jones function [Geankoplis 1993; McCabe et al. 2005]
Equation 2.28
D
AB
=
0.
001858 ⋅T
1.
5
[ ( M + M ) / ( M ⋅ M ) ]
⋅
p ⋅
A
σ AB
2
σ AB is the effective collision diameter in Å and D
AB
A
B
Ω
D
B
A
B
0.
5
Ω the collision integral f ( k T ∈ )
⋅ / with
∈ = ∈ ∈ and ∈= the Lennard-Jones force constant for common gases. Equation 2.28 is
relatively complicated to use and often some of the contents such asσ AB are not available or
difficult to estimate. Hence, the semi-empirical more convenient method of Fuller et al. [1966],
described in Annex A is often used.
2.2.2 Convective mass transfer considerations
The mass transfer from a surface to a streaming fluid depends on the properties of the participating
components and on the flow properties of the fluid. Similar to the possible conditions for convective
heat transfer, an induced fluid flow leads to mass transfer by forced convection, whereas mass
transfer due to density differences caused by temperature or concentration gradient is called mass
transfer by natural convection [Walton 1994]. Considering mass transfer it has to be differentiated
between two-component mass transfer (equimolar diffusion) and one-component mass transfer
(one-way or synonymous unimolar diffusion) [McCabe et al. 2005].
Equimolar diffusion in gases
For equimolar diffusion the mass of component A transferred can be calculated using Fick’s first
law according to Equation 2.26 [Baehr 1998].
Equation 2.29
( c − c ) = k ⋅ ( c − )
dm dc D
= c
A⋅
dt dz δ
A AB
J A −J
B = = −D
AB ⋅ = ⋅ Surface ∞
Surface
= , the partial pressure at the surface, p surface , and at the edge of the layer, p ∞ ,
With c p / ( RT )
Equation 2.29 can be rearranged with the convective mass transfer coefficient k to
k
Equation 2.30 J A
= ⋅ ( pSurface
− p∞
)
R ⋅T
∞
AB

20 SINGLE DROPLET DRYING
General case for diffusion of gases plus convection
For a scientific consideration of the evaporation process it is necessary to look at the diffusion of
gases, when the whole fluid is moving in bulk or convective flow. According to the derivation by
Geankoplis, the rate at which moles of gas A passes a fixed point to the right, will be taken as
positive flux, J A .
Equation 2.31 J A = ν Ad ⋅ cA
The molar average velocity of the whole fluid relative to a stationary point is ν M . The diffusion
velocity ν Ad of component A is now measured relatively to the moving fluid. To a stationary
observer, A is moving faster than the bulk of the phase, since its diffusion velocity ν Ad is added to
the fluid velocity ν M [Geankoplis 1993]
Equation 2.32 ν A = ν Ad + ν M
Multiplying Equation 2.32 with c A , the first term A A c ⋅ ν can be represented by the flux N A of A
relative to a stationary point. The second term is given by Equation 2.31 as J A . The third term is
the convective flux of A relative to a stationary point.
Equation 2.33 N A = J A + ν M ⋅ cA
If N is the total flux of the whole stream relative to a stationary point, then
Equation 2.34 N = ν M ⋅ cA
= N A + N B
Solving of Equation 2.34 for ν M and substituting into Equation 2.33 leads to
cA
Equation 2.35 N A = J A + ⋅ ( N A + N B )
c
Since J A is described by Fick’s first law (Equation 2.26) the final general equation for diffusion
plus convection to use when the flux N A is regarded, relative to a stationary point, is given by
∂cA
cA
Equation 2.36 N A =
−D
AB ⋅ + ⋅ ( N A + N B )
∂z
c

CHAPTER 2 SINGLE DROPLET DRYING 21
Unimolar diffusion (A diffusing through stagnant, non-diffusing B)
It often occurs that only component A diffuses
through a stagnant, non-diffusing component B .
The rate of mass transfer for a given concentration
gradient is then greater than if component B
would diffuse in the opposite direction. A typical
example is the evaporation of liquids into a gas.
The humid surface acts like a one-way permeable
layer. It is permeable for the water vapour Figure 2.4: Diffusion of component A through a
stagnant, non-diffusing B [Geankoplis 1993]
diffusing into the surrounding air but impermeable
for a diffusion of air into the water [Baehr 1998]. This process can be explained by the Maxwell-
Stefan Equation 2.24 as well as Equation 2.36 describing the diffusion of gases plus convection. If
only component A is diffusing in stagnant, non-diffusing B , then Equation 2.36 can be transferred
using = 0
N and the ideal gas law c = p / ( RT )
B
DAB
dpA
p A
Equation 2.37 N A = − ⋅ + ⋅ N A
RT dz p
Rearrangement and integration according to Figure 2.4 of Equation 2.37 leads to
Equation 2.38
N
A
DAB
= ⋅
RT
p
p −
⋅ ln
−
p
A2
( z2
− z1)
p p A1
Equation 2.38 is often rewritten in another form using the log mean value of the inert component B
as follows. Since p p A1
+ pB1
= pA2
+ pB
2
logarithmic mean value is
Equation 2.39
p p + p
p = p + p the
= and B1
= A1
as well as B2
A2
p
BM
pB
2 − pB1
pA1
− p A2
=
=
ln A
( p / p ) ln[
( p − p ) / ( p − p ) ]
B2
B1
Substituting Equation 2.39 in Equation 2.38 leads to [Baehr 1998; Geankoplis 1993]
Equation 2.40
D
A2
AB
N A =
⋅ ⋅ p −
R ⋅T
⋅ 2 1 BM
p
A1
A2
( z − z ) p
The flux of component A for a given concentration difference is therefore greater for one-way
diffusion than for equimolar diffusion, since the term p BM is always less than p . This can also be
p
1

22 SINGLE DROPLET DRYING
seen from the approximated driving force of the Maxwell-Stefan Equation 2.25 [Krishna 2000]. The
term p / pBM
is a kind of correction for unimolar diffusion and is called Stefan-flow [Baehr 1998].
The concentration gradient for one-way diffusion is not linear (Figure 2.5). It is steeper at low
values of p A . There is no transfer of B towards the interface in spite of the large concentration
gradient. The explanation is that B tends to diffuse towards the region of lower concentration, but
the diffusion flux is just matched by the convective flow carrying B in the opposite direction
[McCabe et al. 2005].
Figure 2.5: Concentration gradient for equimolar and unimolar diffusion. On the left side component A and B diffusing
at the same molar rates in opposite directions; on the right side component A diffusion, component B stationary with
respect to interface [McCabe et al. 2005].
Rearrangement of Equation 2.40 similar to Equation 2.29 leads to
DAB
p 1
k′
Equation 2.41 N A = ⋅ ⋅ ⋅ ( pA1
− pA2
) = ⋅ ( pA1
− pA2
)
δ p R ⋅T
R ⋅T
with k = ( D / ) ⋅ ( p / p )
AB
BM
BM
′ δ [Baehr 1998, Kneule 1975, McCabe et al. 2005].
2.2.3 Film theory
The basic concept of the film theory considers the resistance to diffusion equivalent to that in a
stagnant film of a certain thickness δ [McCabe et al. 2005]. This one-dimensional model was
developed to examine the dependence of momentum, heat and mass transfer on the flow properties
of a fluid [Kastner 2001]. Figure 2.6 illustrates the main principles of the film theory for a better
understanding. Component A is transferred from a solid or liquid surface to a streaming fluid. The

CHAPTER 2 SINGLE DROPLET DRYING 23
concentration of A at the surface is c A surface and inside the
fluid c A ∞ . Concentration and diffusion velocity can only
change along the y-axis and not along the other axis or
with time [Baehr 1998]. Depending on equimolar or oneway
diffusion, the concentration profile of A within the
layer can be seen in Figure 2.6 and calculated as shown in chapter 2.2.2.
The two film theory was proposed by Lewis and Whitman in 1924 (Figure 2.7). It assumes
that a stagnant film layer in each phase δ liquid and δ gas represents the resistance to mass transfer and
that the interface concentrations A surface
surfactants at the interface) [Musonge 2005].
p and c A surface are in equilibrium (exception: occurrence of
Figure 2.7: Concentration profile inside the liquid film and the gas film according to the concept of the two-film theory
by Lewis and Whitman in idealized and more realistic form [McCabe et al. 2005]
The more complex aspect than considering heat transfer is the discontinuity at the interface,
which occurs because the concentration or mole fraction of the diffusing component is hardly ever
the same on opposite sides of the interface. The resistance to mass transfer in the two phases is
added to get an overall mass transfer coefficient. If the thickness of the film layer is known, it is
possible to determine the overall mass transfer coefficient of a particular system using k = D / δ .
The derivation and the equation to calculate the film thickness δ and the resulting mass transfer
coefficient k can be seen at Bird [1960] [Kastner 2001].
Figure 2.6: Concentration profile within the
layer of thickness δ at a flat plate
[Baehr 1998].
AB

24 SINGLE DROPLET DRYING
2.2.4 Boundary-layer theory
The boundary layer theory bases upon the assumption that mass transfer takes place in a thin
boundary layer near the surface where the fluid is in laminar flow. In contrast to the film theory,
concentrations and velocities are allowed to change not only along the y-axis but also along the
other axis [Baehr 1998; Schlichting 2000]. If the velocity gradient in the boundary layer is linear
and the velocity at the surface is zero, the equations for diffusion and flow can be solved to give the
concentration gradient and the mass transfer coefficient [McCabe et al. 2005]. For flows over a flat
plate or around a cylinder or sphere, the velocity profiles are also linear at the surface, but the
gradients decrease as the velocity approaches that of the main stream at the outer edge of the
boundary layer (Figure 2.8) [Hampe et al. 2001].
The analogy in heat and mass transfer for boundary-layer considerations permits
correlations for heat transfer to be used for mass transfer, too [McCabe et al. 2005]. Therefore, the
value of the convective mass transfer coefficient depends on the same assumptions than the
convective heat transfer coefficient under natural or free convection and can be described in terms
of these factors grouped in dimensionless numbers [Walton 1994]:
- Sherwood number
- Schmidt number
h ⋅ d
Sh =
D
Sc =
AB
DAB
μ
⋅ ρ
3 2
d ⋅ ρ ⋅ g ⋅ β ⋅ ΔT
- Grashof number Gr =
2
µ
- Reynolds number
d ⋅ ρ ⋅υ
Re =
µ
If we assume that these ratios can again be related by a simple function we can write the most
general equation for mass transfer under natural convection
Equation 2.42 ( ) n
m
Sh = K ⋅ (Sc) ⋅ Gr
and for mass transfer under forced convection
Equation 2.43 ( ) n
m
Sh =
K ⋅ (Sc) ⋅ Re

CHAPTER 2 SINGLE DROPLET DRYING 25
Similar to the equation for convective heat transfer for natural convection, the constants K, m and n
relevant in single droplet drying under natural or forced convection have to be found empirically
and will be discussed in chapter 2.3.
Figure 2.8: Development of laminar boundary-layer conditions at a flat solid surface [Hampe et al. 2001].
2.2.5 Penetration theory
Both, the film theory and the boundary layer theory assume
steady-state mass transfer [Baehr 1998]. The penetration theory in
contrast makes use of the expression for transient rate of diffusion
into a thick mass of fluid with a constant concentration at the
surface. The change in concentration with distance and time is
usually governed by Fick’s second diffusion law (Equation 2.27)
[McCabe et al. 2005]. The penetration model was first developed
by Higbie in 1935 who examined gas absorption in a liquid,
showing that diffusing molecules will not reach the other side of a
thin layer if the contact time is short. He stated that liquid elements
move from the bulk liquid to the interface. These elements are
loaded transient at the interface and penetrate back into the bulk
liquid afterwards (Figure 2.9). According to him, the mass transfer
coefficient is inversely proportional to the square root of the contact time t contact
[Baehr 1998; Hampe et al. 2001; McCabe et al. 2005].
Equation 2.44
k = ⋅
π
2
D
t
AB
contact
Figure 2.9: In-stationary loading of
liquid elements according to the
concept of the penetration theory by
Higbie [Hampe et al. 2001]

26 SINGLE DROPLET DRYING
2.2.6 Surface renewal theory
Danckwerts developed an alternative form of the penetration
theory (Figure 2.10). Because it was unlikely that all elements
of the fluid had the same interfacial residence time, he
considered the case where the elements of fluid at the transfer
surface are randomly replaced by fresh fluid, and the mass
transfer coefficient is given by k DAB
s ⋅ = where s is the
fraction rate of surface renewal in seconds -1 [Hampe et al.
2001; McCabe et al. 2005].
2.3 Heat and mass transfer considerations for pure solvent droplets
2.3.1 The D 2 -law
Figure 2.10: Model of the surface
renewal theory with a randomly
replacement of the liquid elements
according to Danckwerts [Hampe et al.
2001]
Two methods are usually used to analyse the mass transfer from an evaporating droplet through the
gas phase of the surrounding environment. One is to solve the conservation equations for a
motionless droplet in an infinite stagnant medium and to employ an empirical correction factor to
account for natural or forced convection around the droplet [Faeth 1977; Yao et al. 2003]. This
method is termed the “classic method” and will be discussed in this chapter. The other method is to
employ the film theory which involves analysing the thickness of a layer for heat transfer and for
mass transfer [Abramzon 1989; Bird 1960; Sirignano 1999]. The values of the layers are
determined empirically and heat and mass transfer on film thickness are neglected. This last
suggestion leads to two models with almost identical equations for heat and mass transfer rates
[Yao et al. 2003]. Chapter 2.4.2 will address to the basic equations of the model by Abramzon and
Sirignano based on the film theory.
A single droplet with the radius r S (diameter d S ) and the temperature T S is brought into an
environment with the temperature T ∞ and the mass fraction of vapour y A ∞ of the droplet material.
In case the temperature of the ambience is much higher than the initial droplet temperature, the

CHAPTER 2 SINGLE DROPLET DRYING 27
resulting temperature-time curve can be seen in Figure 2.11. First, there is little mass diffusion from
the droplet early in the process due to a low solvent concentration at the liquid surface. Then the
droplet heats up like any other cold body placed into a hot environment. As the liquid temperature
rises, the rate of mass transfer increases as a result of higher solvent vapour concentration at the
droplet surface [Faeth 1977]. According to Frohn and Roth the temperatures are not uniform within
the droplet. There is a maximum liquid temperature at the surface [Frohn 2000]. The increased mass
transfer leads to an increasing portion of energy reaching the drop surface that supplies the latent
heat of vaporization of the evaporating solvent. Also the outward flow of vapour in the boundary
layer reduces the rate of heat transfer to the droplet. This effect slows down the rate of increase of
the liquid surface temperature and later in the process a stage is reached where all the heat utilized
to the surface is needed for the latent heat of vaporization and the droplet stabilizes at the wet bulb
temperature [Faeth 1977].
Figure 2.11: Representation of the mass flux of vapour m& and the heat fluxes in the gas phase vap
Qgas & and in the liquid
Qliq & of an evaporation droplet. In the diagram the mass fraction of vapour Y vap = y and the radial distribution of the
vap
temperature are shown. The profile on the left side is observed, if the temperature of the ambience is much higher than
the initial droplet temperature. The profile on the right side is achieved, if the ambient and initial droplet temperature
are equal [Frohn 2000].
A droplet evaporating at its wet bulb temperature will have a linear decrease of its squared diameter
or radius with time [Faeth 1977; Law 1982]:
2
dd S
Equation 2.45 = −β
d
dt
dr
dt
or
2
S = −β
r
β d and β r are the evaporation coefficients, which are a function of fluid properties and the ambient
conditions. This relationship is called “d 2 -Law”. It is the simplest model describing the

28 SINGLE DROPLET DRYING
vaporisation of a droplet [Law 1982]. The major assumptions built in this theory are discussed by
Law [1982] and can be seen in Table 2.1. Considering that liquid phase heat and mass transport
processes are completely neglected, the d 2 -law is essentially a gas-phase model.
Table 2.1: Major assumptions built into the d 2 -law theory according to Law [1982].
Assumption Explanation
Spherical symmetry
Forced and natural convection are neglected. This reduces the analysis to one
dimension.
No spray effects Isolated one immersed droplet in an infinite environment
Diffusion being rate-controlling
Isobaric process
Constant gas-phase properties Specific heats and thermal conductivities are constant during the evaporation
process
Gas-phase quasi-steadiness Due to significant density disparity between liquid and gas. The liquid possesses
great inertia resulting in a much slower change of e.g. regression rate, species
concentrations and temperature than those of the gas phase transport processes.
Single solvent species Thus it is unnecessary to analyse liquid phase mass transport
Constant and uniform droplet
temperature
Saturation vapour pressure at
surface
No Soret, no Dufour and no
radiation effects
No droplet heating
Phase-change process between liquid and vapour occurs at rates much faster than
those for gas-phase transport. Therefore gasification at the surface is at equilibrium
producing fuel vapour at its saturation vapour pressure at the wet bulb temperature.
No Soret: no mass flow because of a temperature gradient
No Dufour: no heat flow because of a concentration gradient.
No effects due to radiative heat transfer.
The basic gas phase equations for the conservation of mass, vapour and energy are given by Bird
[1960], Faeth [1977] or Law [1982] as well as Frohn and Roth [Frohn 2000]:
Conservation of mass:
d
2
Equation 2.46 ( ρ
gas ⋅ r ⋅ν
r ) = 0
dr

CHAPTER 2 SINGLE DROPLET DRYING 29
Conservation of species (vapour):
d ⎡ 2 ⎛
dyi
⎞⎤
Equation 2.47 ⎢r
⋅ ⎜ ρ gas ⋅ν
r ⋅ yi
− ρ gas ⋅ DAB
⋅ ⎟⎥
= 0
dr ⎣ ⎝
dr ⎠⎦
Conservation of energy:
d ⎡ 2 ⎛
dT ⎞⎤
Equation 2.48 ⎢r
⋅ ⎜ ρ gas ⋅ν
r ⋅ cP
⋅ ( T − T∞
) − λgas
⋅ ⎟⎥
= 0
dr ⎣ ⎝
dr ⎠⎦
In these equations r represents the radial coordinate, ρ gas the density of the gas and ν r the radial
velocity of the gas surrounding the droplet. y i is the mass fraction of vapour, c P the specific heat
of the gas and λ gas the heat conductivity of the ambience. Since only the solvent has net mass
transfer, D AB represents the binary diffusion coefficient of the solvent with respect to the gas phase
species. The analysis considers only two species, solvent and ambient gas. By definition ∑ y i = 1
and only one conservation equation must be solved [Faeth 1977; Law 1982]. Integration of
Equation 2.46 yields
m&
2
vap
Equation 2.49 r ⋅ ρliquid
⋅ν
r = = constant
4π
With boundary conditions
r = r
S
:
r = ∞ :
T = T ,
S
T = T ,
∞
y
y
vap
vap
= y
= y
vap S
vap ∞
the solution of Equation 2.49 leads to the following
Equation 2.50
m&
vap
= 4π ⋅ ρ
gas S
⋅ D
AB
⎛ yvap
S − y
⋅ r ⋅ ⎜ S ln 1−
⎜
⎝ 1−
yvap
Where r S is the droplet radius and ρ gas S the density of the gas at the droplet surface temperature.
The so-called Spalding transfer number B M is a convenient driving potential for the definition of a
mass transfer coefficient for the diffusion of gas through a stagnant gas [Faeth 1977].
vap ∞
S
⎞
⎟
⎠

30 SINGLE DROPLET DRYING
Equation 2.51
B M
=
y
vap S
− y
1 − y
vap S
vap ∞
The conservation of mass for a liquid droplet yields
Equation 2.52
dm
dt
droplet
d ⎛ 4 3 ⎞
2 drS
( ρliquid
⋅Vdroplet
) = ⎜ π ⋅ rS
⋅ ρliquid
⎟ = 4π
⋅ rS
⋅ liquid ⋅ = −m&
vap
d
= ρ
dt
dt ⎝ 3
⎠
Employing Equation 2.51 and Equation 2.52 into Equation 2.50 the radius-time curse is given by
2 2
Equation 2.53 = r − β ⋅ t
where S , 0
rS S,
0 r
r is the initial droplet radius and β r is calculated by
2 ⋅ ρ gas ⋅ DAB
Equation 2.54 β r =
⋅ ln(
1−
BM
)
ρ
liquid
The evaporation model set up in Equation 2.53 and Equation 2.54 is the “classical” way of
predicting the radius-time course of an evaporation droplet following the assumptions of the d 2 -law
mentioned above. To employ an empirical correction to account for forced or natural convection
many experimental approaches where carried out within the 20 th century. Only two of them are
introduced here, because of their most basic character. In 1927 Froessling examined the evaporation
of pure solvent droplets of nitrobenzene, aniline and water under air flow conditions at Reynolds
numbers from 2 to 800 [Froessling 1927]. The droplets with diameters of 0.2 mm to 1.8 mm were
suspended from a thin glass filament or thermocouple and photographed in planned intervals during
the evaporation experiments. In correlation to his theoretical considerations he found:
Equation 2.55
Sh = 2 + 0.
552 ⋅ Re ⋅
1/ 2 1/
3
Sc
Ranz and Marshall constructed a special dryer in form of a hydrophobic glass filament,
thermocouple and capillary burette to investigate the evaporation kinetics of droplets under natural
and forced convection [Ranz 1952 a; Ranz 1952 b]. They examined the evaporation of droplets of
0.6mm to 1.1 mm of pure solvents (water, benzene, aniline), solutions (Water/NH4NO3;
Water/NaCl) and suspensions at temperatures from 20°C to 220°C. The evaporation rate was
determined by monitoring the decrease of the droplet diameter with time or by measuring the
dt

CHAPTER 2 SINGLE DROPLET DRYING 31
decrease in liquid level within the burette while keeping the droplet diameter constant. The
correlation factor found for natural convection is given by
Equation 2.56
and for forced convection by
Equation 2.57
Nu = 2 + 0.
6 ⋅ Pr ⋅
Sh = 2 + 0.
6 ⋅Sc
⋅
Nu = 2 + 0.
6 ⋅ Re ⋅
Sh = 2 + 0.
6 ⋅ Re ⋅
0. 33 0.
25
Gr
0. 33 0.
25
Gr
1/ 2 1/
3
Pr
1/ 2 1/
3
Sc
To describe the mass transfer and the evaporation rate under natural and forced convection for a
pure solvent droplet, Equation 2.54 is changed to
2 ⋅ϕ
gas ⋅ DAB
Sh
Equation 2.58 β r =
⋅ ln(
1−
BM
) ⋅
ρ
2
liquid
2.3.2 Abramzon and Sirignano’s model
An approach based on the film theory was carried out by Abramzon and Sirignano [Abramzon
1989; Sirignano 1999]. The film theory assumes that the resistance to heat and mass transfer
between a surface and a gas flow is modelled by introducing the concept of film thickness: δ T and
δ M [Yao et al. 2003]. The presence of the Stefan flow will influence the values of δ T and δ M , since
a surface blowing results in the thickening of the laminar boundary. [Schlichting 2000]. Abramzon
and Sirignano stated that for an evaporating spherical droplet, the radii of the thermal and
diffusional films are the obtained from [Abramzon 1989].
Equation 2.59
∗
Nu and
∗
Nu
⋅
Nu − 2
film,
T = rS
∗
r
∗
Sh
⋅
Sh − 2
film,
M = rS
∗
r
∗
Sh are the modified Nusselt number and Sherwood number [Kastner 2001]. To
characterise the change of the film thickness relative to the initial film thickness due to the Stefan
flow, the correction factor F is introduced

32 SINGLE DROPLET DRYING
Equation 2.60
FT
FM
δT
=
δ
T , 0
δ
=
δ
M
M , 0
To find T F and F M for the film thickness, the model problem of the laminar boundary-layer flow
past a vaporizing wedge was considered [Abramzon 1989]. In case of isothermal surface and
constant physical properties of the fluid, the correction factors do not depend on local Reynolds
number and are practically insensitive to Prandtl number and Schmidt numbers and can be
approximated as function of the Spalding mass transfer number B M and the Spalding heat transfer
number B T [Abramzon 1989; Kastner 2001].
Equation 2.61 F ( B ) = ( 1 + B )
T
F M
T
T
0.
7
( B ) = ( 1 + B )
M
M
ln
⋅
0.
7
( 1 + B )
ln
⋅
B
T
T
( 1 + B )
Using these factors the modified Nusselt number and Sherwood number are calculated by
Equation 2.62
Nu
Sh
∗
∗
Nu−
2
= 2 +
FT
Sh−
2
= 2 +
F
M
As in other approximate models, the film model assumes that temperature and solvent vapour
concentrations along the surface are uniform [Abramzon 1989; Yao et al. 2003]. Finally, the model
yields the following expressions for the droplet radius-time course and the evaporation coefficient
2 2
Equation 2.63 = r − β ⋅ t
rS S,
0 r , film
2 ⋅ϕ
gas ⋅ DAB
Sh
Equation 2.64 β r,
film = ⋅ ln(
1−
BM
) ⋅
ρ
2
liquid
∗
For a spherical droplet in an environment with no natural or forced convection Sh = Sh = 2.
0 and
Equation 2.64 turns into Equation 2.54. The same considerations are valid for the Nusselt
∗
number Nu = Nu = 2.
0 .
B
M
M
∗

CHAPTER 2 SINGLE DROPLET DRYING 33
2.3.3 Diffusion-controlled evaporation of a single droplet
If it is assumed that the droplet is surrounded
by an atmosphere that has approximately the
same temperature as the droplet liquid and is
low in comparison with the boiling point
temperature of the droplet liquid, the
evaporation can be described by a simpler
equation than Equation 2.54 [Fuchs 1959;
Niven 1980]. Under these conditions the
evaporation process is dominated by diffusion
in the vapour phase. In this special case υr = 0
and the d 2 -law can be derived directly by
integrating Equation 2.47 [Frohn 2000]:
Equation 2.65
dc
2
− m& vap = DAB
⋅ A⋅
= 4π ⋅ r ⋅ DAB
⋅
dr
Equation 2.65 is equal to Fick’s first law for a spherical droplet with the surface area
dc
dr
4 ⋅ r
2
π . Upon
integration dc / dr where c ∞ is the vapour concentration for r → ∞ and r S the droplet radius with
the vapour concentration ( rS
) cS
c = , the rate of evaporation is obtained by the expression
Equation 2.66 & = 4π
⋅ r ⋅ D ⋅ ( c − c )
mvap S AB S
Substituting the vapour concentration by the partial vapour pressure of the liquid at the surface with
the surface temperature T S and in the surrounding air with the temperature T ∞ using the ideal gas
law yields
Equation 2.67 ⎟ M liquid ⎛ pS
p ⎞ ∞
m&
vap = 4π
⋅ rS
⋅ DAB
⋅ ⋅ ⎜ −
R ⎝ TS
T∞
⎠
Figure 2.12: Schematic description of the relevant
variables in diffusion-controlled evaporation of a single
droplet. Droplet shrinkage and water vapour diffusion are
in equilibrium at any time.
To show that the d 2 -law follows from this expression, Equation 2.67 is set equal to the mass flux
caused by the shrinkage of the evaporating droplet following Equation 2.52
∞

34 SINGLE DROPLET DRYING
Equation 2.68 ⎟ 2
dr 2 ⋅ D ⋅ M ⎛ ⎞
S
AB liquid pS
p∞
− =
⋅ ⎜ −
dt ρliquid
⋅ R ⎝ TS
T∞
⎠
Integration leads to decrease of the squared diameter with time according to the d 2 -law
2 ⋅ DAB
⋅ M
2 2
liquid ⎛ p p ⎞
S ∞
Equation 2.69 rS
= rS
, 0 −
⋅ ⋅ t
liquid R ⎜ −
TS
T ⎟
ρ ⋅ ⎝
∞ ⎠
Where the evaporation coefficient is given by
Equation 2.70 ⎟ 2 ⋅ DAB
⋅ M liquid ⎛ p ⎞
S p∞
β r =
⋅ ⎜ −
ρliquid
⋅ R ⎝ TS
T∞
⎠
2.3.4 Evaporation of single droplets containing solvent mixtures
If an evaporating droplet consists of a mixtures of different solvents it is important to look at the
vapour concentration of the components at the droplet surface. If the mass flux of liquid
component A is bigger than of liquid component B , e.g. ethanol in a water/ethanol mixture, two
different drying stages can be seen. In the first stage the evaporation rate is determined by
component A . The droplet radius decreases faster with time than in the second stage. When almost
all of component A has evaporated its mass flux turns little and the evaporation process is
determined by the evaporation of component B . In this second stage the radius of the droplet
decreases slower than in the first stage. The surface temperature of the mixture droplet is always
between the cooling temperatures of the liquid component A and component B [Rensink 2004].
The differential form describing the decrease of the droplet radius of a solvent mixture with time is
given by
Equation 2.71
2⋅
⎡
⋅ ⎢D
⎣
⎤ 2 r
⎥ − ⋅
⎦ 3 ρ
d
⋅
dT
2
∗ ∗
2
dr ρ
S gas
Sh
Sh
ρ
S liquid dTS
=
AB,
A ⋅ln(
1+
BM,
A ) ⋅ + DAB,
B ⋅ln(
1+
BM,
B ) ⋅
⋅
dt ρ liquid
2
2
liquid S dt
The precise derivation of the above equation is shown by Rensink using Raoult’s and Dalton’s law
for the partial vapour pressures and the activity coefficients by Wilson [1964] for two component
mixtures [Rensink 2004]. In contrast to pure solvent droplets the surface temperature is not constant
during the evaporation time and the temperature dependence of the liquid density must be
considered within the calculations.

CHAPTER 2 SINGLE DROPLET DRYING 35
2.3.5 Droplet-Gas Interactions
Liquid droplets may experience mechanical interactions with gas flows. Droplet-gas interactions
can produce changes of resulting flow velocity and surface temperature of the droplets that
influence heat and mass transfer or lead to distortion and break up. For the calculation of droplet
motion it is important to know the forces with which the surrounding fluid acts on the droplets
[Kastner 2001]. These forces are usually expressed in terms of the drag coefficient, CD. When the
viscosity of a liquid is low the deformation is determined primarily by aerodynamic forces and
forces resulting from surface tension [Walton 1994]. For the steady motion of single rigid spherical
particles CD depends only on the Reynolds number. The results of experimental investigation for
this case are known as standard drag curve or standard drag coefficient [Frohn 2000]. The more
realistic case of non-steady particle motion has been studied by Tempkin [1982].
Considering a one-dimensional gas flow parallel to the droplet movement the droplet motion
and radius reduction are governed by the following equations derived by Abramzon and Sirignano
[Abramzon 1989]:
Equation 2.72
du
dt
3 µ
= ⋅
16 ρ
⋅
( u − u )
⋅ Re⋅
D G ∞ droplet
C
2
D
liquid rS
Using Equation 2.72 the relative velocity between droplet u droplet and gas flow u∞ decreases all time,
according to real situations of a non-steady environment. A number of experimental investigations
have been made to determine how C D varies with the droplet Reynolds number [Schlichting 2000;
Kastner 2001].
( Re)

36 SINGLE DROPLET DRYING
Table 2.2: Correlations to calculate the drag coefficient of a rigid sphere atr different Reynolds numbers [Kastner 2001]
Literature Drag coefficient Valid for
Stokes
24
C =
[Schlichting 2000] D
rigid sphere; Re

CHAPTER 2 SINGLE DROPLET DRYING 37
The drying first stage – Constant rate period
The drying of droplets with dissolved or suspended
solids involves a period of surface evaporation
comparable to the vaporisation of pure liquid droplets
at constant wet bulb temperature. The volume change
with time over the first drying stage follows the d 2 -
law, although the droplets contain a solid component
[Kastner et al. 2001]. As long as the surface of the
droplet is completely wetted the evaporated amount
of solvent with time stays constant (Figure 2.13 A-B).
For this reason the first phase in the drying process is
also called “constant rate” [Grassmann et al. 1997;
Masters 2002]. Taking the vapour pressure lowering
effect of the dissolved solid into account the
evaporation coefficient in the first stage can be
calculated using Equation 2.58. The wet bulb
temperature of the solution or suspension presents the
droplet temperature within this stage. Much of the
available moisture in a droplet is removed during the
first period of drying. Moisture migrates from the
droplet interior to the surface at a rate to maintain
surface saturation. Capillary and diffusion
mechanisms are involved depending upon the nature
of the solids in the droplet as a solution or suspension
[Masters 2002].
Figure 2.13: Drying course at constant ambient
conditions. The continuous lines show the drying
behaviour of a hygroscopic substance, the dashed
lines of a non-hygroscopic substance. Diagram (a)
to (c) are the most common way to plot drying
kinetic curves:
(a) Water content with time;
(b) Evaporation rate with time;
(c) Evaporation rate with water content.
[Grassmann et al. 1997]
Due to the loss of liquid mass during the evaporation the solid becomes more and more
concentrated within the remaining droplet and eventually a point is reached when the rate of
migration of moisture to the surface becomes the limiting factor in drying rate. Surface wetness can
no longer be maintained and a falling-off in drying rate results [Geankoplis 1993; Masters 2002].
This can lead to a radial distribution of the solid and furthermore to a crust formation initiated in the
outer region of the droplet close to the surface [Kastner 2001]. Ranz and Marshall explained this
behaviour on the basis, that the rate of diffusion of the dissolved material back into the droplet is
slow compared to the rate of solvent evaporation on the surface [Ranz 1952 a; Ranz 1952 b]. The

38 SINGLE DROPLET DRYING
first stage of droplet drying ends when the solid begins to form a crust at the surface. This may
occur before conditions of uniform saturation throughout the droplet are reached according to the
above considerations by Ranz and Marshall [Walton 1994]. To estimate the drying time of the
constant rate period it is necessary to predict the critical moisture content of a formulation, that is
the moisture content at the end of the first drying stage [Grassmann et al. 1997].
The critical moisture content – Critical point
The change from the first to the second drying stage shows a sharp inflexion point within the
evaporation curve Figure 2.13 B. This point is characterized by the crust formation of the dissolved
solid at the critical moisture point and is therefore termed “critical point” [Elperin 1995; Grassmann
et al. 1997]. At this point the entire surface is no longer wetted and the wetted area continually
decreases in this first period of the falling rate until the surface is completely dry [Geankoplis
1993]. The crust formation of an evaporating droplet with dissolved or suspended solids is generally
a function of the drying conditions (temperature, humidity and relative velocity in relation to the
ambient gas), the physical properties of the liquid solvent (vapour pressure and surface tension), the
chemical and physical properties of the dissolved or suspended solid (solubility and surface
activity) and the initial droplet size [Kastner et al. 2001; Masters 2002]. Because the evaporation
principles in the second drying stage are different to the first stage, it is very important to know the
critical moisture content of a solution for the calculation of drying times
[Walton 1994].
The second drying stage – Falling rate
Discussing the second drying stage, it has to be differentiated between suspension droplets and
solutions droplets with dissolved substances. During this stage the volume of the formed particle
remains constant, although there is still evaporation of liquid solvent from inside the droplet
[Kastner et al. 2001].
When drying suspension droplets, containing an inert solid material, the transition to the next
drying stage occurs when capillary mechanisms in the pores of the arranging solid structure are
insufficient to maintain completely wet surfaces [Masters 2002]. The falling-rate period begins with
the “funicular state” in Figure 2.14 and continues until the liquid fills the pores no longer and the
capillary flow ceases. Then vapour diffusion mechanisms dominate in the so-called “pendular state”
conditions until drying is completed [Masters 2002].

CHAPTER 2 SINGLE DROPLET DRYING 39
Figure 2.14: Drying phases of suspension droplets [Masters 2002]
Drying solution droplets (Figure 2.15), the constant-rate period ceases when the droplet moisture
content falls to the critical value, characterized by the initial presence of a solid phase formed at the
air-liquid-interphase [Kastner et al. 2001]. Heat for the evaporation is transferred through the solid
zone of vaporization, whereas vaporized solvent tends to move through the solid into the air stream.
Movement of moisture from the interior to the surface becomes less and less, owing to increasing
resistance to the mass transfer caused by the solid phase becoming more extensively [Masters
2002]. This results in a permanently decreasing evaporation rate and in the difficulty to remove the
last amounts of moisture in order to produce a particle with specified residual moisture content. For
this reason the second drying stage is also named “falling rate” Figure 2.13 B-C [Walton 1994].
Within this stage the rate of heat transfer exceeds the rate of mass transfer. As a result the droplet
starts to heat up. Sub-surface evaporation occurs if the heat transfer is sufficient high enough to
cause vaporisation within the droplet [Masters 2002].
The rate of mass transfer during the second drying stage is mainly controlled by the following two
mechanisms [Walton 1994]:
1.) The removal of solvent vapour from the solid particle surface due to external conditions like
temperature, humidity, transport properties and relative velocity of the surrounding drying gas,
similar to the conditions determining the first drying stage.

40 SINGLE DROPLET DRYING
2.) The movement of moisture in the solid due to the internal chemical and physical nature of the
solid and the moisture content.
Figure 2.15: Drying stages of solution droplets [Farid 2003]
To calculate the drying time in the second stage, Ranz and Marshall proposed a relationship using
the critical X critical and the final moisture content X final [Ranz 1952 b].
Equation 2.73
t
falling rate
hv
⋅ ρ
=
particle
⋅ d S ⋅ critical
12 ⋅ λ ⋅ ΔT
air
( X − X )
They also proposed an equation for the total drying time of a droplet containing dissolved solids
with negligible vapour pressure lowering effect. To calculate the overall drying time the knowledge
of the relationship between moisture content and droplet temperature is necessary
Equation 2.74
t
overall
hv
⋅ ρliquid
⋅
=
12 ⋅ λ ⋅
air
2 2 ( d − d )
S 0
S critical
( T − T )
∞
S
h
v
⋅ ρ
particle
⋅ d
critical
12 ⋅ λ
air
⋅
critical
final
( X − X )
The evaporation time of droplets where vapour pressure lowering is encountered is usually longer
than for pure liquid droplets and droplets with negligible vapour pressure lowering due to a smaller
temperature driving force and therefore a decreased mass transfer. [Walton 1994]. Also according
to Equation 2.74 the droplet size must be taken into account when evaluating drying times.
⋅ ΔT
critical
final

CHAPTER 2 SINGLE DROPLET DRYING 41
As already mentioned the temperature-drying time course of a droplet with solid content is
different to that of pure liquid droplets. The surface temperature of the evaporating droplet remains
constant and close to the wet bulb temperature during the constant rate period, followed by a
gradual increase approaching the dry bulb temperature of the air during the falling rate [Farid 2003].
Figure 2.16 shows the different temperature stages in relation to Figure 2.15 during drying of a
droplet containing a solid.
Figure 2.16: Surface temperature-time course of a solution droplet in relation to Figure 2.15 [Farid 2003]
2.4.2 The movement of moisture in solids
To evaporate moisture from the exposed surface of a formed solid particle in the second drying
stage, the moisture must move from the depths of the particle to the surface. The mechanisms of the
movement affect the quality of the drying process and the drying time. Some mechanisms advanced
to explain the various types falling rate curves [Geankoplis 1993]
1.) Vapour or liquid diffusion theory
Diffusion of liquid moisture or vapour occurs due to a concentration gradient between the
depths of the formed particle and the surface. This kind of transport is often found in non-
porous solids, where single phase solutions are formed. The moisture diffusivity, D AB , usually
decreases with decreased moisture content, so that the diffusivities are average values over the
range of concentrations used [Geankoplis 1993].
2.) Capillary flow
In porous solids the unbound moisture moves through interconnecting pores and channels or
voids of the solid by capillary action and not by diffusion. As the solvent is evaporated and the
solid structure is built, a meniscus of liquid is formed across each pore in the depths of the

42 SINGLE DROPLET DRYING
solid. This sets up capillary forces by interfacial tension between solvent and solid, providing
the driving force for the movement of the solvent through the pores[Geankoplis 1993]. Small
pores develop greater forces than large pores. The height of the meniscus inside a capillary
h can be calculated by = [ ⋅γ
/ ( r ⋅ g ⋅ ρ ) ]
capillary
2 [Frohn 2000].
hcapillary capillary
3.) Repeated evaporation and condensation
The mechanism of evaporation and condensation is similar to the considerations of heat
transfer within porous humid substances. Initially the pores are full of moisture but then
gradually air pockets appear to replace the moisture lost due to evaporation. The liquid
withdraws to the neck of the pores and migrates either by creeping along the capillary wall or
by successive evaporation and condensation between liquid bridges. This process is also
termed “liquid assisted vapour transfer” [Kneule 1975; Walton 1994].
4.) Effects of shrinkage and pressure gradient
Moisture flow due to morphological changes is often affecting the drying rate. The way the
morphology is changed depends on the particle forming properties of the dissolved substance.
A non-porous skin that is flexible or pliable in nature can lead to particle inflation due to
internal moisture evaporation during the second drying stage. If the internal pressure is too
great, even rupture of the skin can occur releasing the solvent vapour [Masters 1991]. Another
possible effect is the behaviour of a non-porous and rigid skin. The particle may crack or even
explode to release the internal pressure caused by the solvent vapour [Walton 1994]. To
reduce these effects of particle formation it is often desirable to dry with moist air to decrease
the drying rate resulting in a reduction of the shrinkage effects on warping or hardening
[Geankoplis 1993].
2.4.3 Modelling of drying of single droplets containing dissolved or suspended solids
Droplets with dissolved solids
In contrast to the evaporation of pure solvent droplets the effects of changed heat and mass transfer
to and from a solution droplet in the second drying stage have to be taken into account when
modelling the single droplet drying of these droplets. Literature describes different approaches used
to develop an appropriate model. Most of them are based on the absence of a temperature gradient
within the droplet [Farid 2003]. Wijlhuizen et al. [1979] and Sano and Keey [Sano 1982] studied
the drying of droplets assuming a uniform temperature and diffusion of water through the solid with
subsequent evaporation at the surface of the droplet. They used the diffusion equation with an

CHAPTER 2 SINGLE DROPLET DRYING 43
effective diffusivity in contrast to the molar diffusivity to describe the water diffusion. Also
assuming a uniform temperature the model by Nesic and Vodnik [Nesic 1991] was based on the
formation of a crust with a receding crust-bulb interface. To describe the diffusion of vapour
through the crust the diffusion equation with a concentration dependent diffusivity was used. The
crust’s sensible heat was ignored which will have an effect on the calculated droplet temperature at
the later periods of drying [Farid 2003]. Cheong, Jeffreys and Mumford [Cheong et al. 1986]
proposed a receding interface model assuming a linear temperature profile between the droplet
surface and centre. The model also ignored the sensible heating of the crust but offered the
possibility to solve the diffusion equation in the crust using experimentally evaluated physical
parameters. Based on the calculation of the Biot number Bi = h ⋅ rS
/ λ solid , Farid suggested that a
determination of the internal temperature profile is necessary to model single droplet drying within
the falling rate due to a decrease of the thermal conductivity of the droplet as drying processes
[Farid 2003]. His model considers the droplet shrinkage as well as the temperature distribution
within the droplet using the wet bulb temperature as an input value.
Droplets with suspended inert solids
Similar to the solution droplets, the drying of droplets containing inert solids contains at least two
different drying stages. Depending on the physical properties of the solid the suspended particles
form a massive sphere with homogenous particle distribution or a hollow sphere with
heterogeneous particle distribution. To understand the drying process and the mechanisms of
particle formation it is necessary to discuss and calculate the different interface and volume forces
within the suspension droplet. On the basis of the continuity equation described by Bird [1960], a
model calculating the change of the dimensionless mass concentration c ˆ , = c , / c , 0 of the
evaporating suspension droplet with time t and radial coordinate ξ = r / rS
was set up by Kastner
[2001].
2
dcˆ
M , i dcˆ
M , i ⎡2
⋅ Fo ξ K ⎤ Fo⋅
d cˆ
L
M
Equation 2.75 = ⋅ ⎢ − ⋅
2 2 ⎥ + 2 2
dt dξ
⎣ξ
⋅ rˆ
S 2 ⋅ rˆ
S K L,
0 ⎦ rˆ
S ⋅ dξ
K L contains all factors influencing the evaporation of the liquid component except of the droplet
radius r S . It can be derived directly for the model of Abramzon and Sirignano [Abramzon 1989]
discussed in 2.3.2.
∗
Equation 2.76 K L = ρ
gas ⋅ DAB
⋅ ln( 1 + BM
) ⋅Sh
, i
M i
M i
M i,

44 SINGLE DROPLET DRYING
2.5 Particle formation, size and morphology
2.5.1 Spray-dried particles
The size of spray-dried particles depends on the size of the droplets after atomization and the total
solute concentration c in the solution going to be spray-dried. The relationship between these three
parameters is given in Equation 2.77 [Maa et al. 1998 b].
1/
3
⎛ c ⎞
Equation 2.77 d S ( particle)
= ⎜ ⎟ ⋅ d
⎜ ⎟ S ( droplet)
⎝ ρ particle ⎠
Elverson et al. [2003] examined the correlation between droplet and particle size and showed an
almost linear relationship. They also observed that the influence of the solid content in lactose
solutions of 5 to 20% (w/w) resulted in only moderate size increase. The small differences in
particle size implied, that particles obtained from 5% (w/w) solutions had a lower density than
particles from more concentrated solutions (10% and 20% w/w). This may be an effect of loss of
droplets/particles in the drying tower due to an increased loss as the feed concentration increases
[Elverson et al. 2003]. Masters [1991] reported a deficiency in size difference between particles
with different dry matter contents. He stated that products with film-forming materials show a
significant reduction in particle size when concentrations are low.
Not only the droplet size and the total solid content of the liquid feed but also external
drying conditions as well as the material and formulation properties have to be considered when
discussing effects on particle formation and morphology. Maa et al. [1997] carried out one of the
largest studies of effects of operation and formulation variables on the morphology of spray dried
protein particles. After examining effects of the outlet temperature T outlet he stated, that the degree
of deformation like holes and dimples increased with increasingT outlet . Moreover, it was seen in
SEM pictures that lower outlet temperatures resulted in more spherical particles. The protein
formulation itself also had a strong influence on particle morphology as well as possible adjuvant
(e.g. sugars) and the presence of surfactants. Proteins and high molecular weight additives change
the balance of surface-to-viscous forces and result in various particle features [Adler et al. 2000;
Alexander 1978]. Sugar added protein formulations showed different behaviour. Lactose leads to
spray-dried particles with deep holes or donut-like shapes. With mannitol even a drying-timedependent
crystallization occurred [Maa et al. 1997]. Surfactant molecules also may modify the
properties of the dry crust by reducing the tendency of the spray-dried particles to collapse during

CHAPTER 2 SINGLE DROPLET DRYING 45
the falling-rate period. SEM pictures demonstrated a change in particle shape and morphology after
spray-drying a protein/sugar/surfactant formulation compared to pure protein or protein/sugar
compositions [Adler et al. 2000; Maa et al. 1997].
If the drying air temperature in an evaporation process is above the boiling point of the
droplet solution and the liquid trapped inside the droplet crust reaches the boiling point, vapour is
produced causing pressure to begin to build up within the droplet. The effect the pressure has on the
subsequent particle formation during the constant rate depends on the physical properties of the
solid [Masters 1991]. If the layer represents a porous crust, the vapour inside will be released
through the pores. If the solid forms a non-porous plastic (impervious) film, the droplet may
expand, collapse, rupture or even disintegrate. However, droplet temperatures do not often reach
boiling-point levels of the solutions even in spray-dryers at highT inlet [Masters 2002]. Most of the
products show different drying characteristics within the falling-rate. Droplets with an impervious
surface at the critical moisture content result in a sharp fall of the evaporation rate in the second
drying stage. Whereas solution droplets forming a highly porous surface layer lead to an only
gradually falling drying rate because the vapour continues to migrate easily through the droplet-air
interface [Masters 2002]. Figure 2.17 and Table 2.3 show shapes and factors influencing the final
particle shape of spray-dried particles
Table 2.3: Factor influencing the final particle shape [Masters 2002]
Surface characteristic
created during initial
drying phase (1)
Temperature
environment
Effect on droplet during
drying
Plastic, porous Non plastic, porous Plastic, impervious
Temperature distribution under co-current flow drying mode
Shrinkage
Final (2) particle shape Spherical Spherical
Near original size
(Reduction through volatile
loss)
Expansion,
bursting,
collapse on cooling
Misshapen,
fragmented
(1) Dependent upon product formulation, presence of additives
(2) Particles subject to size enlargement by agglomeration, self adhesion effects, and reduction
through mechanical handling

46 SINGLE DROPLET DRYING
2.5.2 Single droplet drying experiments
Figure 2.17: Particle
shapes formed during the
spray-drying process:
Phase 1: atomisation and
contact with hot air; phase
2: crust formation and
beginning of the falling
rate period; phase 3:
various shapes and
structures [Masters 2002].
(1) solid, spherical;
(2) shrivelled, hollow;
(3) hollow, spherical;
(4) cenospherical;
(5) disintegrated.
The photographs show
from top down:
(a) solid, spherical;
(b) misshapen;
(c) cenospherical;
(d) agglomerated;
(e) granulated
Single droplet drying experiments have been used in the study of particle morphology in spray
drying process since in 1952 Ranz and Marshall carried out one of the first examinations
[Ranz 1952 a; Ranz 1952 b]. Due to the larger diameters than spray droplets and the not allowed
free rotation while drying, single droplet drying methods have been criticised for being unrealistic.
Other reasons are that suspension devices provide as a heat source and a site for vapour bubble
nucleation within the drop and may act to deform the droplets in later drying process. Despite these
disadvantages, the larger droplets of single droplet drying studies are the easy to observe, record
and control [Lin 2003]. Table 2.4 gives a brief review on single droplet drying experiments to study
particle formation and morphology.
Charlesworth and Marshall were the first who expressed the drying behaviour of the
droplets in a form of a generalized sequence of morphological events, leading to classification of
the final particle morphology. They interpreted the data from weight loss and temperature versus
time curves and suggested that at the beginning of drying the temperature was slightly above the
wet bulb temperature of the pure solvent due to the vapour pressure lowering effect of the dissolved
solid. The temperature rose with the first appearance of a solid phase and increased rapidly as the
crust formation neared completion [Charlesworth 1960; Walton 1994].

CHAPTER 2 SINGLE DROPLET DRYING 47
Table 2.4: Summary of important studies on drying kinetics and particles morphology of single droplets [Lin 2003;
Walton 1994]
Investigators and
literature
Ranz and Marshall
[Ranz 1952 a;
Ranz 1952 b]
Charlesworth and
Marshall
[Charlesworth 1960]
Futura et al.
[Futura et al. 1982]
El-Sayed et al.
[El-Sayed et al. 1990]
Sunkel and King
[Sunkel 1993]
Walton and Mumford
[Walton 1999]
Lin and Gentry
[Lin 2003]
Suspending method
and temperature
measurement
Glass capillary 80µm;
manganin-constantan
thermocouple
340µm glass filament,
droplets formed from a
microburette;
thermoelement manganinconstantan
wires connected
to a recording
potentiometer
Steady state acoustic
pressure gradient held a
droplet in space against
gravitation;
Thermocouple
Annealed glass with a glass
bead d=100-300µm on the
tip;
0.12mm Type-Ethermocouple
Flexible silica capillary
hollow fibre;
type-K thermocouple
Rotating glass filament in a
wind tunnel;
thermocouple
Capillary filament inside a
drop holder;
Thermocouple
Test material Initial size Heating media
(flow rate)
Sodium chloride,
ammonium nitrate
Sodium sulphate,
potassium sulphate,
copper sulphate,
calcium chloride,
sodium acetate,
coffee extract
Ammonium chloride,
ammonium nitrate,
ammonium sulphate
Sucrose,
maltodextrine,
coffee extract,
skim milk
Coffee extract,
maltodextrine,
non-fat milk
Different inorganic and
organic salts,
gelatine,
semi-instant skimmed
milk,
co-dried egg and
skimmed milk powder,
anionic detergents
Calcium acetate,
sodium acetate,
potassium carbonate,
sodium chloride,
ammonium chloride,
lithium manganous
nitrate,
barium alumino boro
silicate BABS
0.6-1.1 mm
Air at 85-22°C
and 300cm/s
1.3-1.8 mm Air at 31-159°C
and 39-157cm/s
0.9-1.0 mm Air at 65-95°C at
0.6-1.9m/s
1.4-1.5mm Air at 25-250°C
and 10cm/s
0.5-1.8mm Nitrogen at 18°C
and 1.0l/min
1.0-2.0mm Air at 70-200°C
and 1.0m/s
1.2-1.3mm Compressed air at
60-170°C with
Re=4.9-5.2
Based on the idea of a classification system, Walton and Mumford carried out one of the most
extensive studies on particle morphology [Walton 1999]. They produced particles in a convective

48 SINGLE DROPLET DRYING
drying process analogous to spray drying using a rotating glass filament in a kind of wind tunnel.
Different solid or mixtures of solid were dried from solutions, slurries or pastes as single droplets.
Their results were related to the experimental conditions like air temperature, initial solid content
and the degree of feed aeration and to the chemical, physical and crust forming properties of the
solid. Walton’s and Mumford`s studies demonstrated that all of their particle morphologies could be
categorized in skin-forming, crystalline or agglomerate materials. The term “skin” must be regarded
as a generalisation used to describe the particle surface structure built of polymeric (amorphous)
and sub-microcrystalline materials. They showed that both chemical and physical nature of the
material is important to determine the drying behaviour. Regarding external conditions, an increase
in drying temperature from 70°C to 200°C resulted in an increased rate of heat and mass transfer
and shorter drying times. Due to the more violent drying conditions the particles showed a greater
tendency to inflate, shrivel and in some cases explode [Walton 1999]. One of the latest
investigations of drying behaviour and particles morphology of single droplets was done by Lin and
Gentry [Lin 2003]. Their experiments resulted in the summary that low drying temperature and
material with high latent heat of crystallisation, for example endothermic crystallisation, is
favourable for small, dense and regularly-shaped particles. Materials forming elastic shell structures
such as ammonium chloride led to hollow particles and materials with high solubility to small,
dense and irregularly-shaped particles. They also stated that higher initial solute concentration was
favourable for the formation of dense particles. Table 2.5 will give an overview on the external and
internal conditions conducive to form solid or hollow particles [Lin 2003].
Table 2.5: External and internal conditions for the formation of hollow and massive particles [Lin 2003].
Conditions conducive to solid particle formation Conditions conducive to hollow particle formation
- Nuclei-free environment [Leong 1981];
- High solubility solute [Leong 1981];
- Low initial relative saturation droplet [Lin 2003]
- low drying rates [Lin 2003]
- smaller droplet [Leong 1987]
- higher viscosity [Zhang et al. 191]
- lower diffusivity in solvent [El-Sayed et al. 1990]
- Rapid drying of solution droplet
[Leong 1981; Leong 1987]
- Decomposition of thermolabile particles involving a
gaseous component [Roth 1988]

CHAPTER 3 ACOUSTIC LEVITATION 49
3 Acoustic Levitation
3.1 Basic principles of acoustic levitation
3.1.1 Application of acoustic levitation
The phenomenon of contactless positioning of small liquid or solid samples in the pressure nodes of
acoustic standing waves is known from the “Kundt’s tube” experiment in acoustics and is
commonly termed acoustic or ultrasonic levitation. The gravity acting on the sample is compensated
by the forces of the ultrasonic field. The first description of acoustic levitation was published in
1934 by King and later in 1962 by Gorkhoff [Lierke 2002; Yarin et al. 1998] but further technical
development was enforced in the 1970s by the American and European space agencies. They were
interested in a reliable space laboratory tool for containerless processing under microgravity
conditions to carry out experiments in material science, physics and biology [Lierke 2002; Trinh
1985]. Today acoustic levitation is also available to terrestrial laboratory research under normal
gravity conditions. A summary of possible applications of acoustic levitation was given by Lierke
[Lierke 2002]. Table 3.1 presents already published applications apart from experiments of single
droplet drying kinetics and particle formation. In the 1960s Burdukov and Nakoryakov studied the
influence of the ultrasonic field on the evaporation and mass transfer of naphthalene spheres
[Burdukov 1963]. They calculated the acoustic streaming near a small rigid sphere and the mass
transfer rate at the surface of the sphere positioned in a standing plane sound wave. Seaver,
Galloway and Mannucia [Seaver et al. 1989; Seaver et al. 1990] described the evaporation of
volatile non-ideal liquid mixtures, the condensation of water vapour onto evaporating drops of 1butanol
and the remote thermometry of water drops using laser-induced fluorescence using an
acoustic levitator in a free-jet wind tunnel. They levitated liquid droplet in a range from 150µm to
3mm in laminar air streams with velocities from 25 to 350 cm/s. Their evaporation measurements of
water droplets agreed exactly to the calculated predictions using Equation 2.89 together with a
correlation to take the effects of mass transfer by forced convection into account. Gopinath and
Mills [Gopinath 1993] examined the convective heat transfer from a sphere due to the acoustic
streaming of an ultrasonic levitator for large Reynolds numbers. The results obtained were
important for thermal analysis of containerless processing in space. They used analytical and
numerical techniques to obtain Nusselt number correlations for a wide range of Prandtl numbers.
Tian and Apfel [Tian 1996] introduced a new multiple droplet electro-acoustic levitation system to
study the various phenomena associated with droplet array and the influence of the ultrasonic field

50 ACOUSTIC LEVITATION
on the evaporation of single droplets. In their experiments they showed that the perturbation of the
acoustic field to the droplet evaporation process is negligible. Yarin, Brenn, Tropea et al. disagreed
with the statement of Tian and Apfel. They showed an influence of the acoustic streaming on
Sherwood number and mass transfer, as well as an enrichment of gas at the outer boundary of the
acoustic boundary layer by liquid vapour [Yarin et al. 1999]. A more detailed view at these
influencing factors on the evaporation kinetics of levitated droplets will be discussed in chapter 3.2.
The opposite effects of increased mass transfer due to the acoustic streaming and decreased
evaporation rate due to the enrichment of liquid vapour around the droplet surface compensate each
other. This may lead to a statement of Tian and Apfel regarding the evaporation process equal to
that of undisturbed droplet [Kastner 2001]. Kastner and Brenn investigated the influence of
evaporating droplets on the acoustic field and vice versa. He examined single droplet drying of
solvents and suspension droplets under various drying conditions using an acoustic tube levitator.
His experimental data was used to verify a model describing the evaporation process of binary
mixtures of solvents as well as of suspension droplets [Kastner 2001; Kastner et al. 2001; Yarin et
al. 2002a]. Further work with same system was done by Yarin, Brenn and Rensink to investigate the
effect of droplet surface oscillations on the evaporation rate of pure solvents and binary solvent
mixtures [Rensink 2004; Yarin et al 2002 b]. They showed an increased evaporation rate of solvent
as well as of suspension droplet due to oscillations of the droplet surface. Tuckermann, Bauerecker
and Neidhardt used an open levitation system at ambient conditions to look at the evaporation rates
of alkanes and alkanols. They additionally installed an IR-thermography system to look at the
course of the surface temperature of the evaporating droplet. They used the experimental data to
determine and to verify binary diffusion coefficients form literature [Tuckermann et al. 2002 b].
Groenewold et al. also determined the evaporation rates of single suspension droplets with γ-Al2O3
within the two drying stages. They used an acoustic tube levitator in combination with a dew point
hygrometer to measure the moisture content of the outlet air stream [Groenewold et al. 2002; Möser
et al. 2001].

CHAPTER 3 ACOUSTIC LEVITATION 51
Table 3.1: Experimental research in material science, physics and biotechnology using an acoustic levitation system
Author and literature Research area Details
Trinh and Hsu
[Trinh 1986]
Seaver and Frost
[Frost 1993]
Tuckermann
[Tuckermann 2002]
Welter and Neidhart
[Welter 1997];
Eberhardt and Neidhart
[Eberhardt 1999];
Rohling et al.
[Rohling et al. 2000]
Ohsaka et al.
[Ohsaka et al. 2002]
Ohsaka et al.
[Ohsaka et al. 2003]
Kavouras and Krammer
[Kavouras 2003]
Sacher and Krammer
[Sacher 2005]
Weis and Nardozzi
[Weis 2005]
3.1.2 Fundamentals of acoustics
Density measurements of liquids and
low density solid metals
Surface tension of one-octa-decanol
monolayer
Surface tension of surfactantmonolayers
Micro and trace analysis in
acoustically levitated droplets
Viscosity measurements of highly
viscous, particularly under-cooled
liquids
Thermal diffusion coefficients of
under-cooled liquids
Gas/solid-reactions of Ca(0H)2 and
humid, HCl-gas
Crystallisation of CaCO3
Enzyme kinetics of alkaline
phosphatase-catalyzed hydrolysis of 4methylum-belliferone
phosphate
Use of two different techniques based on the static
equilibrium position of levitated samples and on
the dynamic interaction of a levitated sample and
the acoustic field
Formation of liquid-condensed phase of oneoctadecanol
thin films on the surface of levitated
drops
Investigation of the liquid-condensed state of
surfactant monolayers of levitated droplets using
an infra-red camera
Levitation of analytes containing liquid droplets
in combination with absorption and fluorescence
measurements for acid-base titrations with
absorption and fluorescence indicator.
Levitation of liquid samples and elongation of
drops by rotating them beyond the point of
bifurcation. After the drop was allowed to restore
by surface tension driven relaxation, the viscosity
was determined via a relaxation model.
Levitation of laser-heated droplet with subsequent
natural cooling by heat loss from the surface.
Infra-red camera measurement of the cooling rate
in combination with a radial heat conduction
model enables the calculation of the diffusion
coefficient.
Levitation of single Ca(OH)2 particles and
exposition to a defined gas atmosphere.
Measurement of the particle weight change to
calculate SO2 and HCl absorption.
Investigation of the influence of temperature,
resident time and specific forces on the
crystallisation of CaCO3 containing levitated
droplets.
Measurement of the rate of product formation of
alkaline phosphatase-catalyzed hydrolysis of 4methylum-belliferone
phosphate in super-cooled
levitated droplets.
The velocity of sound waves depends on the properties of the material or medium through which
the sound waves pass. In a liquid or gas it can be described by the following equation

52 ACOUSTIC LEVITATION
Equation 3.1
ν =
0
EBM
ρ
ρ is the density of the liquid of gaseous material of medium and E BM represents the bulk modulus
of elasticity. The change of sound velocity with the absolute temperature T , the most important
factor, is given by
Equation 3.2
ν 0 ( air)
⋅ R ⋅T
=
M
α
(air)
R is the universal gas constant, M (air) the molecular weight of air and α the adiabatic index,
which is 1.402 for air [Tipler 2000]. An acoustic field is usually characterized by the gas particle
velocity and the sound pressure. The gas particle velocity or short particle velocity B is the real or
imagined velocity of a particle in a medium on a longitudinal wave of pressure. It can be calculated
as the product of particle displacement ξ and angular frequency ω .
Equation 3.3 B = ξ ⋅ω
= ξ ⋅ 2 π ⋅ f
The particle velocity level, sometimes called sound velocity level (SVL), gives the ratio of a
particle velocity 1 B to the reference particle velocity B ref .
Equation 3.4
= 20 ⋅ log
B
→
1
Lυ 10
ref
Bref
B
= 5⋅10
The unit of the SVL is named decibel (dB) and is a dimensionless unit expressing the ratio between
two quantities.
The sound pressure, p sound , is the force per area in N/m 2 of the root mean square pressure
deviation caused by a sound wave passing through a fixed point. It is calculated as the product of
medium density ρ , speed of sound ν 0 and particle velocity B
Equation 3.5 ρ ⋅ν
⋅ B
p sound
= 0
The logarithmic measure of the sound pressure related to the pressure of a reference noise is called
sound pressure level (SPL) or sound level L P .
−8
m
s

CHAPTER 3 ACOUSTIC LEVITATION 53
1
psound
−5
N
Equation 3.6 Lp = 20 ⋅ log10
→ pref
= 2 ⋅10
2
p
m
ref
Two other standardized values are important when dealing with acoustics. The sound or acoustic
intensity I and the sound or acoustic power W . The sound intensity is calculated as the product of
sound pressure p sound and particle velocity B . The logarithmic measure of the sound intensity in
relation to the standard reference sound intensity is called sound intensity level (SIL) L I and given
by
I
−12
W
Equation 3.7 LI = 10 ⋅ log10
→ I ref = 1⋅10
2
I
m
ref
The power is a measure of sonic energy per time. It is the product of sound intensity I and area A .
According to all other values before, the sound power level (SWL) L W is the logarithmic measure
of sound power in relation to a standard reference sound power Wref and calculated by
W
−12
Equation 3.8 LW = 10 ⋅ log10
→ Wref
= 1⋅10
W
W
3.1.3 Forces of a standing acoustic wave
ref
The concept of standing waves depends on the reflection of sound waves and is known from
Kundt’s tube experiment shown in Figure 3.1. The length of the tube has to be a integer multiple of
the half wavelength to create a standing acoustic wave inside [Tipler 2000].
λn
Equation 3.9 l = n ⋅ n = 1,
2,
3,...
2
According to Equation 3.9 the relation between frequency of the ultrasonic transducer and the
length of the tube can be calculated by [Tipler 2000]
ν
0 ν 0
Equation 3.10 f n = = n ⋅ n = 1,
2,
3,...
λ 2 ⋅ l
n

54 ACOUSTIC LEVITATION
Figure 3.1: Kundt’s tube: apparatus consisting of a glass tube supported on a metal base. The clamp on the left side
holds a metal rod with a metal disk attached to one end. Rod and disk extend inside the glass tube, whose position can
be adjusted to centre the tube about the disk. The disk must not touch the glass because the vibrations set up in the rod
will break the glass. The tube is closed by a stopper on the other end [Nave 2005]
In the case of an acoustic levitator, whose basic
set-up can be seen in Figure 3.2, a standing wave
is formed between an ultrasonic transducer (e.g. a
piezocrystal) producing a sound wave with the
wavelength λ and a transducer at the distance
LR = n ⋅ λ / 2 ( n = 1,
2,
3,...
) . Assuming a one-
dimensional ultrasound wave inside the levitation
system, the one–dimensional wave equation with
appropriate boundary conditions at the sound
source ( x = 0)
and the reflector ( x = L ) can be
used for mathematical description according to
Yarin et al. [1998].
2
2
∂ p′ i 2 ∂ p′
i
Equation 3.11 = c 2 0 ⋅ 2
∂t
∂x
x
R
= 0 : pi
= A0
x = L
R
′
⋅ e
∂p′
i : = 0
∂x
−iωt
transducer
reflector
sound particle
velocity
sample
sound pressure
Figure 3.2: Axial sound pressure and particle velocity
distribution of a standing acoustic wave leading to
pressure nodes and antinodes. Liquid and solid samples
can be levitated within the pressure nodes [Tuckermann
et al. 2001; Yarin et al. 1998]

CHAPTER 3 ACOUSTIC LEVITATION 55
p′
i is the pressure perturbation in the incident wave, A 0 its amplitude at the source surface, ω the
angular frequency corresponding to the ultrasonic range, c 0 the speed of sound in air, t the time, x
the vertical coordinate and i the imaginary unit. The axial position of the pressure nodes x within
the standing acoustic wave can be calculated by
ν 0 ⎛ π ⎞
Equation 3.12 x = LR
− ⋅ ⎜ + π n⎟
n = 0, 1, 2, 3, ..., n
ω ⎝ 2 ⎠
The position of the maxima and minima can be determined by
ν 0
Equation 3.13 xmax = LR
− ⋅ π n n = 1, 3, 5,...,
n
ω
ν 0
xmin = LR
− ⋅ π n n = 0,
2,
4,...,
n −1
ω
The approximate solution of Equation 3.12 for the incident wave in an infinite levitator is given by
Yarin et al. [1998].
−iωt
ω
Equation 3.14 p′
i = A0e
⋅ e ⋅ cos x
ν
A0 e is the effective amplitude of the acoustic field and is calculated by
Equation 3.15
A0
A0e = −
cos ω R ν 0
0
( L / )
Yarin et. al [1998] as well as by Kastner [2001] state that the approximation (Equation 3.14 and
Equation 3.15) leads to almost identical results regarding the amplitude of the sound wave and
number of pressure nodes as the exact solution of Equation 3.11. Only the position of the pressure
nodes differs by about 5% from the exact result. Figure 3.3 shows the sketch of the incident
acoustic wave, the pressure nodes and the acoustic levitation force.

56 ACOUSTIC LEVITATION
Figure 3.3: Incident acoustic wave with levitation force FL on a rigid sphere. Z is the vertical coordinate with z=0 as
position of the centre of the rigid sphere and L the displacement of the centre of this sphere relative to the pressure
antinode [Yarin et al. 1998]
If a spherical droplet or a rigid sphere is levitated within the pressure node of a standing acoustic
wave, a scattered acoustic field appears in addition to the incident one [Yarin et al. 1998]. Due to
interaction the overall pressure perturbation at the droplet surface p′ is the amount of pressure
perturbation of the incident wave p′ i plus the scattered acoustic wave p′ S [Kastner 2001]. The
scattered acoustic pressure is given by
−iωt Equation 3.16 ′ = A ⋅ e ⋅ p ( r)
pS 0 e
S
where the function p S of the radius-vector r is found from the Helmholtz equation [Yarin et al.
1998].
⎛ ω ⎞
Equation 3.17 Δ p ⎟ ′
S + ⎜ pS
= 0
⎝ν
0 ⎠
2
The mathematical solution of Equation 3.17 can be seen from King [1934] or Yarin et al. [1998].
Using the equation for the acoustic radiation pressure given by Landau und Lifshitz [Kastner 2001]

CHAPTER 3 ACOUSTIC LEVITATION 57
Equation 3.18
p
a
2
p′
ρ
= −
2 ⋅ ρ ⋅ν
2
gas
2
0
gas
ν ′
⎟ 2
2 A ⎛ ⎞
0 2 ω
p′
= ⋅ cos ⎜ x
2 ⎝ν
0 ⎠
⎟ 2
2 A0
2⎛
ω ⎞
ν ′ = ⋅ sin ⎜ x
2 2
2 ⋅ ρ gas ⋅ν
0 ⎝ν
0 ⎠
2
ν ′ is the squared acoustic gas velocity time averaged (denoted by ) over a period long
enough compared to the wave cycle [Yarin et al. 1998]. The acoustic radiation pressure produced
by a standing acoustic wave at the droplet or particle surface derived from Equation 3.14, Equation
3.16 and Equation 3.18 can be used to calculate the acoustic levitation force according to King
[1934] and Yarin et al. [1998].
⎛ A ⎞
2
Equation 3.19 F ρ r ⎜ 0e
L = π gas ⋅ S ⋅ ⎟ ⋅ sin(
2k
Δ xD
) ⋅ f ( Ω )
⎜ ρ gas ν ⎟
⎝ ⋅ 0 ⎠
with = k0 ⋅ rS
= ( ω /ν 0 ) ⋅ rS
Ω where 0 = ω /ν 0
2
2
k is the wave number and Δ xD
the distance from the
mass centre of the droplets to its next upper pressure node.
The function f ( Ω ) is given by
( ) 1 ( Ω )
⎡ 1 F0F1
+ G0G
Equation 3.20 f ( Ω ) = ⎢ 3 2 2
⎣(
Ω ) H 0 H1
−
+
( Ω )
∞
∑
n=
2
( F F + G G )
⎪⎧
⎨
⎪⎩
2 ! 2 1 2 2 ( Ω )
5 2 2
H1
H 2
2
⎛ ρ
− 3⋅
⎜1
−
⎜
⎝ ρ
gas
liquid
⎞⎪⎫
⎟
⎬
⎠⎪⎭
n ( )
( n + 1)
( Fn+
1Fn
+ Gn+
1Gn
) 2
−1
( Ω ) − n ⋅ ( n + 2)
2n+
3
2 1
( Ω
) H H
n+
1
n
⎤
{ }⎥⎦

58 ACOUSTIC LEVITATION
The values F i , G i and H i are functions of Ω and are defined by
1−i
i
Equation 3.21 F i ( Ω ) = ( Ω ) ni+
1(
Ω ) + n i i
Ω
( )
1−i
i
Gi ( Ω ) ( Ω ) ji
1(
Ω ) − ji
= +
2
2
( ) = F ( Ω ) G ( Ω )
i ( Ω )
[ ] 2 / 1
H i Ω i + i
( )
Ω
( )
Ω
Equation 3.21 is valid for all values of Ω . The functions ( Ω )
j and n ( Ω ) are the spherical Bessel-
and Neumann-Functions [Kastner 2001; King 1934]. In case of Ω

CHAPTER 3 ACOUSTIC LEVITATION 59
Equation 3.25
A
0e
=
4 rS
⋅ ρ
⋅
3 f
gas
⋅ ρ
liquid
2
⋅ g ⋅ν
( Ω ) ⋅ sin(
2k
⋅ Δ x )
0
A slow decrease in driving voltage of the ultrasonic transducer towards the minimum driving
voltage at unchanged transducer-reflector distance will lead to the positioning of the mass balance
point of the droplet or particle at Δ x = π/ 4Ω
. A further decrease results in a dropout of the
D
sample because the acoustic levitation force is now small to compensate the gravitations force of
the sample. At this so called dropout-point the effective amplitude A0 em can be directly calculated
from the properties of the levitated liquid droplet or rigid sphere [Yarin et al. 1998].
Equation 3.26
A
0em
=
4 rS
⋅ ρ
⋅
3
liquid
f
⋅ ρ
gas
( Ω )
D
0
2
⋅ g ⋅ν
On the assumption that the oscillation amplitude of the transducer varies linearly to the driving
voltage, which was proven by Yarin et al., the relation between both under the conditions of droplet
levitation ( 0 ,U 0
Equation 3.27
A e ) and dropout ( A0 em, U 0m
) is
A
0e
= A
0em
U
⋅
U
0
0m
A second possibility to determine the SPL inside the ultrasonic levitation system is using the aspect
ratio of a levitated droplet. The aspect ratio is the relation between the horizontal and the vertical
diameter. The deformation of a droplet depends on the droplet size, the surface tension of the liquid
solvent within the surrounding gas and the different values of the axial and radial levitation forces
determined by the SPL . The standardised radial levitation force F r , also termed Bernoulli force,
results from the particle velocity and sound pressure distribution at the levitation axis. It can be
calculated by [Lierke 1996]
Equation 3.28
F
r
kr
= 4 ⋅
k
⋅
J1(
kr
r)
2 ( k ⋅ r)
r
⎡
⋅ ⎢J
⎣
0
( k r)
r
0
2 ⋅ J
−
k
1
r
( k r)
⎤ r
⎥⎦
k r is the radial wave number and J i the Bessel function of the order i . The ratio of the axial and
radial wave numbers r z k k q = / is a main design parameter of an acoustic levitation system. They
are combined in the so called wave number equation [Lierke 2002]
⋅ r

60 ACOUSTIC LEVITATION
Equation 3.29
⎛ ω ⎞
⎜ ⎟
⎝ ⎠
2
2
2 2
k = ⎜ ⎟ = k r + k z
ν 0
According to Lierke, the relation between axial and radial levitation
force is 5:1 [Lierke 1996]. This means, that acoustic levitation is
preferably used to compensate gravitational forces. If deformable
samples are investigated, for example liquid solvents, solutions or
suspensions, it leads to a deformation of the sample according to
Figure 3.4. The droplet will take the shape of an oblate ellipsoid.
Deformation increases with an increase of SPL until the droplet
disintegrates.
Theoretical investigations on droplet deformation and sound
pressure level were done by Marston [1980], Tian and Apfel [Tian
1996], Shi and Apfel [Shi 1996] and Yarin et al. [1998]. Yarin et al.
managed to determine the SPL from the aspect ratio of the levitated liquid droplet by numerical
solution.
Figure 3.4: Axial and radial
levitation forces. The relation of
5:1 between axial force Fz and
radial force Fr leads to
deformation of the droplet to an
oblate ellipsoid [Kastner 2001;
Tuckermann et al. 2001].

CHAPTER 3 ACOUSTIC LEVITATION 61
3.2 Influences on droplets inside an acoustic levitator
3.2.1 Interactions with the acoustic field
If a liquid droplet containing a pure solvent, a solution or suspension is levitated inside an acoustic
levitator, it is influenced by the standing acoustic wave in multiple ways. One is the deformation of
the droplets due to the different strength of the axial and radial levitation forces, already discussed
in chapter 3.1.3. More important for determining the drying kinetics of single droplets is the
influence of the acoustic streaming field near the levitated droplet leading to an acoustic convection
and of the system of the outer toroidal vortices resulting in an accumulation of solvent vapour
[Rensink 2004]. Additionally, there is a heating of the sample area due to oscillations of the
ultrasonic transducer changing the temperature of the ambient drying air [Kastner 2001].
Furthermore, acoustic radiation pressure increases during evaporation experiments due to a volume
decrease of the levitated droplet [Kastner 2001]. It is essential to look at all these interactions of
liquid droplet and acoustic field precisely to characterise the drying kinetics of single droplets inside
an ultrasonic field.
3.2.2 Acoustic streaming
The acoustic streaming around a spherical levitated liquid droplet can be divided into an inner and
an outer system of vortices also termed the inner and outer acoustic streaming, according to Yarin et
al. [1999] and Rensink [2004]. This is shown in Figure 3.5. Kastner [2001] termed both system
outer acoustic streaming and the acoustic boundary layer inner acoustic streaming. In this work the
terminology of Yarin et al. and Rensink will be used. Directly at the surface of the levitated droplet
an acoustic boundary layer is formed due to the inner acoustic streaming shown in Figure 3.6. The
radial dimension of this acoustic boundary layer was compared to the diffusion boundary layer by
Lee and Wang [Lee 1990], Yarin et al [1999] and Kastner [2001] using Equation 3.30 for the inner
acoustic boundary and Equation 3.31 for the diffusion layer of an evaporation droplet within an
ultrasonic levitator.

62 ACOUSTIC LEVITATION
Figure 3.5: Acoustic streaming field near a levitated droplet with the system of outer toroidal vortices. The inner
acoustic streaming is positioned directly at the acoustic boundary layer, whereas the outer acoustic streaming (outer
toroidal vortices) are emerging in space of the levitator [Yarin et al. 1999].
Equation 3.30
Equation 3.31
δ
δ
IAS
diff
⎛ 2μ
gas ⎞
= ⎜ ⎟
⎝ ω ⎠
⎛ d S = ⎜
⎝ B / D
AB
1/
2
⎞
⎟ ⎟
⎠
⎛ μgas
⎞
= ⎜ ⎟
⎝ π⋅
f ⎠
1/
2
Yarin et al. calculated the thickness of both boundary layers for a water droplet with a diameter
−5
2
d = 1.
0 mm in air with the kinematic viscosity μ = 1.
5⋅
10 m /s using an 56 kHz acoustic
S
levitator. Their results showed that the acoustic boundary layer δ = 9.
23µm
is small compared
with the diffusion boundary layer δ = 92μm
[Kastner 2001; Yarin et al. 1999].
diff
1/
2
gas
IAS
Inner acoustic streaming at
the boundary of the acoustic
boundary layer
Outer acoustic streaming

CHAPTER 3 ACOUSTIC LEVITATION 63
Figure 3.6: Acoustic streaming as well as acoustic and diffusion boundary layer over a small sphere positioned at the
pressure node of a standing acoustic wave [Yarin et al. 1999]
Influence of the inner acoustic streaming on mass transfer
The inner acoustic streaming induces a flow field at the surface of the droplet which is important for
all mass transfer considerations inside an acoustic levitation system. The continuity of the shear
stress at the surface leads to an evacuation of liquid from the droplet also resulting in internal
circulation movement. Yarin et al. calculated the velocity of the inner acoustic streaming in case of
a small spherical droplet with a radius r ≤ 0.
137 mm much smaller than the wavelength of the
standing acoustic wave λ 6.
1mm
[Yarin et al. 1999] using the approximation
0 =
δ diff
2
45 B
Equation 3.32 u acoustic = ⋅ sin 2θ
32 ω ⋅ r
SW
S
δ IAS
S
where u acoustic is the velocity of the inner acoustic streaming averaged of multiple cycles of the
standing acoustic wave and θ is the perimeter angle measured from the bottom point of the droplet.
According to their calculations u acoustic for a water droplet at a SPL of 165 . 7 dB is
0 . 93m/s
[Rensink 2004; Yarin et al. 1999]. Therefore, the standing acoustic wave induces an
additional convective blowing during droplet evaporation, resulting in an increase in Sherwood
x
x1

64 ACOUSTIC LEVITATION
Number according to mass transfer considerations. The basic formula for the average Sherwood
Number of an acoustically levitated droplet is derived by Yarin et al. [1999].
Equation 3.33
Sh
= K
acoustic
⋅
( ) 2 / 1
ω ⋅ D
SW
B
AB
where the factor K is given by the acoustic boundary layer considerations of the inner acoustic
streaming near the droplet surface. The exact derivation can be seen in Yarin et al. [1999] and
Rensink [2004]. If an approximation is used, K is be calculated by
Equation 3.34
K
acoustic
=
2
π
⎜
⎛
⎝
∫
x
x2
u
u
acoustic
acoustic
r
2
r dx
⎟
⎞
⎠
1/
2
⎛
⎜
ωSW
⋅ r
⋅
⎜
⎝ A0e
/
/ ν
S 0
2 ( ρ ⋅ν
)
r is the distance of a point on the droplet surface to the semi-minor axis set dimensionless with the
initial droplet radius 0
r S . The term u acoustic is set dimensionless with the particle velocity B and
uacoustic r is averaged over the whole droplet surface. Due to a permanently changing droplet
shape, the factor K acoustic has to be re-calculated continuously [Rensink 2004]. For a small spherical
droplet levitated directly within the pressure node of a standing acoustic wave the Sherwood
number is given by
Equation 3.35
Sh
⎛ 45 ⎞
= ⎜ ⎟
⎝ 4 π ⎠
1/
2
⋅
B
( ) 2 / 1
ω ⋅
SW DAB
Influences caused by flows inside the levitated droplet are not considered in Equation 3.33 and
Equation 3.35, though this effect could increase the velocity of the inner acoustic streaming up to
10%. However, the Sherwood number would only increase by the factor ( 1.
1)
1.
049
gas
0
⎞
⎟
⎠
1/
2
1 / 2
= [Yarin et
al. 1999]. Therefore, the circulation inside the droplets can be neglected for mass transfer
considerations [Rensink 2004].

CHAPTER 3 ACOUSTIC LEVITATION 65
Influence of the outer acoustic streaming on mass transfer
In contrast to the increased mass transfer due to an additional convective influence of the inner
acoustic streaming, the outer acoustic streaming leads to a decrease of evaporation rate. According
to Figure 3.5, the outer acoustic streaming forms a system of toroidal vortices, in which solvent
vapour of the evaporated droplet is accumulated. If this volume is considered a closed system, heat
and mass transfer from the vortices to the outside is repressed. Kastner determined the volume of
the vortices experimentally to be approximately V = 87µl
[Kastner 2001] and showed that the
accumulation of solvent vapour proceeded to saturation p / p = 1 within 0.6 seconds for a 2 µl
ethanol droplet.
V droplet [µl]
2.00
1.98
1.96
1.94
Figure 3.7: Evaporation of a 2µl ethanol droplet neglecting any convective mass transfer considerations (Sh=2.0).
Shown is the linear decrease of the droplet volume with time and the pressure ratio of the solvent vapour pressure in
relation to its saturation vapour pressure at 25°C [Kastner 2001].
To overcome the effect of the outer acoustic streaming on reduction of the evaporation rate, the
system of toroidal vortices needs to be embedded into an axial ventilation air stream. The
accumulated solvent vapour is now blown out of the vortices. If the flow of ventilation air stream is
large enough, the amount of solvent vapour blown out of the vortices equals the amount solvent
vapour transported into the vortices from the evaporation droplet [Rensink 2004]. To determine the
necessary magnitude of the air stream it is also important to consider influences of the standing
acoustic wave. Yarin et al. visualize the air stream and the system of vortices around a levitated 5µl
n-hexadecane droplet inside an acoustic levitator at a SPL of approximately 156 dB. The series of
images (Figure 3.8) indicate that the air stream flow only succeeds in passing around the droplet for
vortices
1.92
Droplet volume
Pressure ratio
1.90
0.1
0.0 0.5 1.0 1.5 2.0
t [s]
s
10
1
p / p sat [-]

66 ACOUSTIC LEVITATION
Reynolds numbers exceeding about 100 to 150 calculated at the orifice of the air stream [Yarin et
al. 1997].
ReO=70
Figure 3.8: Flowfield around a levitated 5µl n-hexadecane droplet at a SPL of 156.29dB at different Reynolds numbers
of the ventilation air stream [Yarin et al. 1997].
According to Rensink [2004], the minimal flow velocity of a ventilation air stream u ventilation
dependent on the SPL of the standing acoustic wave is given by
Equation 3.36
u
ventilation
A0
≥
ρ ⋅ν
gas
0
For a levitated water droplet at a SPL of 165.7dB (above example) the minimal flow velocity is
u = 4.
3m/s
. Rensink demonstrated that lower air velocities can also be used for ventilation
ventilation
ReO=190
ReO=290
as long as they overcome the effect of the standing acoustic wave shown in Figure 3.8. An air
velocity lower than u ventilation
with a distance of 20mm between orifice and droplet does not reach the
droplet surface but is large enough to blow the solvent vapour out of the toroidal vortices
completely. This has been shown experimentally by Rensink in Figure 3.9 for different solvent
droplets [Rensink 2004]. At a velocity of 1.0m/s the evaporation rate increased by the factor 2.6 for
all tested solvents. At this velocity the solvent vapour is blown out of the vortices completely. A
further increase leads to an additional convective influence on the droplet surface resulting in a
further increase of evaporation rate [Rensink 2004].

CHAPTER 3 ACOUSTIC LEVITATION 67
Figure 3.9: Diagram showing the influence of the ventilation air stream on the evaporation rate of levitated droplets of
pure solvents. The y-axis plots the ratio between the evaporation rate with and the without ventilation. Therefore all
curves start at y=1.0 for 0.0m/s ventilation velocity [Rensink 2004]
3.2.3 Influence of the droplet volume
A levitated liquid droplet is deformed to an oblate ellipsoid caused by the different values of axial
and radial levitation forces. During the evaporation of this droplet the aspect ratio of the semi-axis
r hor / rvert
changes due to an increase in liquid pressure in the interior. This pressure increase results
from a decrease in droplet radius according to Laplace’s Law
Equation 3.37
2 2 2
) / (d/dt (dS / dS )0
0
2 / dS 0
d/dt (d S
4.0
3.5
3.0
2.5
⋅γ
p =
r
2
Δ
S
Furthermore, a decrease in droplet volume leads to an increase in the effective SPL of the standing
acoustic wave. This increase is the effect of a resonance shift caused by reflections of the acoustic
wave at the droplet surface that change with difference droplet size [Kastner 2001]. On basis of
these assumptions, Yarin et al. developed a method numerically calculating the effective SPL from
a droplet volume and its aspect ratio in an open levitator [Yarin et al. 1998]. Using this
mathematical procedure, Rensink determined the SPL change dependent on the droplet volume for
different pure solvent droplets, verifying an increase in SPL with decreasing droplet volume
[Rensink 2004]. During the whole droplet evaporation the values of the effective SPL for water
were much larger than for the other solvents. The reason is the difference in liquid density of water
3
ρ water = 1000 kg/m and of hydrocarbon
2.0
n-decane
1.5
water
n-octane
1.0
2-propanol
methanol
0.5
0.0
ethanol
n-heptane
0.0 0.4 0.8 1.2 1.6
u ventilation [m/s]
3
ρ hydrocarbon
≅ 800 kg/m . The levitation force needed to

68 ACOUSTIC LEVITATION
levitate a 3µl water droplet has therefore to be much larger to compensate the gravitational force
than for a hydrocarbon droplet with the same volume [Rensink 2004].
SPL [dB]
171
170
169
168
167
166
165
164
163
162
161
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Figure 3.10: Computed evolution of the effective SPL during the evaporation process of drops of water, alcohols and
alkanes in the acoustic field [Rensink 2004]
3.2.4 Vertical position of the levitated droplet
V droplet [µl]
Under the gravitational influence of the earth, the position of a droplet’s centre of mass is not
exactly at the pressure node of the acoustic field. Due to the mass of the droplet and mass
distributions inside it, the centre of mass is displaced to a stable position under the pressure node.
Additionally, the strength of the ultrasonic field leads also to a larger or smaller displacement of the
droplet. A decrease in droplet volume during drying increases the SPL, resulting in a vertical rise of
the levitated droplet to the adjacent upper pressure node. According to Equation 3.19, the same
effect should be observed if the SPL increases keeping the droplet volume and droplet properties
constant. If the mass of a levitated droplet is changed, the vertical position of the droplet has to
change also, according the balance of forces of the gravitational and the levitation force
[Kastner 2001].
4
⎛ A ⎞
3
2
Equation 3.38 r ρ g ρ r ⎜ 0e
π⋅
S ⋅ droplet ⋅ = π gas ⋅ S ⋅ ⎟ ⋅ sin(
2 ⋅ k ⋅ ΔxD
) ⋅ f ( Ω )
⎜ ρ gas ν ⎟
0
3
⎝ ⋅ 0 ⎠
2
water
ethanol
methanol
n-heptane

CHAPTER 3 ACOUSTIC LEVITATION 69
3
If the mass of the droplet ( / 3⋅
π⋅
⋅ ρ ⋅ g)
4 decreases due to evaporation of solvent, the
rS droplet
position between droplet centre of mass and pressure node ( x )
Δ gets smaller and the droplet rises
within the stationary ultrasonic field. Equation 3.38 illustrates the influence of mass loss on the
vertical position of the droplet in the case of mass loss with a decrease in volume at constant
density, or in the case of constant volume with a decreasing density. It can be seen, that changes in
displacement are larger for a decrease in density than in volume [Rensink 2004].
Δ x D [mm]
0.23
0.22
0.21
0.20
0.19
0.18
0.17
0.16
Figure 3.11: Diagram illustrating the change of the distance between geometric mass balance point of the droplet and
pressure node of the standing acoustic wave with droplet mass. The change in density at constant droplet volume have a
stronger influence on the vertical position than the decrease in volume at constant droplet density [Kastner et al. 2001]
3.2.5 Influences of the ultrasonic transducer
1500 1600 1700 1800 1900 2000
m D [µg]
Oscillation of the ultrasonic transducer causes heating of the interior of the levitation chamber. The
increase in temperature leads to an increase in evaporation rate of liquid droplets and a decrease in
evaporation time. Kastner measured a temperature increase of 5°C inside the levitator at an ambient
temperature of 20°C without any additional ventilation [Kastner 2001]. This thermal effect has to be
kept in mind for any experiments at ambient temperature without a ventilation air stream. In the
case of experiments at elevated temperature the thermal effect can be neglected, because the heat
quantity supplied by external heaters achieves the target value. The total heat quantity needed for
the target temperature is the sum of the heat quantity supplied by the external heater and the heat
quantity supplied by the ultrasonic transducer itself. Temperature measurements are carried out
inside the levitations system to have precise temperature information.
D
Volume decrease
at constant density
Density decrease
at constant volume

70 ACOUSTIC LEVITATION
3.3 Single droplet drying in an acoustic levitator
3.3.1 Pure solvent droplets
A model to calculate the kinetics for diffusion controlled evaporation of a single droplet of pure
solvents was set up in chapter 2.4.3. The decrease in the squared radius with time is described in
Equation 2.89, where Equation 2.90 gives the evaporation coefficient β r . To account for increased
mass transfer due to the influence of the inner acoustic streaming of the standing wave, Equation
2.90 is changed to introduce the Sherwood number
Equation 3.39
2 ⋅ D
β r =
ρ
AB
liquid
⋅ M
⋅ R
liquid
⎛ p
⋅ ⎜
⎝ T
S
S
p
−
T
Together with Equation 3.33 the evaporation coefficient β r is now given by
Equation 3.40 ⎟ B ⋅ M liquid ⎛ D ⎞ ⎛ ⎞
AB pS
p∞
β r = K acoustic⋅
⋅ ⎜
⎟ ⋅ ⎜ −
ρliquid
⋅ R ⎝ ωSW
⎠ ⎝ TS
T∞
⎠
The droplet surface temperature T S results form heat transfer from the ambient air to the droplet
and of heat loss due to evaporation of liquid. Additionally, condensation of water vapour from the
ambient air on the droplet surface must be taken into account when calculating the surface
temperature. Even though there is little condensation in experiments with low relative humidity of
the ambient air, it still supplies heat to the droplet. According to Yarin et al. [1999] and Rensink
[2004], the surface temperature of a levitated droplet can be calculated by
Equation 3.41
T
S
∞
∞
⎞
⎟ ⋅
⎠
1/
2
Sh
2
( T )
1/
2
⎡ D ⎛ κ
⎤
gas ⎞ psat
S ⋅ M
2 AB
liquid
= Y + ⎢Y
− ⋅ ⎜
⎟ ⋅
⋅ hv
⎥
⎢ λ
⋅
⎣ gas ⎝ DAB
⎠ R TS
⎥⎦
Y
=
1 ⎡
⋅ ⎢T
2 ⎢⎣
1/
2
( T )
D ⎛ κ ⎞
air/water gas ϕ ⋅ psat
∞ ⋅ M water
+ ⋅ ⎜
⎟ ⋅
⋅ h
λgas
⎝ Dair/water
⎠ R ⋅T∞
∞ v water
κ gas and λgas are the diffusivity and the thermal conductivity of the ambient gas, D AB the binary
diffusion coefficient of the solvent in the ambience and h v its latent heat of evaporation. The term
in the second row of Equation 3.41 represents the condensation of water vapour on the droplet
surface. Because the substance property values depend on the surface temperature, Equation 3.41
⎤
⎥
⎥⎦

CHAPTER 3 ACOUSTIC LEVITATION 71
has to be solved iteratively to find T S . The calculation of the temperature-dependent values of T S
can be found in Annex A. The evaporation coefficient for pure solvent droplets under Stefan flow is
derived from Equation 2.64 using Equation 3.33 for the Sherwood number, to yield
B ⋅ ρ gas ⎛ D ⎞ AB
Equation 3.42 β r,
Stefan = K acoustic⋅
⋅ ⎜
⎟ ⋅ ln(
1 − BM
)
ρliquid
⎝ ωSW
⎠
3.3.2 Droplets of binary liquid mixtures
The evaporation of droplets of binary liquid mixtures was described in detail by Yarin et al.
[2002 b] and summarized by Rensink [2004]. According to Rensink, the radius-time course is given
by
Equation 3.43
h c1
and c2
ρ
liquid
( T )
1/
2
d r ⎡ ⎛ p1,
sat S ⋅ M
S
liquid 1
⎞
= −⎢
hc1
⋅ ⎜
⋅ψ
1 ⋅ Z1(
rS
) − cS∞1
⎟
d t ⎣ ⎝ R ⋅TS
⎠
( T )
⎛ p2,
sat S ⋅ M liquid 2
hc ⋅ ⎜
⋅ψ
2 ⋅ Z
⎝ R ⋅TS
⎞⎤
( rS
) − c ⎟
⎟⎥
⎠⎦
+ 2 2
S∞2
h are the time averaged heat transfer coefficients of the whole droplet surface of the
liquid components 1 and 2. They can be calculated using the following equation together with
Equation 3.33 and Equation 3.34
Equation 3.44
Sh
i
=
hc1
⋅ 2r
D
AB,
i
S
The activity coefficients ψ 1 and ψ 2 are given in Hirata et al. [Yarin et al. 2002 b].
Equation 3.45
1
⎡ ⎛ Ldw
L
ψ i =
⋅ exp⎢−
Z ⋅ ⎜
−
Zi + Lwd
⋅ i ⎣ ⎝ i dw i wd 1
i
( 1 − Z ) ( 1 − Z ) + L ⋅ Z L ⋅ ( − Z )
wd
i
⎞⎤
⎟
⎟⎥
+ Zi
⎠⎦
The coefficients L dw and L wd are characteristics of a specific liquid pair and are given for
water/ethanol mixtures by L dw = 0.
1108 and L wd = 0.
956 [Yarin et al. 2002 b]. Z i is the mole
fraction of the component i in the binary liquid mixture.

72 ACOUSTIC LEVITATION
The mixture density of the droplet ρ liquid can be calculated using the density of the pure solvents ρ i
and their mass fraction Y i [Rensink 2004]
Equation 3.46
ρ
liquid
1
=
Y / ρ +
1
1
( 1 − Y1
) / ρ 2
where Y1 = ( Z1
⋅ M 1)
/ ( Z1
⋅ M 1 + Z 2 ⋅ M 2 ) . To calculate Z 1 ( r = rS
) and Z 2 ( r = rS
)
, the diffusion
equation inside the droplet must be solved to find the mole (or mass) fraction distributions along the
droplet radius at each instant of time. The solution of this diffusion problem can be seen at Yarin et
al. [2002 b]. The surface temperature of a droplet of binary liquid mixtures is given by Rensink
[2004].
3.3.3 Solution and suspension droplets
The drying of droplets containing dissolved or suspended solids can be divided into two different
stages and for hygroscopic substances even in three different stages. The first drying stage
resembles the evaporation of pure solvent droplets (Figure 3.12 a) and can therefore by described by
the same equations but also taking vapour pressure lowering effects into account due to dissolved
substances (see chapter 3.3.1). The decrease of droplet volume within the first drying stage can be
used directly to determine the evaporation rate [Kastner et al. 2001].
Equation 3.47
m&
liquid
= −ρ
liquid
ΔV
⋅
Δ t
droplet
In this phase the squared diameter or radius decreases almost linearly with time according to the
d 2 -law (Figure 3.12 a). After the critical point, marking the change from the first to the second
drying stage, the volume of the levitated droplet remains constant with time even though there is
still evaporation of solvent from inside the droplet. This evaporation of solvent leads to a decrease
in mass and density of the particle. This causes a rise of the particle within the stationary ultrasonic
field (Figure 3.12 b) that can be used to determine the quantity of solvent evaporated in the second
drying stage. It is vital that the SPL does not change within the second drying stage due to the
change in density of the particle. Otherwise determination of drying kinetics would not be possible.
In chapter 3.2.3 the influence of the droplet on the standing acoustic wave and SPL was discussed.
Experiments by Kastner [2001] showed that the working voltage of the ultrasonic transducer and

CHAPTER 3 ACOUSTIC LEVITATION 73
therefore the SPL according to Equation 3.27 is indeed constant during the second drying stage
(Figure 3.12 c).
[mm 2
]
2
Δ x D,0 - Δ x D
d S
U [mV]
2.0
1.5
1.0
0.5
0.0
0.05
0.00
-0.05
-0.10
-0.15
-0.20
36
34
32
(a)
(b)
First drying stage
(constant rate)
(c)
30
0 50 100 150 200 250
Figure 3.12: Drying characteristics of a 1.2 µl suspension droplet containing ethanol and small glass spheres
dglass=30 µm at 25°C. The solid content was Y0=0.05. (a) decrease of the squared diameter with time; (b) vertical
position of the droplet; (c) voltage at the ultrasonic transducer proportional to the SPL of the standing acoustic wave
[Kastner 2001].
t [s]
Second drying stage
(falling rate)

74 ACOUSTIC LEVITATION
The rise of the particle within the ultrasonic field is therefore only caused by change of the mean
particle density. The droplet diameter, the aspect ratio and the characteristics of the ultrasonic field
at the beginning of the drying experiment must now be known. The strength of the ultrasonic field
and the displacement of the droplet centre of mass from the adjacent pressure node are measured.
With this information and that from the first drying stage, the ΔxD at the critical point is determined.
Assuming a constant SPL within the second drying stage, a new constant describing the
strength and properties of the acoustic field is introduced using Equation 3.19 [Kastner et al. 2001]
2
ρ gas ⋅ rS
A0e
Equation 3.48 K SPL = π
f ( Ω )
g ρ ⋅ c
gas
0
The evaporation rate is then determined via the changing position of the centre of mass of the
particle using [Kastner et al. 2001]
K SPL
Equation 3.49 m& L = ⋅ sin(
2 ⋅ k0
⋅ Δ xD
1)
− sin(
2 ⋅ k0
⋅ Δ xD
2 )
Δ t
2
[ ]
If the evaporation rate is known, then calculation of the mean particle density ρ particle , the mean
moisture content of the droplet X particle and the mean particle porosity ε mean is possible [Kastner et
al. 2001]
m
Equation 3.50 ρ () t =
particle
Equation 3.51 X particle () t =
m
Equation 3.52
liquid
solid
V
m
liquid
( t)
msolid
ε mean = 1 −
ρ ⋅V
+ m
particle
solid
liquid ( t)
() t + msolid
paricle
Ultrasonic levitation is therefore one of the few techniques to investigate the drying process of
solution or suspension droplets within both drying stages. It is suitable to determine the evaporation
rate and solvent content of a formulation at any desired point of time during evaporation. The set-up
also enables measurements at various temperatures and humidity to check influences of ambient
conditions on the drying characteristics. Furthermore, droplets / particles can be removed from the
levitation chamber for further analysis at any time.

CHAPTER 4 MATERIALS AND METHODS 75
4 Materials and Methods
4.1 Materials
4.1.1 Proteins
Bovine Serum Albumin (bSA)
Bovine serum albumin is a single polypeptide chain consisting of about 583 amino acids residues
and no carbohydrates [Sigma 2005]. The molecular weight of 66.430 kDa is cited by
Hirayama et al. [1990]. At pH 5-7 it contains 17 intrachain disulfide bridges and one sulfhydryl
group. None of the disulfide bonds was accessible to reducing agents in this pH range [Katchalski et
al. 1957]. Based on hydrodynamic experiments and low angle X-ray scattering, serum albumin was
postulated to be an oblate ellipsoid with dimensions of 140 x 40 Å, with a secondary structure of
50-68% alpha-helix and 16-18% beta-sheet (Figure 4.1).
Figure 4.1: Classical preception of the structure of BSA [Friedli 1996]
Studies using a 1H NMR and X-ray crystallographic data indicate a heart shaped structure.
According to X-ray crystallography there is no beta-sheet in the structure of native serum albumin
but 67% alpha-helix. The remaining polypeptide exists in turns and extended flexible regions
between subdomains with no beta-sheet [Friedli 1996]. Albumins in general are characterized by a
low content of tryptophan and methionine and a high content of cysteine and the charged amino
acids aspartic and glutamic acids, lysine and arginine. The glycine and isoleucine content of bSA is
lower than in the average protein [Friedli 1996; Peters 1985]. Figure 4.2 shows that the bSA
molecule is made up of three homologous domains (I, II, III), divided into nine loops (L1-L9) by
the 17 disulfide bonds. Each domain can be classified into 10 helical segments, 1-6 for subdomain
A and 7-10 for sub-domain B.

76 MATERIALS AND METHODS
Figure 4.2: Secondary and tertiary structure of BSA. (a) Heart shaped structure of BSA, according to 1H NMR and
X-ray crystallography; (b) motif for sub-domain A; (c) motif for sub-domain B [Friedli 1996]
A lyophilized powder of the pure protein, prepared by a modification of Cohn et al. [Cohn et al.
1946], using cold ethanol, pH and low temperature precipitation followed by an additional pH
adjustment step prior to final drying, was supplied by Sigma (Sigma-Aldrich; 82024 Taufkirchen,
Germany) and used without further purification. The product was specified as follows: pH 7.0 in
1% (w/v) aqueous solution, min. 96% (electrophoresis) lyophilised powder [Sigma 2004].
Catalase from bovine liver (CAT)
(a) (b) (c)
Catalase from bovine liver is a tetramer of four identical sub-units, each consisting of 506 amino
acids. It has an overall molecular weight of 250 kDa [Sigma 2005]. Each monomer contains a heme
prosthetic group at the catalytic centre. The enzyme also binds NADP strongly, of which the NADP
and heme group are within 13.7 Å of each other [Sigma 2005]. Only about 60% of the catalase
structure is composed of regular secondary structure motifs. Alpha-helices account for 26% of its
structure and beta-sheet for 12%. Irregular structure includes a predominance of extended single
stands and loops that play a major roll in the assembly of the tetramer [Boon et al. 2001].
Considering the tertiary structure, each sub-unit has four domains (Figure 4.3). The first is made up
of the amino-terminal 75 residues and form an arm with two alpha-helices and a large loop
extending from the globular sub-unit. The second and largest domain is composed of residues 76 to
320 and may be classified as a α plus β type domain including a beta-barrel, several helical
segments of 3 to 4 turns each and various loops. This domain contains the heme moiety. The third
domain is made up by residues 321 to 436 and is referred to as wrapping domain. It lacks
discernable secondary structure except for two helices. The carboxy-terminal part of catalase

CHAPTER 4 MATERIALS AND METHODS 77
contains residues 437 to 506 and forms the surface of the enzyme along with 3 alpha-helices of the
heme-containing second domain [Boon et al. 2001].
(a) (b)
Figure 4.3: Crystal structure of bovine liver catalase by X-ray diffraction. (a) Entire catalase molecule; (b) NADPH
binding site of catalase molecule [PDB 2005].
Catalase is present in the peroxisomes of nearly all aerobic cells. It protects the cell from the toxic
effects of hydrogen peroxide by catalysing its decomposition into molecular oxygen and water
without the production of free radicals. The mechanism of the catalysis can be seen in Figure 4.4.
( III)
− E → H O + O = Fe(
IV)
− E
H 2O
2 + Fe
2
( IV)
− E → H O + O + Fe(
III)
− E
H 2O
2 + O = Fe
2
2
Figure 4.4: Chemistry of catalase catalysis. The catalytic process is thought to occur in two stages, where Fe-E
represents the iron centre of the heme attached to the rest of the enzyme E [Boon et al. 2001]
Catalase does not require any activators, but it can be inhibited by cyanide, azide, hydroxylamine,
cyanogens bromide, 2-mercaptoethanol, dithiothreitol dianisidine and nitrate. Catalase activity is
constant over a pH range of 4.0-8.5 [Sigma 2005].
The pure protein was supplied as powder by Sigma (Sigma-Aldrich; 82024 Taufkirchen,
Germany) and used without further purification. The product was specified: 2000-5000 units /mg
protein, cell culture tested. One unit will decompose 1.0 µmole of H2O2 per minute at pH 7.0 at
25°C while the H2O2 concentration falls from 10.3 to 9.2 mM, measured by the decrease of
absorption at 240nm using UV-spectroscopy [Sigma 2005].

78 MATERIALS AND METHODS
4.1.2 Excipients and Reagents
All excipients and reagents used for preparation of levitator-dried formulations, spray-dried
formulations and bubble pressure tensiometry formulations, as well as all other substances used
during this work are summarized in Table 4.1. Aqueous solutions were prepared in water for
analysis and filtered prior to use via a cellulose nitrate membrane filter with a pore diameter of
0.22 µm.
Table 4.1: Excipients used to formulate the solutions and suspensions for the use in an acoustic levitator, spray-dryer
and bubble pressure tensiometer.
Excipients Lot-No. Supplied by
Proteins
Albumin, bovine serum, Fraction V 025K1031
103K1373
Sigma, Germany (A-2153)
Catalase from bovine liver
Sugars
013K7055
024K7034
Sigma, Germany (C-1345)
D-Mannitol 100K0129 Sigma, Germany (M-9546)
D (+) Trehalose dehydrate 133K 3775
122K3801
Sigma, Germany (T-5251)
Maltodextrin 15 from maize starch 404054/1 Fluka, Switzerland (31412)
Surfactants
1-Octadecanol, approx. 99% 023K1276 Sigma, Germany (S-5751)
Pluronic F-127 99H1194 Sigma, Germany (P-2443)
Stearic acid S3818073 317 Merck, Germany (8.00673.1000)
Polysorbate 80 440327/1 Fluka, Switzerland (93781)
Other substances
Sodium chloride 10670 Riedel-de Haën (31434)
Trizma pre-set crystals pH 8.0 122K5436 Sigma, Germany (T-8443)
Solvents
Hexane
Ethanol 96% p. a. 10570238 Carl Roth GmbH, Germany
(P-0751)
Water p. a. OC328373
OC522462
Merck, Germany (1.16754.5000)

CHAPTER 4 MATERIALS AND METHODS 79
Table 4.2: Reagents used for catalase activity assay.
Reagents Lot-No. Supplied by
Catalase activity assay
Potassium hydroxide ≥85% 113K0019 Sigma, Germany (P-5958)
Potassium phosphate monobasic 99.0% 024K0050 Sigma, Germany (P-5379)
Hydrogen peroxide 30 wt.% 044K13332 Sigma, Germany (H-1009)
Table 4.3: Reagents used for determination of residual water content via Karl-Fischer Titration.
Reagents Lot-No. Supplied by
Karl-Fischer Titration
Nitrogen, gaseous Linde, Germany
Hydranal © -Coulomat AG Oven 4056B Riedel-de Haën (34739)
Hydranal © -Coulomat CG 4268A Riedel-de Haën (34840)
Hydranal © -Humidity Absorber 03390 Riedel-de Haën (34788)
4.1.3 Acoustic levitation system
Acoustic levitator
The acoustic levitator used in this work was a 58 kHz levitator supplied by tec5 AG (61440
Oberursel, Germany). The acrylic process chamber (inner acrylic chamber) was built in the Institute
of Fluid Mechanics of the Friedrich-Alexander-University in Erlangen, Germany. The original setup
is shown in Figure 4.5. Technical specifications according to tec5 AG are listed in Table 4.4.
The acoustic wave inside the acoustic levitator is created by an oscillating transducer and reflected
at a reflector positioned opposite to the transducer. The end plate of the transducer has a diameter of
12mm and the transfixion has a diameter of 2mm. The horn is attached to a piezo-crystal connected
to a power supply unit. The power input in the transducer depends not only on the working voltage
of the power supply unit but also on the distance L R between transducer and reflector. If this
distance is set to a multiple of half wavelengths, n ⋅ λ / 2,
a standing wave with equally space
pressure nodes and antinodes is created. In every pressure node the levitation of a liquid or solid
sample is possible.
0

80 MATERIALS AND METHODS
Table 4.4: Technical specifications of the acoustic levitator according to tec5 AG
Technical specifications
Power supply unit
Operation frequency 58 kHz
Particle diameter range ≈15µm to ≈2.5mm
Wavelength of the standing acoustic wave 5.71mm
HF-Power (continuously variable) 0.65 to 5 Watt
Modulation frequency 10Hz – 2kHz
Modulation amplitude 0 – 2 VPP
Modulation input impedance 20kΩ
Operation temperature range 0-70°C
Relative humidity (no condensation) 10-90%
The reflector is positioned opposite the transducer at the
variable distance L R . The distance can be set precisely
with a micrometer screw. Additionally, the horizontal
position can be adjusted with two other micrometer screws.
The reflector consists of a round flat metal plate with a
diameter of 25.0mm and a height of 11.0mm. In the centre
of the plate is a hole with a diameter of 3.6mm and a thread
(Figure 4.6). It is used for conditioning of the levitation
chamber and the ventilation air stream. The levitation
chamber built around the transducer and reflector was
made of acrylic glass and had the size given in Figure
4.7 a. It is the inner acrylic glass box or process chamber.
The base had a small hole for the tube supplying the
ventilation air stream. A second hole in the back with a
diameter of 17.3mm enabled the measurement of
temperature and humidity inside the process chamber by
installing a dew point hygrometer. A rectangular recess in
the front was made for the injection of the samples by a
gas-chromatography syringe in case of liquid samples, or
micro tweezers in case of solid samples.
Figure 4.5: Original set-up of the acoustic
levitator.

CHAPTER 4 MATERIALS AND METHODS 81
10.7 mm
25 mm
3.75 mm
25 mm
3.75 mm
Figure 4.6: Reflector dimensions of the acoustic levitator with borehole for the ventilations air stream.
The acoustic levitator was assembled into an outer acrylic glass box similar to a glove box for
microbiological research to isolate it from environmental conditions. An additional heater (Leister
Heater 8D1-3000W; Leister, Switzerland) was installed to heat the whole unit up to 60°C. The
dimensions of the acrylic glass box are shown in Figure 4.7.
124.9 mm
49.7 mm
15.3 mm
62.2 mm
7.1 mm
58 mm 30.6 mm
17.3 mm
95.7 mm
88.6 mm
29.2 mm
(a)
11 mm

82 MATERIALS AND METHODS
55 mm
130 mm
55 mm
145 mm
185 mm 130 mm
380 mm 190 mm 400 mm
580 mm
40 mm
60 mm
Figure 4.7: Dimensions of the acrylic glass containers built around the levitation system. Two gloves are fixed at the
two holes in the front side to reach inside the container and to inject the sample into the levitator. Through the larger
hole at the back side an additional heated air stream is blown into the container to heat the entire system. The small hole
is used for electric cables and the tube for the ventilation air stream. The part on the right side of the hatched area
contains a door to pass samples and material into the container. The hatched area itself is movable and can be drawn out
of the container a sluice.
Controlled evaporation mixer (CEM)
The CEM-system is a liquid delivery system that can be applied for atmospheric or vacuum
processes. It consists of a liquid flow controller, a mass flow controller for the carrier gas and a
temperature controlled mixing and evaporation device. All three were made by Bronkhorst (NL)
and supplied by Wagner (“Mess- und Regeltechnik”, 63067 Offenbach, Germany). The technical
specifications and calibration details of the CEM-unit can be seen in Table 4.5 and Figure 4.8.
According to the technical specifications it was possible to condition the levitation chamber from
room temperature up to 70°C with a relative humidity from a few ppm to almost 100% depending
on the air flow rate. The relation between evaporated liquid, air flow velocity and temperature was
calculated using Fluidat © on the net V1.12/5.59 [Bronkhorst 2005]. Knowing the velocity and the
relative humidity of the air stream the orifice Reynolds number, Re orifice , at the reflector was
calculated.
50 mm
150 mm
340 mm
380 mm
(b)

CHAPTER 4 MATERIALS AND METHODS 83
Table 4.5: Technical specifications and calibration details of the controlled evaporation mixer
Technical specifications
Liquid flow controller type L1-FAC-33-0
Serial number M2207627B
Medium water
Feeding pressure 1 bar
Flow range 0.2 to 10.0 g/h
Mass flow controller type F-201C-FAC
Serial number M2207627A
Medium dry air / nitrogen
Feeding pressure 1 bar
Flow range 0.04 to 2.0 ln/min
Temperature controlled mixing unit type W-202-330-P
Serial number M2207627C
Range up to 200°C
compressed
air
cleaning unit
water tank
Mass
flow
Liquid
flow
mixing unit
with heater
Figure 4.8: Components and adjustment of the controlled evaporation mixer.
to acoustic
levitator

84 MATERIALS AND METHODS
CCD-camera and imaging software
To record and measure the decrease of the droplet radius with time and the change in
position of the centre of mass of the levitated droplet during the drying experiments, a JAI CV-M4
2/3” monochrome CCD-camera for progressive scan with a bellow and a Nikon 60mm objective 2.8
diaphragm was used. For back light illumination either a VLP CIS-50/50-R-24 red LED or a Schott
KL 1500 electronic microscope illumination was used. The CCD camera was connected to a PC via
a PcDIG LVDS frame grabber (32-bit). The pictures were recorded and analysed using Image Pro
Plus Software Version 4.51 (mediaCybernetics © ). All parts of the imaging system were supplied by
Weiss Imaging and Solutions GmbH, 85232 Günding , Germany. Figure 4.9 gives a summary of all
parts of the levitation system except for the outer acrylic glass container and the additional heater.
In Figure 4.10 the whole set-up can be seen.
CCD-camera
bellows
to PC with
imaging software
levitation chamber
macrolens
sample
reflector
micrometer
screw
transducer
piezo-crystal
back light
illumination
micrometer
screw
Controlled
evaporation
mixer
CEM
air flow
liquid flow
Figure 4.9: Sketch of the composition of all parts of the acoustic levitation system used in this work, except of the outer
acrylic glass container and the additional heater.

CHAPTER 4 MATERIALS AND METHODS 85
(6)
(4)
(5)
(2)
(1)
Figure 4.10: Complete set-up of the acoustic levitation system. (1) outer acrylic glass chamber;
(2) acoustic levitator with inner acrylic glass chamber and LED; (3) external heating system; (4) CCD-camera system
with bellow and macro lens; (5) controlled evaporation mixer with liquid flow and mass flow controller; (6) pressure
reducer; (7) PC with imaging software; (8) power supply and control unit for the acoustic levitator (left) and the CEM
(right).
(3)
(7)
(8)

86 MATERIALS AND METHODS
4.2 Methods
4.1.4 Acoustic Levitation
Camera system and imaging software
To determine the evaporation rate of a single droplet dried in an acoustic levitator by measuring the
decrease in diameter or by change in position of the centre of mass, the camera system and the
imaging software had to be calibrated. For every adjustment of the macro lens and the bellow the
system was calibrated using a microscope slide with a micrometer. The calibration was verified
measuring levitated spheres of polypropylene with a diameter of 1500µm, 1850µm and 2000µm ±
30µm (Kugel Pompel, 1160 Vienna, Austria) (Spherotech GmbH; 36041 Fulda; Germany). The
experiments were performed with the largest magnification still giving a focused image. The shutter
of the camera was set to 1/3000 seconds. Pictures were taken every 0.25, 0.5, 0.75, 1.0, 2.0, 3.0, 4.0
and 5.0 s depending on the rate of evaporation. The horizontal, vertical and Ferret diameter as well
as the aspect ratio and the position of the centre of mass was measured for every picture. The data
were collected from the imaging software and transferred to Microsoft Excel © for further analysis.
Acoustic levitator
The SPL of the acoustic levitator was calibrated using a method reported by Rensink [Rensink
2004]. The distance between transducer and reflector was initially set to 2.8 mm at ambient
conditions. Then an n-decane droplet with an initial volume >2.0 µl was levitated and recorded by
the imaging software until the volume decreased to exactly 2.0 µl. At this point the magnitude of
the SPL, adjustable at the power supply, was set to a value such that the aspect ratio of the n-decane
droplet was 1.5. For a more stable levitation the distance between transducer and reflector was
increased by 0.7 mm. This adjustment corresponds to an effective SPL of exactly 162.47 dB at
ambient conditions at a temperature of about 20°C.
Controlled evaporation mixer (CEM)
The settings of the CEM for the desired air flow velocity, the temperature and relative humidity
inside the process chamber were determined using Fluidat © on the net V1.12/5.59 [Bronkhorst
2005]. Additionally, the external heater was set to the same temperature to heat the outer acrylic
glass container. Before starting any levitation experiments the system was equilibrated for 1 h. The
temperature and the relative humidity inside the process chamber were verified using a Testo 605-

CHAPTER 4 MATERIALS AND METHODS 87
H1 Dew Point Hygrometer. The temperature inside the outer acrylic glass container was determined
using a Testo Mini-Thermometer 150°C (Testo AG; 79853 Lenzkirch, Germany).
Levitation procedure
The sample solvents or solutions used were first filtered through a 0.2 µm filter (Schleicher &
Schull FP 30/0.2 CA-S, sterile, non pyrogenic) and then filled into 2µl Clear Crimp Seal Vials
(Supelco; Bellefonte PA, USA) sealed with 11 mm PTFE Liners (Supelco; Bellefonte PA, USA).
Vials containing proteins were put on ice and stored in a fridge at 4°C. Immediately before the
experiment the imaging software was started. A droplet of the sample of between 1.0 and 2.5µl was
positioned into the middle pressure node using a Hamilton 75 ASN 23s 5 µl or a 710 ASN 23s 10 µl
gas chromatography syringe (Hamilton Bonaduz AG; 7402 Bonaduz, Switzerland). During the
drying experiments, pictures were taken after a predefined time interval until the droplet had either
evaporated completely, dropped out of the standing acoustic wave, or, in the case of solutions, the
particle formed did not change shape and position for more than 5 minutes. To determine the
evaporation rate of the liquid sample the data was analysed according to Chapter 3.3.3.
4.1.5 Maximum bubble pressure tensiometry
Measurement of the dynamic interfacial tension was performed using a Lauda MPT2 maximum
bubble pressure tensiometer (Lauda Dr. R. Wobser GmbH, 97955 Lauda-Konigshofen, Germany).
It had a dynamic time range of 0.0001 to 100 seconds. The set-up of the tensiometer is shown in
Figure 4.11.
Figure 4.11: Lauda MPT 2 maximum bubble
pressure tensiometer:
(1) pump;
(2) filter unit;
(3) measurement volume;
(4) bubble detector;
(5) test vessel
(6) temperature cleading;
(7) mount with capillary;
(8) control unit;
(9) personal computer.
[Lauda 2005]

88 MATERIALS AND METHODS
To determine the dynamic surface tension of a liquid, an air
stream is blown through a thin capillary into the liquid
forming bubbles. The pressure at the entrance of the
capillary, the volume of air flowing through the capillary and
the time necessary for the formation of the bubble are
measured. Depending on the flow volume per time either a jet
or individual bubbles are produced. If the pressure is plotted
against the flow volume per time, curves with different slopes
are obtained. The linear area with the largest slope represents Figure 4.12: Pressure of air emerging
the jet area where the air flows laminar through the capillary into water plotted against the air flow rate
to determine the transition between
according to the Hagen-Poiseuille law. If the flow is reduced bubble and jet regime [Lauda 2005]
sufficiently, the jet reduces to individual bubbles. The pressure inflating the bubbles remains
independent of the flow volume, but depends on their interfacial tension and their radius. This
relationship is described by the Laplace equation. The transition between jet range and bubble range
leads to a change in the slope of the pressure / flow rate curve, which is used to calculate the critical
flow, L C , and the corresponding critical pressure, p C (Figure 4.12).
Within the bubble range, the pressure at the outlet of the capillary where the bubble is
formed increases from an initial pressure, p initial , to the maximum pressure, p max , (Figure 4.13;
phase 1-3). This maximum pressure is the same pressure as the constant pressure at the inlet of the
capillary, p MPT 2 , and it occurs when the radius, r , of the bubble at the outlet of the capillary is
equal to the radius, r cap , of the capillary itself (Figure 4.13; phase 3). Shortly after the maximum,
the pressure decreases to a minimum (Figure 4.13; phase 4-5). At this point, the bubble detaches
from the capillary and a new bubble is formed (Figure 4.13; phase 5). Using the maximum bubble
pressure, p max , the surface tension of the liquid corresponding to the surface age t of the bubble is
calculated. The surface age is the time from the beginning of the bubble formation to its radius, r cap .
At this point the bubble has the shape of a hemisphere. The time necessary to inflate the bubble
from the hemispherical shape to detachment is called dead time, t d . According to Faineman [Lauda
2000] it is calculated by
Equation 4.1 t = t p − td
Equation 4.2
t
d
t
=
p
⋅
( p ⋅ L)
L
C
C
⋅ p

CHAPTER 4 MATERIALS AND METHODS 89
Capillary
1
2
3
4 5
Rejection surface
Figure 4.13: Phases of bubble formation and internal bubble pressure [Lauda 2000]
10.0 ml aqueous solution of the desired concentration was investigated using capillary 41 with a
radius r cap of 0.075 mm and an immersion depth of 2.5 mm. The flow rate was decreased stepwise
from 100 mm 3 /s to 2.5 mm 3 /s. All experiments were performed at 25.0 ± 0.5°C using a Julabo UC-
5B water bath (Julabo GmbH; 77960 Seelbach, Germany). The surface excess of the dissolved
sample substance was calculated using the Gibbs Equation [Fuhrling 2004; Hiemenz 1986]
Equation 4.3
4.1.6 Ring tensiometer
pressure
1 ⎛ dγ
⎞
Γ = − ⋅ ⎜ ⎟
R ⋅ T ⎝ d ln c ⎠
Measurement of the equilibrium interfacial tension was
performed using a Kruss Digital Tensiometer K10ST (Kruss
GmbH; 22452 Hamburg, Germany) with platinum-iridium
ring. It had a range from 5 to 90mN/m and an accuracy of
±0.1mN/m. The ring is submerged below the interface and
subsequently raised upwards until contact with the surface is
registered. Then the sample is lowered so that the liquid film
produced beneath the ring is stretched (Figure 4.14). As the
film is stretched, a maximum force is experienced which is
T
1
2
3
4
t
5
time
t p
t d
Figure 4.14: Sketch of the ring method
[Kruss 2005]

90 MATERIALS AND METHODS
recorded in the measurement. At the maximum the force vector Fmax r
is exactly parallel to the
direction of motion. At this moment the contact angel θ is zero. Figure 4.15 illustrates the change
in force as the distance of the ring from the surface increases [Kruss 2005].
Figure 4.15: Change of force with ring distance above the interface of the liquid sample [Kruss 2005]
The calculation of the resulting interfacial tension is made according to the following equation
Equation 4.4
F [mN]
r r
Fmax − FG
γ =
l ⋅ cosθ
with the wetted length l of the platinum-iridium ring and the weight FG r of the volume of liquid
lifted [Kruss 2005]. Measurements of the equilibrium interfacial tension were performed with
20.0ml of aqueous solution at a temperature of 25.0 ± 0.5°C using a Julabo UC-5B water bath
(Julabo GmbH; 77960 Seelbach, Germany). Each solution was equilibrated for 180 minutes before
measurement.
4.1.7 Spray-Drying
10.0
8.0
6.0
4.0
2.0
F max
F 1
Lamella
breaks
0.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0
Distance above surface [mm]
Spray-drying experiments were performed using a Buchi Mini Spray Dryer B-191 (Buchi AG; 9230
Flawil, Switzerland) and a Niro Mobile Minor (Niro A/S; 2860 Soeborg, Denmark). The basic setup
of the Buchi B-191 is shown in Figure 4.16. Aqueous solutions in the desired concentration were
prepared in water p.a. and spray-dried under standard conditions in a temperature range comparable
F 3

CHAPTER 4 MATERIALS AND METHODS 91
to the levitator experiments. These conditions can be seen in Table 4.6. For the experiments carried
out with the Buchi B-191 an improved cyclone was used for a better powder recovery [Maury
2005].
Table 4.6: Standard conditions of the spray-drying experiments.
Figure 4.16: Sketch of the Buchi B-191
(1) air inlet;
(2) inlet air heating element;
(3) two-component nozzle;
(4) cyclone separator;
(5) aspirator;
(6) thermocouple for Tinlet;
(7) thermocouple for Toutlet;
(8) product collector;
(9) peristaltic pump;
[Büchi 2005]
Buchi Mini Spray-Dryer B-191 Niro Mobile Minor
Inlet temperature 100°C 115°C
Outlet temperature 60°C 60°C
Drying air flow rate 54 m 3 /h -
Atomization two-fluid nozzle two-fluid nozzle
Atomization flow rate 700 liters/h 2 bar
Nozzle cooling yes no
Nozzle purification yes (4.5 bar) no
Liquid feed 3.0 ml/min 15.0 ml/min
Volume of solution 15.0 ml 500 ml
Volume of collect vessel 7.1 ml 1000 ml
Flush time after spray-drying 5 min 5 min

92 MATERIALS AND METHODS
4.1.8 Karl-Fischer Titration
The residual moisture content of the spray-dried formulations was determined using a Mitsubishi
Moisture Meter CA-06 Coulometric and a Mitsubishi Water Vaporizer VA-06. First the weight of
an empty glassy sample holder and its glassy closure was determined by a Mettler Toledo AT261
Delta Range © analytical balance. The sample holders were transferred into a dry air-purged glove
box. The humidity inside was ≤3.0% all time at room temperature. Samples of 80 to 120mg of the
spray-dried powder were filled into the sample holders with subsequent sealing still inside the glove
box. Then the samples were transferred into the glass boat pick-up of the moisture meter by
connecting the sample holder to the water vaporising unit. Afterwards the glass boat pick-up was
pushed automatically into the heating unit. All measurements were taken at a temperature of 130°C,
an initial rate ≤10µg H2O per minute and a N2 gas stream of 200ml/min. Formulations with a glass
transition temperature lower than 130°C (data obtained from literature [Labuza et al. 1992]), were
measured at a temperature 10 to 20°C lower than their published glass transition temperature. The
percentage of moisture content was calculated by using the reweighed sample holders. All
measurements were performed in triplicate.
4.1.9 Enzyme Activity Assay of Catalase
Catalase catalyses the decomposition of hydrogen peroxide H2O2 to water and oxygen according to
Figure 4.4. One unit enzyme will decompose 1.0 µmole of H2O2 per minute at pH 7.0 at 25°C,
while the concentration of H2O2 decreases from 10.3 to 9.2 mM. The rate of disappearance of H2O2
is followed by observing the decrease in the absorbance at 240 nm, suggested by Beers and Sizer
[Beers 1952]. A PerkinElmer Lambda 25 UV/VIS spectrometer connected to a PC with
PerkinElmer UV WinLab V 5.0 software (PerkinElmer LAS GmbH; 63100 Rodgau, Germany) was
used. At first, a 50mM potassium phosphate buffer (reagent A) was prepared using potassium
phosphate monobasic and deionised water and adjusted to pH 7.0 using 1 M KOH solution. Reagent
A acted as blank solution for calibration of the spectrometer at 240 nm. Then a 0.0036% (w/w)
hydrogen peroxide solution (reagent B) was prepared in reagent A as substrate solution and
equilibrated at 25°C. Reagent B was used when the A240nm was between 0.550 and 0.520. Hydrogen
peroxide was added to increase, or reagent A was added to decrease the absorption. Immediately
before use, the catalase solution (reagent C) containing 50 to 100 units enzyme per ml was prepared
in cold reagent A. Catalase was completely dissolved before assaying. In a quartz cuvette 2.9 ml of
the substrate solution reagent B was mixed with 0.1 ml of enzyme solution reagent C by inversion

CHAPTER 4 MATERIALS AND METHODS 93
and the time t decrease required for the A240nm to decrease from 0.45 to 0.40 absorbance units was
recorded. The activity of catalase was calculated by
Equation 4.5
units / ml enzyme =
t
3.
45⋅
df
⋅ 0.
1
decrease
The factor 3.45 corresponds to the decomposition of 3.45 micromoles of hydrogen peroxide in a
3.0 ml reaction mixture producing a decrease in the A240nm from 0.45 to 0.40 absorbance units, df
is the dilution factor, and the factor 0.1 holds for the volume in millilitre of the enzyme used. The
enzyme activity refers to the mass of solid or protein, and is given by
Equation 4.6
Equation 4.7
units / ml enzyme
units / mg solid =
mg solid / ml enzyme
units /ml enzyme
units /mg protein
=
mg protein /ml enzyme
The final assay concentrations in a 3.0 ml reaction mix were 50 mM potassium phosphate, 0.035%
(w/w) hydrogen peroxide and 5-10units catalase. Untreated catalase was used as reference with an
activity of 100%. All measurements were performed in triplicate.
4.1.10 Kinematic viscosity
The kinematic viscosity was measured using a Schott Ubbelohde Viscometer Type 501 13/Ic
(Schott GmbH; 55014 Mainz, Germany) with a capillary diameter of 0.84 mm. Before use it was
cleaned with 15% H2O2 and 15% HCl and rinsed with deionised water. When the viscometer was
completely dry and dust free, 15 ml of the liquid sample were transferred through the filling tube
into the reservoir. A vacuum was applied to the capillary tube with simultaneous closing of the
venting tube. This caused the subsequent filling of the reference level vessel, the capillary tube, the
measuring sphere and the pre-run sphere. Then the suction was discontinued and the venting tube
was opened again. This caused the liquid column to separate at the lower end of the capillary ant to
form the suspended level at the dome-shaped top part. The time it took the leading edge of the
meniscus of the sample to descend from the upper edge of the upper timing mark to the upper edge
of the lower timing mark was measured [Schott 2005]. The kinematic viscosity is calculated by
Equation 4.8 ν
= K ⋅ ( t − HC)
viscometer

94 MATERIALS AND METHODS
K viscometer is the viscometer constant of approximately 0.03 and HC is the kinetic energy correction
dependent on the viscometer and flow time. The values for HC can be found in the instruction
manual of the viscometer [Schott 2005]. All measurements were performed in triplicate.
4.1.11 Liquid density
Density measurement was performed with a Blaurand © Glass Pyknometer (VWR International
GmbH; 64295 Darmstadt, Germany). The pyknometer had a volume of 5.370 ± 0.001 cm 3 .The
empty weight of the pyknometer and its glassy closure with a small capillary inside was determined
using a Mettler Toledo AT261 DeltaRange © analytical balance. The liquid sample, equilibrated at
25.0 ± 0.5°C using a Julabo UC-5B water bath (Julabo GmbH; 77960 Seelbach, Germany) was then
filled into the pyknometer up to a height, that liquid effused out of the capillary of the glassy
closure when closed. The outside of the pyknometer was cleaned before reweighing of the
analytical balance. The density was calculated by
Equation 4.9
ρ
liquid
w filled − w
=
V
pyknometer
empty
All measurements were performed in triplicate.
4.1.12 Scanning electron microscopy (SEM)
Particle size and morphology of all dried particles were examined using an Amray 1810T scanning
electron microscope (Amray; Bedford, USA) at 20 kV. Samples were fixed on aluminium stubs
(G301, Plano) with self-adhesive films and spluttered with gold at 20 mA / 5 kV (Hummer JR
Technics; Munich, Germany) for 1.5 min.

CHAPTER 5 RESULTS AND DISCUSSION 95
5 Results and discussion
5.1 Pre-liminary levitation tests
5.1.1 Size measurement
The calibration of the imaging software is performed with a microscope slide with micrometer and
verified using polypropylene spheres with a diameter of 1500 µm, 1850 µm and 2000 µm ± 30µm.
The precision of size measurements of a sample within an acoustic levitation system depends not
only on the reproduction scale, the resolution of the CCD-chip, the intensity of the back
illumination and the calibration of the system, but also on the dynamics of the levitated droplet or
particle. Vibrations, air flow or a not ideal adjusted standing acoustic sound wave can lead to a
deflection of the sample out of its rest position resulting in oscillations [Schnitzler 1998;
Tuckermann 2002]. To eliminate out-of-focus pictures the levitation system is adjusted very
precisely and the shutter time of the camera is 1/5000 s. The intensity of illumination is chosen not
to obscure the outline of the levitated sample. Levitated liquid samples are also influenced by
interior oscillation resulting in a continuous deformation of the droplet shape with change of the
aspect ratio. This kind of droplet oscillation leads to an additional factor complicating the precise
measurement of the size of liquid droplets. Figure 5.1 shows the larger inaccuracy of measurement
of a levitated Migliol N812 droplet due to the internal oscillation compared to the smaller
inaccuracy of a rigid polypropylene sphere. The difference between horizontal and vertical diameter
of the Migliol N812 droplet is caused by the different values of the axial to radial levitation force
[Lierke 1996]. The larger standard deviation of the vertical diameters of the Migliol droplets shows
that the internal oscillations occur in the axial direction. Another important factor was the influence
of the intensity of back illumination on size measurement of the levitated droplet or particle. An
illumination too intense caused an obscuration of the outline of the sample as shown in Figure 5.1.
The stronger the illumination, the larger is the decrease in diameter determined by the imaging
software. This effect is tested with a levitated polypropylene sphere at different intensity of back
light illumination. The first three levels do not cause a substantial change in the measured horizontal
diameter, but level 4 to 6 obscures the outline increasingly (Figure 5.3 a). This leads to a smaller
determined diameter as well as to a larger standard deviation of the diameter means (Figure 5.3 b).
Therefore level 2 or level 3 are chosen for the back illumination of the levitation experiments.

96 RESULTS AND DISCUSSION
Counts [-]
Counts [-]
200
150
100
50
0
1830 1835 1840 1845 1850 1855 1860 1865
140
120
100
80
60
40
20
0
(a)
(b)
Diameter [µm]
1500 1550 2050 2100 2150
Diameter [µm]
Horizontal diameter
Vertical diameter
Gauss-Fit horizontal diameter
X mean = 1848.3 µm
SD = 2.8 µm
Gauss-Fit vertical diameter
X mean = 1849,1 µm
SD = 3.2 µm
Horizontal diameter
Vertical diameter
Gauss-Fit vertical diameter
X mean = 2118.7 µm
SD = 12.5 µm
Gauss-Fit horizontal diameter
X = 1530.8 µm
mean
SD = 17.8 µm
Figure 5.1: Statistics of the recorded horizontal and vertical diameter at 25.3°C and 20.4% humidity. (a) Levitated
polypropylene sphere. (b) Levitated Migliol N812 droplet.
Level 1 Level 2 Level 3
Level 4 Level 5 Level 6
Figure 5.2: Pictures of a levitated poly- propylene sphere at 25°C with different intensity of the illumination.

CHAPTER 5 RESULTS AND DISCUSSION 97
Horizontal diameter [µm]
Counts [-]
Figure 5.3: (a) Diagram of the diameter determined by the calibrated imaging software in relation to the intensity of the
back light illumination; (b) Direct statistical correlation between the back illumination at level 2 and at level 6.
5.1.2 Injectable volume
To levitate a liquid sample at the pressure node of the ultrasonic levitation system, gas
chromatography syringes with different volume are used depending on the viscosity of the sample
solution. Due to deformation of the levitated droplet, volumes and surfaces from the recorded
pictures are calculated assuming an oblate ellipsoid using the horizontal radius rhor and vertical
radius r vert .
1860
1840
1820
1800
1780
1760
1740
1720
1700
1680
(a)
180
160
140
120
100
80
60
40
20
0
(b)
1 2 3 4 5 6
Back illumination level [-]
1670 1680 1690 1700 1840 1850
Horizontal diameter [µm]
4 2
Equation 5.1 Vdroplet = ⋅ π⋅
rhor
⋅ rvert
3
Back illumination level 2
Back illumination level 6
Gaussian Fit (level 2)
X mean = 1848.2 µm
SD = 2.5 µm
Gaussian Fit (level 6)
X mean = 1685.6 µm
SD = 8.7 µm

98 RESULTS AND DISCUSSION
2
2
2 rvert
⎛1
+ E ⎞
r
Equation 5.2 S droplet = 2 π⋅
rhor
+ π⋅
⋅ ln⎜
⎟ with E = 1-
2
E ⎝1
− E ⎠
r
First it is necessary to determine if the injected volume corresponds to the volume calculated from
the pictures recorded by the imaging software. Different volumes of water, ethanol and solutions
with low viscosity using the 5µl Hamilton 75 ASN syringe and maltodextrin solution > 200 mg/ml
using the 10µl Hamilton 710 ASN syringe, are levitated at ambient conditions. The injected volume
is determined from the recorded pictures using Equation 5.1. Figure 5.4 shows the relationship
between the injected and calculated volume.
Calculated volume [µl]
3.0
2.5
2.0
1.5
(a)
Water
Kinematic viscosity = 1.00mm 2 /s
1.5 2.0 2.5 3.0
Injected volume [µl]
Figure 5.4: Diagram of the volume determined by the imaging software versus the injected volume for (a) water and
(b) maltodextrin solution 20% (w/V) at 25°C.
The smallest injectable droplet that separates from the syringe without any problems has a volume
of 1.0 µl for both substances. It can be seen that the determined volume matches almost exactly the
injected one, independent of the viscosity of the liquid sample and the syringe.
Secondly, the influence of the effective sound pressure level on the precision of the size
measurement is tested. 2 µl of water are levitated at different effective SPL, determined via the
method of aspect ratio explained in Chapter 3 [Yarin et al. 1998]. An increase in the sound pressure
level leads to a strong deformation of the droplet. This results in an increase of the aspect ratio and
the ellipticity, E , in Equation 5.2. Up to an effective SPL of 164.9 dB, corresponding to an aspect
ratio of 1.26 for water at 25.1°C, the injected and calculated volume match very well (Figure 5.5).
At larger SPLs and aspect ratios the determined volume continuously becomes smaller than the
injected one. To overcome this effect of the SPL for later examinations, the volume is calculated
Calulated volume [µl]
3.0
2.5
2.0
1.5
(b)
vert
hor
Maltodextrin solution 20% (w/v)
Kinematic viscosity = 3.75mm 2 /s
1.5 2.0 2.5 3.0
Injected volume [µl]

CHAPTER 5 RESULTS AND DISCUSSION 99
using Equation 5.2 as the volume of a surface equivalent sphere. Figure 5.5 shows, that the SPL
does not affect this kind of volume determination of the liquid sample.
Determined volume [µl]
2.2 Volume via Equation 5.1
Volume of a surface
equivalent sphere
2.1 Aspect ratio
2.0
1.9
1.8
Figure 5.5: Diagram of the influence of the effective SPL on the volume determined by the imaging software and the
aspect ratio of the levitated droplet at 25.1°C and 26.8% relative humidity. Additionally, the volume of a surface
equivalent sphere calculated using Equation 5.2 is plotted into the diagram.
5.1.3 Heating of the process chamber
163 164 165 166 167 168
1.0
169
Effective SPL [dB]
Oscillation of the ultrasonic transducer causes a heating of the process chamber of the levitation
system. The increase in temperature inside can lead to an increase in evaporation rate of liquid
droplets and a decrease in evaporation time [Kastner 2001]. To investigate the influence of the
effective SPL, the temperature inside the process chamber in the area of the middle pressure node
was measured within the first 15 min after the ultrasonic levitator has been switched on at ambient
conditions. Three different effective SPLs are investigated (Figure 5.6 a). The results show a
dependence of the temperature development inside the levitator on the effective SPL. After
10 to 15 min an equilibrium temperature is reached for all given SPLs. Measurements of the
evaporation rate of solvents or solutions at ambient conditions need therefore at least an
equilibration time of 15 min before starting the first experiment. The influence of the SPL on the
temperature inside the process chamber with additional heating by the external heater and
ventilation using the CEM is also tested. The temperature of the external heater is set to either 40°C
or 60°C. The conditions at the CEM are set to produce an air flow of 40 or 60°C with an orifice
Reynolds number of 200 at a relative humidity of 0.1%. The results are shown in Figure 5.6 b. As
stated by Kastner [2001] an additional heating with an external heater suppresses the influence of
the heat input due to the oscillation of the ultrasonic transducer. The presence of air flow is of no
2.0
1.8
1.6
1.4
1.2
Aspect ration [-]

100 RESULTS AND DISCUSSION
account. The experiments also show a temperature fluctuation of only ± 0.1°C of the preset
temperature value.
Temperature in process chamber [°C]
Temperature in process chamber [°C]
26
25
24
23
22
21
20
(a)
62.0
61.0
60.0
59.0
40.5
40.0
39.5
39.0
(b)
0 2 4 6 8 10 12 14 16
Time [min]
Effective SPL 163.7 dB
Effective SPL 166.4 dB
Effective SPL 167.9 dB
Heater 40°C - SPL 166.3 - Ventilation 0.000 m/s
Heater 40°C - SPL 166.3 - Ventilation 0.885 m/s
Heater 60°C - SPL 166.9 - Ventilation 0.000 m/s
Heater 60°C - SPL 166.9 - Ventilation 0.992 m/s
0 2 4 6 8 10 12 14
Time [min]
Figure 5.6: (a) Diagram of the temperatures increase with time at different SPLs inside the process chamber of the
acoustic levitation system at ambient conditions of approximately 20.4°C and 27.8% relative humidity. (b) Diagram of
the influence of the SPL on the temperature inside the process chamber of the levitation system in case of additional
heating with an external heater and ventilation at 40°C and 60°C and a relative humidity of 0.1%.

CHAPTER 5 RESULTS AND DISCUSSION 101
5.1.4 Parametric studies
Levitation capabilities in a single-axis levitator are improved by using a curved reflector and
enlarging its section so as to levitate dense materials or liquids under large ventilation air streams
[Xie 2001]. To describe the standing acoustic wave the amplitude distribution of an axially
emerging Gaussian stream is used (Figure 5.7) [Schnitzler 1998].
Figure 5.7: Axial dispersion of a standing
acoustic wave in Gaussian approximation
according to Schnitzler [Bauer et al. 1999;
Schnitzler 1998]
Prediction of the stability of the standing acoustic wave can be made, based on the geometry of the
ultrasonic transducer and reflector. The stability depends on their distance, L R , and their radius of
curvature, R i [Tuckermann 2002]. The relation between both is given by
Equation 5.3
L
gi = 1 −
R
R
i
Stable levitation conditions are given for < g g < 1.
In the stability diagram shown in Figure 5.8,
0 1 2
all values of g i with stable levitation are marked by the hatched area.
not stable
2
not stable
semi-concentric
flat-flat
1
0
semi-confocal
stable
-2 -1 0
stable
-1
1
symmetricalconfocal
2
symmetricalconcentric
-2
not stable
not stable
Figure 5.8: Stability diagram of different transducer-reflector set-ups of an acoustic levitation system calculated using
Equation 5.3 [Tuckermann 2002].

102 RESULTS AND DISCUSSION
According to Schnitzler [1998] and Tuckermann [2002] the semi-confocal set-up is the least
problematic, because its values are inside the stable levitation area and not at any of the boundaries.
On these assumptions a semi-confocal set-up is built by manufacturing a reflector with a radius of
curvature of twice the distance between transducer and reflector L R (Figure 5.9 [Schnitzler 1998]).
The advantage of the semi-confocal set-up compared to the flat-flat one is tested by levitating a
water droplet at high ventilation air stream at 60°C and monitoring the vertical and horizontal
position of the centre of mass of the droplet. Figure 5.10 shows the more stable levitation conditions
using the semi-confocal set-up of the acoustic levitator at an air velocity of 2.0m/s than the flat-flat
one. The semi-confocal set-up the droplet varies within an amplitude of only ± 100µm, whereas the
amplitude of the flat-flat levitator was ± 500µm. Considering the vertical position, the difference
between both set-ups is however not that large. The reason is the internal oscillation of the levitated
droplet causing large changes of its vertical diameter of the droplet. This is also seen in Figure 5.3
As a result, the imaging software determined an “apparent” movement of the droplet centre of mass,
even though the levitation is more stable than that using the flat-flat set-up of the levitation system.
Figure 5.9: Sketch of the semi-confocal set-up of the ultrasonic levitator on the left [Schnitzler 1998] and picture of the
ultrasonic reflector with a radius of curvature of twice the transducer-reflector distance one the right.

CHAPTER 5 RESULTS AND DISCUSSION 103
Horizontal distance to initial position [µm]
600
400
200
0
-200
-400
-600
(a)
Figure 5.10: Diagram comparing the semi-confocal with the flat-flat set-up of an acoustic levitator at 60.0°C and a
relative humidity of 20.0%. (a) Levitation experiment in still air without ventilation. (b) To stress the levitated water
droplet the ventilation air stream was set to 2.012m/s, equal to an orifice Reynolds number of 400.
5.2 Evaporation of pure solvent droplets
5.2.1 Data analysis
Droplets of different initial size are levitated with the acoustic levitation system. It is to be expected
that the evaporation process can be described by the d 2- law [Frohn 2000].
Different initial droplet size
Droplets of the same liquid but of different initial droplet size or volume have different evaporation
lifetimes but the same evaporation rate. There are various possibilities to plot the data obtained from
single droplet drying experiments. Figure 5.11 shows plots of the decrease in radius, mean ferret
diameter, squared radius, squared mean ferret diameter, volume and surface of an evaporating water
droplet with time. The plots of the squared radius, squared diameter or surface with time each yields
an approximate straight line. On differentiating Equation 2.53, the change of droplet radius with
time dt
drS / is obtained as dr / dt −(
β / 2r
)
S
= . For constant evaporation coefficient β r the
r
S
change of radius per time drS / dt depends only on the momentary radius r S . This explains the
influence of the initial droplet size on the plots shown in Figure 5.11. If the d 2- law describes the
evaporation process with sufficient accuracy, the influence of different initial sizes can be
eliminated by dividing Equation 2.53 by the initial radius r S 0 . The evaporation process is then
described by
semi-confocal
flat-flat
0 20 40 60 80 100 120 140
Time [sec]
Vertical distance form initial point [µm]
600
400
200
0
-200
-400
-600
(b)
semi-confocal
flat-flat
0 20 40 60 80 100 120 140
Time [sec]

104 RESULTS AND DISCUSSION
2
rS
t
Equation 5.4 = 1 − β
2
r ⋅ 2
r
r
S 0
S 0
The evaporation coefficient β r depends on the thermodynamic properties of the droplet liquid and
on drying air temperature and relative humidity [Frohn 2000]. Figure 5.12 shows two plots of the
data from Figure 5.11 according to Equation 5.4.
Droplet radius [µm]
Mean Ferret diameter [µm]
Droplet volume [µl]
800
700
600
500
400
300
200
100
1600
1400
1200
1000
800
600
400
200
0
0 200 400 600 800 1000 1200 1400
Evaporation time [s]
V 0 = 2.014 µl
V 0 = 1.618 µl
V 0 = 1.153 µl
0
0 200 400 600 800 1000 1200 1400
2.0
1.5
1.0
0.5
Evaporation time [s]
V 0 = 2.014 µl
V 0 = 1.618 µl
V 0 = 1.153 µl
0.0
0 200 400 600 800 1000 1200 1400
Evaporation time [s]
V 0 = 2.014 µl
V 0 = 1.618 µl
V 0 = 1.153 µl
0.0
0 200 400 600 800 1000 1200 1400
Figure 5.11: Different diagrams of droplet size as a function of evaporation time. The droplets had different initial
droplet radii and were levitated at a temperature of 25.0°C and relative humidity of 3.0%. The initial effective SPL was
163.5 dB for the droplet with V0= 2.014 µl.
Squared radius [mm 2 ]
Squared mean Ferret diameter [mm 2 ]
Droplet surface [mm 2 ]
0.7
0.6
0.5
0.4
0.3
0.2
0.1
2.5
2.0
1.5
1.0
0.5
Evaporation time [s]
V 0 = 2.014 µl
V 0 = 1.618 µl
V 0 = 1.153 µl
0.0
0 200 400 600 800 1000 1200 1400
8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.0
Evaporation time [s]
V 0 = 2.014 µl
V 0 = 1.618 µl
V 0 = 1.153 µl
0.0
0 200 400 600 800 1000 1200 1400
Evaporation time [s]
V 0 = 2.104 µl
V 0 = 1.618 µl
V 0 = 1.153 µl

CHAPTER 5 RESULTS AND DISCUSSION 105
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
0.0
0 200 400 600 800 1000 1200 1400
(a)
Figure 5.12: (a) (rS 2 / rS 0 2 ) as a fuction of evaporation time. (b) (rS 2 / rS 0 2 ) as a function of (t / rS 0 2 ). The water
droplets with different initial volume were levitated in an acoustic levitator at 25.0°C and a relative humidity of 3.0%.
The initial effective SPL was 163.5 dB for the droplet with V0= 2.014 µl.
The plots of
2
rS rS
0
2 / as a function of time, t , (Figure 5.12 a) result in approximate straight lines
from unity independent of the initial droplet size. From a linear regression for each measurement
the slope
β / of the curves was obtained. If
2
r rS 0
Evaporation time [s]
V 0 = 2.014 µl
V 0 = 1.618 µl
V 0 = 1.153 µl
2
rS rS
0
0.0
0 500 1000 1500 2000 2500
2 / is now plotted against the
2
t rS
0
/ (Figure
5.12 b) the negative slope directly represents the evaporation coefficient β r [Frohn 2000]. Small
differences between the measurements may be caused by slightly differing air conditions or
differing internal oscillation of droplets [Rensink 2004]. The evaporation coefficient β r
characterizes the evaporation process for a given pure solvent droplet under conditions valid for the
d 2 -law [Frohn 2000].
The acoustically levitated droplets of pure liquids can be described as oblate ellipsoid. Thus,
a direct determination of the droplet radius was not possible. Three possible techniques to obtain the
radius from the measured data are available. First, by calculating the radius of a volume equivalent
sphere using Equation 5.1. Secondly, by calculating the radius of a surface equivalent sphere
according to Equation 5.2. Thirdly, by direct determination of the mean ferret radius of the levitated
droplet using the imaging software. A comparison of the plots for all three radii is shown in Figure
5.13.
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
(b)
2 2
( t / r ) [s/mm ]
S 0
V 0 = 2.014 µl
V 0 = 1.618 µl
V 0 = 1.153 µl

106 RESULTS AND DISCUSSION
2 ) [-]
2 / rS 0
( r S
Figure 5.13: Plot of the evaporation experiment and the evaporation coefficient of a levitated water droplet at a
temperature of 25.0°C and a relative humidity of 3.0%. The radius was calculated of a surface equivalent sphere,
volume equivalent sphere or the mean ferret diameter. The initial droplet volume was 2.014µl at an initial effective SPL
of 163.5 dB.
There is a close match of the evaporation coefficients calculated from the radius of a volume
2
equivalent sphere ( β = 0.
000501mm
/s ) and the radius of a surface equivalent sphere
r
2
( β = 0.
000505mm
/s).
The evaporation coefficient calculated from the directly determined mean
r
1.0
0.8
0.6
0.4
0.2
0.0
0 500 1000 1500 2000 2500
(a)
2
ferret diameter differs with β = 0.
000470 mm /s . This is caused by fluctuations in the horizontal
r
and vertical diameters due to internal oscillation of the levitated droplet. The determination of the
mean ferret diameter always leads to a larger radius than the other two methods, except for the case
of a purely spherical droplet. A comparison between radii calculated by volume or surface always
leads to almost identical results. Since large SPL leads to inaccuracy determining the actual volume
of the droplet using Equation 5.1 (Figure 5.5) the data of all the following experiments were
calculated using the radius of a surface equivalent sphere.
Different droplet liquids
Surface equivalent sphere
Volume equivalent sphere
Radius of the mean ferret diameter
2 2
( t / r ) [s/mm ]
S 0
Different liquids have different vapour pressures, resulting in different evaporation coefficients β r
under the same drying conditions [Frohn 2000]. Figure 5.14 shows the results for the evaporation of
levitated water, hexane and ethanol droplets. The different behaviour of the three solvents is clearly
shown by a different evaporation rate under the same drying conditions. The shortest drying time
2
and largest evaporation coefficient β = 0.
008329 mm /s at 25.0°C and 3.0% relative humidity is
r
Evaporation coefficient β r [mm 2 /s]
0.00051
0.00050
0.00049
0.00048
0.00047
for hexane, whose vapour pressure at this temperature is p = 18891.
8 Pa [EngineeringToolBox
2005]. The evaporation coefficient of the ethanol droplet with a vapour pressure of
(b)
vap
surface volume ferret
Type of calculated droplet radius

CHAPTER 5 RESULTS AND DISCUSSION 107
2
p = 7208.
7 Pa under the same ambient conditions is β = 0.
002136mm
/s . The flattened course
vap
of the ethanol plot near the end of the experiment results from condensation of water vapour from
the drying air onto the droplet surface. This effect and its influence on the evaporation of ethanol
droplets will be discussed in detail later. The longest evaporation time and also the smallest
2
evaporation coefficient is found for the drying of the water droplet, with β = 0.
000505mm
/s . The
water vapour pressure at 25.0°C temperature is p = 3174.
5 Pa [EngineeringToolBox 2005].
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
0.0
0 500 1000 1500 2000 2500
vap
Figure 5.14: Variation of (rs 2 /rS 0 2 ) with (t/rS 0 2 ) for three droplets, consisting of water, ethanol and hexane levitated at a
temperature of 25.0°C and a relative humidity of 3.0%. The initial effective SPL was 163.5dB for the water droplet,
162.3dB for ethanol and 160.5dB for hexane.
Multicomponent droplets
2 2
( t / r ) [s/mm ]
S 0
Water
Ethanol
Hexane
Evaporation coefficient β r
Droplets consisting of a mixture of two or more pure solvents are used in many technical
applications, especially in combustion processes. Experimental investigations of the evaporation
and combustion of droplets of binary mixtures have been performed by Law [1982], Yang et al.
[1989] and using the method of acoustic levitation by Yarin et al. [2002 b]. In all studies it was
found that the evaporation coefficient β r changed with time under constant drying conditions.
Figure 5.15 shows the result of evaporation of a levitated droplet consisting of a binary mixture of
water and ethanol at 30°C and 0.1% relative humidity.
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0.000
r
r
water ethanol hexane
Solvent

108 RESULTS AND DISCUSSION
Figure 5.15: Variation of (rS 2 /rS 0 2 ) with (t/rS 0 2 ) for three different droplets, consisting of pure water, pure ethanol and a
mixture of both. The experiments were carried out at 30.0°C and a relative humidity of 0.1% to prevent water vapour
condensation at the droplet surface. The initial effective SPL was 163.5 dB for water, 162.3 dB for ethanol and
161.8 dB for the mixture.
2 2
2
The plot shows the evolution of ( r / r ) as a function of ( t / r )
S
S 0
S 0
during the evaporation process.
For pure water and ethanol droplets, a linear behaviour is obtained according to the d 2 -law. For the
mixture of these solvents a non-linear behaviour is observed. The slope of the curve changes with
time. Initially, the momentary β r lies in between the values found for the pure liquids, but more on
the side of the more volatile solvent. Towards the end of the evaporation process the slope has
become approximately the same as that for the less volatile liquid. The same observations were
found for mixtures of pentadecane and hexadecane in optically levitated droplet [Frohn 2000], and
for mixtures of methanol and water in acoustically levitated droplets [Kastner 2001].
The differences between pure solvent and mixtures of binary liquids can be well illustrated
from a plot of the rate of size change as a function of time according to
Equation 5.5
( r S
1.0
0.8
0.6
0.4
drS
β r = −
dt 2r
S
Figure 5.16 presents the data for water, ethanol and the binary mixture plotted using Equation 5.5.
Initially, the evaporation rate of the mixture droplet is closer to that of the more volatile pure
solvent. Towards the end of the evaporation process drS /dt converged towards, but does not reach,
the values of the less volatile liquid.
2 ) [-]
2 / rS 0
mainly ethanol
evaporation
0.2
0.0
mainly water
evaporation
0 500 1000 1500 2000 2500
2 2
( t / r ) [s/mm ]
S 0
Pure water
Ethanol 60% (V/V)
Pure ethanol

CHAPTER 5 RESULTS AND DISCUSSION 109
dr S / dt [mm/s]
0.000
-0.001
-0.002
-0.003
Figure 5.16: Size change rate as function of time for pure water and ethanol droplets and droplets consisting of binary
mixture of both substances. The droplets were levitated at a temperature of 30.0°C and 0.1// relative humidity. The
initial effective SPL was 163.5dB for the waterdroplet, 162.3dB for the ethanol droplet and 161.8dB for the mixture
droplet.
5.2.2 Evaporation of pure water droplets
-0.004
Pure water
Ethanol 60% (V/V)
-0.005
Pure ethanol
0 200 400 600 800 1000
Evaporation time [s]
Water in its pure form is the most universal solvent in spray-drying [Masters 2002]. It has a surface
−6
2
tension of 72 . 75mN/m
and a kinematic viscosity of 1.
004 ⋅ 10 m /s at 20°C
[EngineeringToolBox 2005]. Its single molecules are linked by hydrogen bonds to form a kind of
dynamic cluster structure. The size of these clusters depends on the temperature of the water itself.
At 0°C a cluster consists of about 300 molecules, at 100°C of about 20 molecules and at the critical
temperature of 374.1°C of one to two molecules [Bauer et al. 1999; Burger 1998]. The structural
composition can be seen in Figure 5.17.
Figure 5.17: Structural composition of water [Burger 1998].

110 RESULTS AND DISCUSSION
The average lifetime of the hydrogen bonds that determine the structural composition decreases
with increasing temperature. At room temperature the lifetime is about 10 -4 s. The short lifetime of
the hydrogen bonds combined with the thermal mobility of the molecules lead to a high velocity of
structural changes without loosing the basic composition principle [Bauer et al. 1999]. These
characteristics determine the solvent properties of water. The larger the concentration of
imperfections in the structural composition, the better is the potential to dissolve other substances.
This explains the high temperature dependence of the solvent properties of water.
Calculation of limits of the levitation range for water droplets
Samples with a diameter d ≥ 2 / 3⋅
λ0
cannot be levitated within the standing acoustic wave of an
S
ultrasonic levitator, because the SPL decreases with increasing droplet size [Lierke 1996]. The
maximum levitation size of liquid samples is also dependent on the surface tension and the density
of the liquid. Experiments performed by Lierke showed that droplets with an acoustic Bond
Number ≥ 1.5 cannot be levitated. This Bond number is independent of the ultrasonic frequency,
which means that these figures are absolute values [Tec5 2002]. It is calculated by Tuckermann
[Tuckermann 2002] that
Equation 5.6 ( Bo)
acoustic
ρ
=
liquid
2
⋅ vˆ
⋅ d
8⋅
γ
max S
The minimum diameter of a levitated sample depends on the frequency of the ultrasonic levitator
and on the viscosity of the surrounding gas [Tuckermann 2002]. For water droplets the minimum
and maximum droplet sizes at 20°C are calculated according to Equation 5.6 and are shown in
Table 5.1.
Table 5.1: Overview of the minimum and maximum diameter and volume of levitated water droplets for
(Bo)acoustic = 1.5 in an 58 kHz acoustic levitator.
Liquid
Surface
tension γ
[ ]
Density
ρ liquid
3
mN/m [ ]
Maximum
diameter
Maximum
volume
Minimum
diameter
Minimum
volume
g/cm [ mm ] [ µl ] [ µm ] [ µl ]
Water 72.75 0.9982 6.67 155.37 15µm 1.77⋅10 -6

CHAPTER 5 RESULTS AND DISCUSSION 111
The optimal diameter for a stable water droplet in an acoustic levitator is determined according to
Lierke [1996], using:
d S opt
Equation 5.7 ( )
c0
=
3⋅
f
At a temperature of 20°C with a sound velocity of 343 m/s, the optimal stable droplet diameter in a
58 kHz levitator is ( ) = 1.
97 mm
d , corresponding to a volume of 4.01 µl.
S
opt
Levitation of water droplets
The evaporation of a pure water droplet is performed in the acoustic levitator at 25°C and a relative
humidity of 3.0% without forced air. The data is plotted in Figure 5.18 a. Figure 5.18 b shows the
course of the effective sound pressure level calculated using the method of Yarin et al. [1998],
together with droplet volume.
2 ) [-]
2 / rS 0
( r S
2 2 1.0 ( r / rS )
S 0
volume
0.8
0.6
0.4
0.2
0.0
0 250 500 750 1000 1250
(a)
Evaporation time [s]
2.5
2.0
1.5
1.0
0.5
0.0
Droplet volume [µl]
0.0
0 250 500 750 1000 1250
Figure 5.18: Evaporation of a pure water droplet at 25°C and 3.0% relative humidity at an initial effective SPL of
163.25 dB.(a) Size and volume change of the droplet versus time. (b) Influence of the volume change on the course of
the sound pressure level.
The decrease in droplet volume has a substantial influence on the development of the effective SPL
values. A decreasing droplet volume leads to increasing effective SPL due to a resonance shift
caused by changing reflections of the acoustic wave at the droplet surface [Kastner 2001]. The
theoretical evaporation curve for the diffusion-controlled evaporation of a single droplet with the
same initial size in still air, and wet bulb temperature calculated using Equation 2.69 shown in
Figure 5.19.
Droplet volume [µl]
2.5
2.0
1.5
1.0
0.5
(b)
Droplet volume
Effective SPL
Evaporation time [s]
166
165
164
163
Effective SPL [dB]

112 RESULTS AND DISCUSSION
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
0.0
0 500 1000 1500
(a)
Evaporation time [s]
Diffusion model
Experimental data
1.75
0 500 1000 1500
Figure 5.19: Comparison of the evaporation of a levitated droplet with the diffusion-controlled evaporation model
without convective influence at 25°C and 3.0%relative humidity. The droplet had an initial volume of 2.0 µl and the
initial effective SPL was 163.25 dB. (a) (rS 2 /rS 0 2 ) with evaporation time. (b) Comparison of the Shwerwood numbers.
The diffusion-controlled evaporation of a single droplet according to Equation 2.69 has a longer
(4.3 min) evaporation time than the experimental evaporation curve. The Sherwood number
calculated from the experimental data is 2.5, 0.5 larger than expected for diffusion-controlled
evaporation in still air [Masters 1991]. The reason for the increased Sherwood number can be
explained by influences of inner acoustic streaming. The continuity of shear stress at the surface
leads to extra loss of liquid from the droplet resulting in the observed increased mass transfer
[Rensink 2004; Yarin et al. 1999]. To account for inner acoustic streaming the data were calculated
again using Equation 3.40 and Equation 3.34. Figure 5.20 shows that the calculated evaporation
curve now yields a larger evaporation rate with shorter evaporation time than the experimental
evaporation curve. The Sherwood number is averaged to 4.9, which is about twice as large as the
Sherwood number of 2.5 for the experimental data determined only from the d 2 -law. The reason is
to be found in the outer acoustic streaming, in which solvent vapour of the evaporated droplet is
accumulated. This accumulation decreases heat and mass transfer from the outer streaming vortices
to the drying air and causes a decrease in evaporation rate and hence an increase in evaporation time
[Kastner 2001; Yarin et al. 1999]. This hindering effect can be overcome by using a forced drying
air stream [Rensink 2004]. The influence of different drying air flow velocities on the droplet
evaporation is therefore tested and compared to the calculated data.
Sherwood number
3.00
2.75
2.50
2.25
2.00
(b)
Evaporation time [s]
Diffusion model
Experimental data

CHAPTER 5 RESULTS AND DISCUSSION 113
S ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
0.0
0 250 500 750 1000 1250
(a)
Evaporation time [s]
Levitation model
Experimental data
Figure 5.20: Comparison between the evaporation model for levitated droplets with increased Sherwood numbers due
to the inner acoustic streaming and experimental data of a 2.0µl droplet in still air at 25°C and 3.0% relative humidity.
(a) (rS 2 /rS 0 2 )-course with evaporation time. (b) Comparison of the Sherwood numbers.
2.0 µl droplets of water are levitated at 25.0°C and 3.0% relative humidity and evaporated at
different velocities of the drying air stream. A comparison of the experimental results to the model
data calculated using Equation 3.40 and Equation 3.34 can be seen in Figure 5.21. A velocity of
0.41 m/s corresponding to an orifice Reynolds number of 100 (Figure 5.21 a) leads to an
evaporation time still larger than the calculated one. The water vapour is evidently not removed of
the system of vortices completely and accumulation still occurs. At an air stream of 0.82 m/s
(Figure 5.21 b) the experimental data matches almost exactly with the calculated curve. The water
vapour is removed completely from the outer streaming vortices without causing any additional
convective droplet drying. This result was also found by Rensink, who found a suitable drying air
stream of 1.0 m/s [Rensink 2004]. Higher drying air velocities cause a further decrease in the
evaporation time (Figure 5.21 c), resulting now from additional convective droplet drying due to the
forced air stream. The Sherwood number for experiments with drying air velocities lower than
1.0 m/s are well described by Equations 3.33 and Equation 3.34 (Figure 5.21 d). The Ranz-
Marshall-Equation 2.57 provides a better solution for calculation of the radius-time course of
levitated droplet at air velocities ≥ 1.0 m/s [Ranz 1952 a; Ranz 1952 b].
Sherwood number
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
(b)
0 250 500 750 1000 1250
Evaporation time [s]
Levitation model
Experimental data

114 RESULTS AND DISCUSSION
S ) [-]
2 / rS 0
( r S
S ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
0.0
(a)
1.0
0.8
0.6
0.4
0.2
Levitation model
ν air = 0.41 m/s (Re orifice = 100)
0 250 500 750 1000
Evaporation time [s]
0.0
0 250 500 750 1000
(c)
Evaporation model
ν air = 1.23 m/s (Re orifice = 300)
Evaporation time [s]
0.0
0 250 500 750 1000
Figure 5.21: Comparison of the model data with increased Sherwood numbers with the evaporation results of levitated
water droplets at 25°C, 3.0% relative humidity and different ventilation air stream velocities. (a) (rS 2 /rS 0 2 )-evaporation
time course for a levitated droplet with a ventilation of νair = 0.41 m/s, corresponding to an orifice Reynolds number of
100. (b) (rS 2 /rS 0 2 )-evaporation time course for a levitated 2.0 µl droplet with a ventilation of νair = 0.82 m/s,
corresponding to an orifice Reynolds number of 200. (c) (rS 2 /rS 0 2 )-evaporation time course for a levitated 2.0 µl droplet
with a ventilation of νair = 1.23 m/s, corresponding to an orifice Reynolds number of 300. (d) Comparison of the
Sherwood numbers with time between model and experiment at Reorifice = 200.
Figure 5.22 compares Equation 2.57 with the experimental data at 25.0°C, 3.0% relative humidity
and different air velocities. The air velocity of 1.23 m/s corresponds to an orifice Reynolds number
of 300, and the velocity of 1.64 m/s to an orifice Reynolds number of 400. It can be seen that the
model of Equation 2.57 predicts the radius-time course and the Sherwood number almost exactly
for both data sets.
S ) [-]
2 / rS 0
( r S
Sherwood number
1.0
0.8
0.6
0.4
0.2
(b)
6.0
5.0
4.0
3.0
2.0
(d)
Levitation model
ν air = 0.82 m/s (Re orifice = 200)
Evaporation time [s]
Levitation model
ν air = 0.82 m/s (Re orifice = 200)
0 250 500 750 1000
Evaporation time [s]

CHAPTER 5 RESULTS AND DISCUSSION 115
S ) [-]
2 / rS 0
( r S
S ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
0.0
0 100 200 300 400 500 600 700
(a)
1.0
0.8
0.6
0.4
0.2
Evaporation model Ranz-Marshall
Experiment ν air = 1.23 m/s
Evaporation time [s]
0.0
0 100 200 300 400 500 600 700
(a)
Evaporation model Ranz-Marshall
Experiment ν air = 1.639 m/s
Evaporation time [s]
0 100 200 300 400 500 600 700
Figure 5.22: Comparison of the Ranz-Marshall correlation with experimental data from levitation experiments at 25°C,
3.0% relative humidity and different ventilation air stream velocities. The initial effective SPL for both data sets was
163.5 dB. (a) (rS 2 /rS 0 2 ) with evaporation time for a 1.51 µl droplet at νair = 1.23 m/s (Reorifice = 300). (b) Comparison of
the Sherwood numbers of the experimental data in (a). (c) (rS 2 /rS 0 2 ) with evaporation time for a 1.64 µl droplet at
νair = 1.64 m/s (Reorifice = 400). (d) Comparison of the Sherwood numbers of the experimental data in (c).
The following experimental results with water droplets at various temperatures were compared to
the three different evaporation models outlined above:
- evaporation model for diffusion-controlled evaporation without any convective influence
(Equation 2.69);
- evaporation model (levitation model) including influence of the inner acoustic streaming
(Equation 3.40 and Equation 3.34);
- evaporation model at high drying air velocities using the Ranz-Marshall correlation
(Equation 2.57).
The results at 40°C are given in Figure 5.23, and the results at 60°C in Figure 5.24.
Sherwood number
Sherwood number
10.0
8.0
6.0
4.0
2.0
(b)
10.0
8.0
6.0
4.0
2.0
(d)
Evaporation model Ranz-Marshall
Experiment ν air = 1.23 m/s
Evaporation time [s]
Evaporation model Ranz-Marshall
Experiment ν air =1.639 m/s
0 100 200 300 400 500 600 700
Evaporation time [s]

116 RESULTS AND DISCUSSION
2 ) [-]
2 / rS 0
( r S
2 ) [-]
2 / rS 0
( r S
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
0.0
0 200 400 600 800 1000
(a)
1.0
0.8
0.6
0.4
0.2
0.0
0 200 400 600 800
(c)
1.0
0.8
0.6
0.4
0.2
Levitation model at 40°C
Experimental data ν air = 0.00 m/s
Evaporation time [s]
0.0
0 200 400 600 800
(a)
Diffusion-controlled evaporation
Experiment in still air at 40.0°C
Evaporation time [s]
Levitation model at 40°C
Experimental data ν air = 0.88 m/s
(Re orifice = 200)
Evaporation time [s]
0 200 400 600 800
Figure 5.23: Comparison of the evaporation models with experimental data from levitated water droplets at 40°C and
0.1% relative humidity. The initial droplet volume of all experiments was 2.0 µl at an initial effective SPL of 166.0 dB.
(a) Comparison of the diffusion-controlled evaporation model with experimental data in still air. (b) Comparison of the
Sherwood numbers of the diffusion-controlled evaporation model and experiments in air. (c) Comparison of the
levitation model with experimental data in still air. (d) Comparison of the Sherwood numbers of the levitation model
with experiments in still air. (e) Comparison of the levitation model with experimental data at a ventilation velocity of
0.88 m/s. (f) Comparison of the Sherwood number of the levitation model with experimental data at a ventilation
velocity of 0.88 m/s.
Sherwood number
Sherwood number
Sherwood number
10
8
6
4
2
0 200 400 600 800
(b)
10.0
8.0
6.0
4.0
2.0
(d)
10.0
8.0
6.0
4.0
Leviation model at 40°C
Experimental data ν air = 0.00 m/s
Evaporation time [s]
2.0
(Re = 200)
orifice
0 200 400 600 800
(f)
Diffusion-controlled evaporation
Experimental data ν air = 0.00 m/s
Evaporation time [s]
Levitation model at 40°C
Experimental data ν air = 0.88 m/s
Evaporation time [s]

CHAPTER 5 RESULTS AND DISCUSSION 117
2 ) [-]
2 / rS 0
( r S
2 ) [-]
2 / rS 0
( r S
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
0.0
0 100 200 300
(a)
1.0
0.8
0.6
0.4
0.2
Diffusion-controlled evaporation
Experimental data ν air = 0.00 m/s
Evaporation time [s]
0.0
0 100 200 300
(c)
1.0
0.8
0.6
0.4
0.2
Levitation model at 60°C
Experimental data ν air = 0.00 m/s
Evaporation time [s]
0.0
0 100 200 300
(e)
Levitation model at 60°C
Experimental data ν air = 1.0m/s
(Re orifice = 200)
Evaporation time [s]
0 100 200 300
Figure 5.24: Comparison of the evaporation models with experimental data from levitated water droplets at 60°C and
0.1% relative humidity. The initial droplet volume of all experiments was 1.0 µl at an initial effective SPL of 167.0 dB.
(a) Comparison of the diffusion-controlled evaporation model with experimental data in still air. (b) Comparison of the
Sherwood numbers of the diffusion-controlled evaporation model with experimental data in air. (c) Comparison of the
levitation model with experimental data in still air. (d) Comparison of the Sherwood numbers of the levitation model
with experimental data in still air. (e) Comparison of the levitation model with experimental data at a ventilation
velocity of 1.0 m/s. (f) Comparison of the Sherwood number of the levitation model with experimental data at a
ventilation velocity of 1.0 m/s.
Sherwood number
Sherwood number
Sherwood number
10.0
8.0
6.0
4.0
2.0
(b)
10.0
8.0
6.0
4.0
2.0
10.0
8.0
6.0
4.0
(d)
Diffusion-controlled evaporation
Experimental data ν air = 0.00 m/s
Evaporation time [s]
Levitation model at 60°C
Experimental data ν air = 0.00 m/s
0 100 200 300
Evaporation time [s]
2.0
(Re = 200)
orifice
0 100 200 300
(f)
Levitation model at 60°C
Experimental data ν air = 1.0 m/s
Evaporation time [s]

118 RESULTS AND DISCUSSION
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
0.0
0 200 400 600 800
(a)
Ranz-Marshall correlation
Experiment ν air = 1.77 m/s
(Re orifice = 400)
Evaporation time [s]
2.0
(Re = 400)
orifice
0 200 400 600 800
Figure 5.25: Comparison of the Ranz-Marshall correlation with experimental data from levitation experiments at 40°C,
0.1% relative humidity and a ventilation velocity of 1.77 m/s (Reorifice = 400). The initial effective SPL was 166.0 dB
and the initial droplet volume was 1.7 µl. (a) (rS 2 /rS 0 2 ) with evaporation time. (b) Comparison of the Sherwood numbers
of the Ranz-Marshall correlation with experimental data.
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
0.0
0 50 100 150 200 250 300
(a)
Evaporation Ranz-Marshall
Experiment ν air = 1.98 m/s
(Re orifice = 400)
Evaporation time [s]
Figure 5.26: Comparison of the Ranz-Marshall correlation with experimental data from levitation experiments at 60°C,
0.1% relative humidity and a ventilation velocities of 1.98 m/s (Reorifice = 400). The initial effective SPL was 166.8 dB
and the initial droplet volume was 1.7 µl. (a) (rS 2 /rS 0 2 ) with evaporation time. (b) Comparison of the Sherwood numbers
of the Ranz-Marshall correlation with experimental data.
Figure 5.23 presents that the levitation experiments for water droplets at 40°C and 0.1% relative
humidity show agreement with the levitation model, as also observed in Figure 5.21 for the
experiments at 25°C and 3.0% relative humidity. The comparison between the Ranz-Marshall
correlation and the experimental data at a drying velocity of 1.77 m/s in Figure 5.25 shows,
however, a larger difference in the later times of droplet evaporation. This is caused by differing
values of the Sherwood number within the later part. According to the Ranz-Marshall correlation
Sherwood number
Sherwood number
10.0
8.0
6.0
4.0
18.0
16.0
14.0
12.0
10.0
(b)
8.0
6.0
4.0
Ranz-Marshall correlation
Experiment ν air = 1.77 m/s
Evaporation time [s]
2.0
0 50 100 150 200 250 300
(b)
Evaporation Ranz-Marshall
Experiment ν air = 1.98 m/s
(Re orifice = 400)
Evaporation time [s]

CHAPTER 5 RESULTS AND DISCUSSION 119
the Sherwood number decreases to values under 6.0 with decreasing droplet diameter Figure 5.25 b.
The Sherwood number does not, however, decrease under 6.0 during the whole experiment, due to
the influence of the inner acoustic streaming. Figure 5.23f shows that the Sherwood number will be
> 6.0 at all times for this combination of initial droplet diameter and effective SPL.
The experiments performed at 60°C with a drying air velocity up to 0.99 m/s could be
described almost exactly with the levitation model (Figure 5.24 e). At velocities larger than 1.0 m/s
the experimental results do not match with the Ranz-Marshall correlation (Figure 5.26 a). The
experimental data at 1.98 m/s show a higher evaporation rate and smaller evaporation time than
predicted by the model. A comparison of the Sherwood numbers of the levitation model and the
Ranz-Marshall correlation shows that these are similar (Figure 5.24 f and Figure 5.26 b). The
Sherwood number according to the levitation model is on average about 7.5. The increase in drying
air velocity from 1.0 m/s to 1.98 m/s does not correlate with an adequate increase in Sherwood
number calculated via the Ranz-Marshall correlation. Consequently the experiments at 60°C, 0.1%
relative humidity and a drying air velocity > 1.0 m/s cannot be described using the Ranz-Marshall
correlation.
An explanation for the discrepancy between the Ranz-Marshall model and experimental data
at 60°C and 0.1% relative humidity may be the unstable droplet position within the standing
acoustic wave. In almost dry air and at velocities of about 2.0 m/s very strong oscillation of the
droplet occurred. Rensink [2004] showed that oscillations of the droplet in relation to its
environment as well as internal oscillations of the droplet surface itself can lead to an increase in the
Reynolds number and therefore also to an increase in the evaporation rate. At higher relative
humidity of the drying air at 60°C both kinds of droplet oscillations decreased visibly, which led to
a better correlation between the experimental data and the predictions of the radius-time course by
the Ranz-Marshall correlation (Figure 5.27).

120 RESULTS AND DISCUSSION
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
0.0
0 100 200 300 400
(a)
Ranz-Marshall correlation
at 60°C and 40% rel. humidity
Experimental data ν air = 2.04 m/s
Evaporation time [s]
2.0
0 100 200 300 400
Figure 5.27: Comparison of the Ranz-Marshall correlation with experimental data from levitation experiments at 60°C,
40% relative humidity and a ventilation velocity of 2.04 m/s (Reorifice = 400). The initial effective SPL was 166.8 dB and
the initial droplet volume was 1.7 µl. (a) (rS 2 /rS 0 2 ) with evaporation time. (b) Comparison of the Sherwood numbers of
the Ranz-Marshall correlation with experimental data.
The calculation of a single evaporation coefficient describing the whole radius-time course of
droplet evaporation is thus not possible because of the influence of both inner acoustic streaming
and drying air velocity on the Sherwood number. As already discussed, the relation between the
volume of a levitated droplet and the effective SPL determines indirectly the Sherwood number via
Equation 3.33 and Equation 3.34. If each experiment starts with the same droplet volume at the
same effective SPL, a range can be chosen in which the evaporation coefficient can be calculated
for differing drying conditions. Droplets with an initial volume of 1.5 µl were levitated at the
pressure node of the standing acoustic wave at an initial effective SPL of 165.5 dB. The influences
of temperature, humidity and drying air velocity on the evaporation coefficient, as well as a
correlation to the different models were investigated. Typical raw data of these droplet drying
experiments at different temperature and humidity without any drying air stream are shown in
Figure 5.28. The evaporation coefficients were calculated in the range between 1.0 µl and 0.5 µl of
droplet volume from the d 2 -law using Equation 5.4. The influence of temperature and humidity can
clearly be seen.
Sherwood number
10.0
8.0
6.0
4.0
(b)
Ranz-Marshall correlation
at 60°C and 40% rel. humidity
Experimental data ν air = 2.04 m/s
Evaporation time [s]

CHAPTER 5 RESULTS AND DISCUSSION 121
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
0.0
0 500 1000 1500 2000 2500
Figure 5.28: Raw data of evaporation experiments at different temperatures and relative humidity of the drying air. The
initial effective SPL was 165.5 dB and the initial droplet volume was 1.5 µl. All experiments were performed without
ventilation air stream. (a) (rS 2 / rS 0 2 ) with (t / rS 0 2 ) at different temperatures and 0.1% relative humidity of the drying air.
(b) (rS 2 / rS 0 2 ) with (t / rS 0 2 ) at 60°C and different humidity of the drying air.
Evaporation coefficient β r [mm 2 /s]
(a)
0.0030
0.0025
0.0020
0.0015
0.0010
0.0005
2 2
( t / r ) [s/mm ]
S 0
25°C
40°C
50°C
60°C
70°C
0.0000
20 30 40 50 60 70
(a)
Rel. humidity 0.1%
Rel. humidity 20%
Rel. humidity 40%
Rel. humidity 60%
Rel. humidity 80%
Drying temperature [°C]
0 1000 2000 3000 4000 5000 6000
Figure 5.29: Influence of temperature and relative humidity of the drying air on the evaporation coefficient of levitated
water droplets inside an acoustic levitator. The evaporation coefficients were determined between 1.0 µl and 0.5 µl of
the droplet volume. The initial effective SPL for all experiments used in this comparison was 165.5 dB and the initial
droplet volume was 1.5 µl. (a) evaporation coefficients with drying temperature at different humidity. (b) Evaporation
coefficients with the relative humidity of the drying air at different temperature.
To compare the various experiments performed at differing drying velocity, the influence of
changing diameter on the Reynolds and Sherwood numbers has to be taken into account. In these
experiments the evaporation coefficient was determined at droplet diameter between 1200 µm and
800 µm. The influences of temperature, humidity and drying air velocity on the evaporation rate of
levitated water droplets are determined starting with an initial volume of 2.0 µl and at an initial
effective SPL of 165.5 dB. Representative raw data as well as evaporation coefficient are plotted in
Figure 5.30 and Figure 5.31.
2 ) [-]
2 / rS 0
( r S
Evaporation coefficient β r [mm 2 /s]
1.0
0.8
0.6
0.4
0.2
0.0
(b)
0.0030
0.0025
0.0020
0.0015
0.0010
0.0005
0.0000
(b)
Drying temperature 60°C
Rel. humidity 0.1%
Rel. humidity 20%
Rel. humidity 40%
Rel. humidity 60%
Rel. humidity 80%
2 2
( t / r ) [s/mm ]
S 0
0 20 40 60 80
Relative humidity of drying air [%]
25°C
40°C
50°C
60°C
70°C

122 RESULTS AND DISCUSSION
2 ) [-]
2 / rS 0
( r S
Figure 5.30: Typical raw data of evaporation experiments at different temperatures and drying air velocity of the drying
air. The initial effective SPL was 165.5 dB and the initial droplet volume was 2.0 µl. All experiments were performed at
a relative humidity of 0.1%. (a) (rS 2 / rS 0 2 ) with (t / rS 0 2 ) at different ventilation velocities at a temperature of 40° of the
drying air. (b) (rS 2 / rS 0 2 ) with (t / rS 0 2 ) at different temperatures with a ventilation velocity corresponding to an orifice
Reynolds number of 400.
Evaporation coefficient β r [mm 2 /s]
1.0
0.8
0.6
0.4
0.2
0.0
0 200 400 600 800 1000 1200 1400
(a)
0.006
0.005
0.004
0.003
0.002
0.001
(a)
25°C
40°C
60°C
T∞ = 40°C; rel. humidity 0.1%
Ventilation ν air = 0.00 m/s
Ventilation ν air = 0.88 m/s
Ventilation ν air = 1.77 m/s
Ventilation ν air = 2.65 m/s
2 2
( t / r ) [s/mm ]
S 0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ventilation velocity ν air [m/s]
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Figure 5.31: Influence of temperature and relative humidity of the drying air on the evaporation coefficient of levitated
water droplets inside an acoustic levitator at different ventilation velocities. The evaporation coefficients were
determined between 1200 µm and 800 µm of the droplet diameter. The initial effective SPL for all experiments used in
this comparison was 165.5 dB and the initial droplet volume was 2.0 µl. (a) evaporation coefficients with ventilation
velocity at different drying temperature and 0.1% relative humidity. (b) Evaporation coefficients with ventilation
velocity at 60.0°C and different relative humidity.
An increase in drying air velocity or an increase in temperature or a decrease in relative humidity of
the drying air lead to an increase in the evaporation coefficient β r . The largest jump of the values
of the evaporation coefficient is seen between the experiments at 0.0 m/s and 0.88 m/s ventilation
velocity. This shows clearly the effect of the accumulation of water vapour in the toroidal vortices
of the outer acoustic streaming and its influence on the evaporation time of a single levitated
droplet.
2 ) [-]
2 / rS 0
Evaporation coefficient β r [mm 2 /s]
( r S
1.0
0.8
0.6
0.4
0.2
0.0
0 200 400 600 800
(b)
0.006
0.005
0.004
0.003
0.002
0.001
(b)
2 2
( t / r ) [s/mm ]
S 0
Drying temperature 60°C
Rel. humidity 0.1%
Rel. humidity 20%
Rel. humidity 40%
Re orifice = 400; rel. humidity 0.1%
25°C; ν air = 1.67 m/s
40°C; ν air = 1.77 m/s
60°C; ν air = 1.98 m/s
Vemtilation velocity ν air [m/s]

CHAPTER 5 RESULTS AND DISCUSSION 123
A comparison between the data from droplet experiments with drying air velocity larger than about
0.8 m/s and the Ranz-Marshall correlation for the Sherwood number is given in Figure 5.33. The
results at 25°C with a relative humidity of 0.1% (Figure 5.33 a) show a close match to the predicted
values calculated from the Ranz-Marshall equation for all tested ventilation velocities. The results
of the experiments at 60°C and 0.1% relative humidity show, however, poor match to the Ranz-
Marshall equation, as already discussed above (result not shown). At a higher relative humidity of
the 60°C hot drying air (Figure 5.33 b), the experimental evaporation coefficients match quite
closely to the calculated ones using the Ranz-Marshall correlation. The droplets at 60°C and 40%
humidity are visibly more stable and do not oscillate in the ultrasonic field, accounting for the better
fit than at 0.1% relative humidity.
Evaporation coefficient β r [mm 2 /s]
0.0018
0.0016
0.0014
0.0012
Drying temperature 25°C
Rel. humidity 0.1%
0.0010
0.0008
Model Ranz-Marshall
Model acoustic levitation
Experimental data
0.8 1.2 1.6 2.0 2.4 2.8
(a)
Ventilation velocity ν air [m/s]
0.0020
0.0018
0.0016
0.0014
0.0012
1.0 1.2 1.4 1.6 1.8 2.0 2.2
Figure 5.32: Comparison of the evaporation coefficients of experimental data with the coefficients predicted using the
Ranz-Marshall correlation. The evaporation coefficients were determined between 1200 µm and 800 µm of the droplet
diameter. The initial effective SPL for all experiments used in this comparison was 165.5 dB and the initial droplet
volume was 2.0 µl. (a) evaporation coefficients with ventilation velocity at 25°C and 0.1% relative humidity.
(b) Evaporation coefficients with ventilation velocity at 60°C and 40% relative humidity.
Evaporation coefficient β r [mm 2 /s]
(b)
Drying temperature 60°C
Relative humidity 40%
Model Ranz-Marshall
Experimental data
Ventilation velocity ν air [m/s]

124 RESULTS AND DISCUSSION
5.2.3 Evaporation of pure ethanol droplets
Calculation of limits of the levitation range for ethanol droplets
The maximum droplet diameter for the levitation of ethanol droplets depends on the surface tension
and density of ethanol as well as on the effective SPL of the standing acoustic wave [Lierke 1996;
Tuckermann 2002]. The minimum diameter depends on the frequency of the levitator and the
viscosity of the surrounding gas [Tuckermann 2002]. Table 5.2 gives an overview of the size range
for ethanol droplets in a 58 kHz levitation system.
Table 5.2: Overview of the minimum and maximum diameters and volume of levitated ethanol droplets for
(Bo)acoustic = 1.5 in an 58 kHz acoustic levitator [EngineeringToolBox 2005; Tuckermann 2002].
Liquid
Surface
tension γ
[ mN/m ]
Density
ρ liquid
3
[ g/cm ]
Maximum
diameter
[ mm ]
Maximum
volume
[ µl ]
Minimum
diameter
[ µm ]
Minimum
volume
[ µl ]
Ethanol 22.3 0.785 4.21 39.03 15µm 1.77⋅10 -6
At a temperature of 20°C with a sound velocity of 343 m/s the optimal droplet diameter in a 58 kHz
levitator is ( ) = 1.
97 mm
d corresponding to a volume of 4.01µl, according to Equation 5.7. The
S
opt
−6
2
kinematic viscosity of ethanol at 20°C is 1.
52 ⋅ 10 m /s [EngineeringToolBox 2005].
Levitation of pure ethanol droplets
The evaporation of a pure ethanol droplet at 25.0°C and a relative humidity of 4.1% without
ventilation air stream is analysed here according to chapter 5.2.1 and is plotted in Figure 5.33 a. The
influence of the decreasing droplet volume on the effective sound pressure level of the standing
acoustic wave is shown in Figure 5.33 b calculated using the method of Yarin et al. [1998]. As with
water, a decrease in droplet volume leads to an increase of the effective SPL. The values of the SPL
for ethanol droplet volume are smaller than those for water droplets with the same volume. This
effect was also shown by Rensink [2004] and is caused by the different densities of the two liquid
solvents. The experimental data is first compared to the model for diffusion-controlled evaporation
of single ethanol droplet. The surface temperature of the model droplet with the same initial droplet
size is then calculated using Equation 3.41. The comparison between model and experiment can be
seen in Figure 5.34.

CHAPTER 5 RESULTS AND DISCUSSION 125
2 ) [-]
2 / rS 0
( r S
2 2
1.0 ( r / rS )
S 0
Droplet volume
0.8
0.6
0.4
0.2
0.0
0.0
0 100 200 300 400
(a)
Evaporation time [s]
2.5
2.0
1.5
1.0
0.5
Droplet volume [µl]
161
0.0
0 100 200 300 400
Figure 5.33: Evaporation of a pure ethanol droplet at 25°C and 4.1% relative humidity in still air. The initial volume of
the droplet was 2.2 µl at an initial effective SPL of 161.9 dB. (a) Change of size and volume with evaporation time. (b)
Influence of the volume on the effective SPL.
The diffusion-controlled evaporation of a single ethanol droplet calculated according to
Equation 2.89 has an approx. 2.2 minutes longer evaporation time than the experimental
determination of a levitated ethanol droplet with the same initial droplet size. The Sherwood
number calculated from the experimental data starts at 4.0 and decreases to 2.2 at the end of the
evaporation process. As seen with water, the Sherwood number increases with shear stress at the
droplet surface caused by the inner acoustic streaming [Rensink 2004; Yarin et al. 1999]. To
account for increased mass transfer via inner acoustic streaming, the evaporation rate and the
Sherwood number are calculated again using the levitation model of Equation 3.40 and
Equation 3.34. The results and the comparison with experimental data at 25°C and 4.7% relative
humidity are shown in Figure 5.35.
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
0.0
0 100 200 300 400
(a)
Diffusion-controlled model
Experimental data ν air = 0.0 m/s
Evaporation time [s]
Figure 5.34: Comparison of experimental ethanol data with the model for diffusion controlled evaporation of a single
droplet at 25°C and 4.7% relative humidity. The initial droplet volume was 1.3 µl at an initial effective SPL of
162.0 dB. (a) (rS 2 / rS 0 2 ) vs. evaporation time. (b) Comparison of the Sherwood numbers.
Effective SPL [dB]
2 ) [-]
2 / rS 0
( r S
165
164
163
162
(b)
5.0
4.0
3.0
2.0
(b)
Evaporation time [s]
Effective SPL
Droplet volume
2.5
2.0
1.5
1.0
0.5
Diffusion-controlled model
Experimental data ν air = 0.0 m/s
Droplet volume [µl]
0 100 200 300 400
Evaporation time [s]

126 RESULTS AND DISCUSSION
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
0.0
0 100 200 300 400
(a)
Levitation model at 25.0°C
Experimental data ν air = 0.0 m/s
Evaporation time [s]
0 100 200 300 400
Figure 5.35: Comparison of experimental data of a pure ethanol droplet with the levitation model for evaporation of a
single droplet at 25°C and 4.7% relative humidity with increased Sherwood number due to he inner acoustic streaming.
The initial droplet volume was 1.3 µl at an initial effective SPL of 162.0 dB. (a) (rS 2 / rS 0 2 ) with evaporation time. (b)
Comparison of the Sherwood numbers.
The levitation model predicts a faster evaporation than the experimentally measured one. The
accumulation of solvent vapour in the toroidal vortices caused by the outer acoustic streaming now
decreases the evaporation rate of the pure ethanol droplet. As seen with water this effect can be
overcome by introducing an axial ventilation air stream with a velocity of about 1.0 m/s. Figure
5.36 shows the comparison between the levitation model and experimental data at a ventilation
velocity of 0.83 m/s. At larger ventilation velocity the radius-time course of the evaporating ethanol
droplet can be modelled using the Ranz-Marshall correlation for the Sherwood number. A
comparison with experimental data at a velocity of 1.67 m/s corresponding to an orifice Reynolds
number of 400 can be found in Figure 5.37.
Sherwood number
8.0
6.0
4.0
2.0
(b)
Levitation model at 25.0°C
Experimental data ν air = 0.0 m/s
Evaporation time [s]

CHAPTER 5 RESULTS AND DISCUSSION 127
2 ) [-]
2 / rS 0
( r S
Figure 5.36: Comparison of the levitation model with experimental data of a pure ethanol droplet at a ventilation
velocity of 0.83 m/s, 25°C and 4.7% relative humidity. The initial droplet volume was 1.3 µl at an initial effective SPL
of 162.0 dB. (a) (rS 2 / rS 0 2 ) with evaporation time. (b) Comparison of the Sherwood numbers.
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
0.0
0 50 100 150
(a)
1.0
0.8
0.6
0.4
0.2
Ranz-Marshall correlation
Experimental data ν air = 1.67 m/s
(Re orifice = 400)
0.0
0 50 100 150 200
(a)
Levitation model at 25.0°C
Experimental data ν air = 0.83 m/s
Evaporation time [s]
Evaporation time [s]
2.0
(Re = 400)
orifice
0 50 100 150 200
Figure 5.37: Comparison of the Ranz-Marshall correlation with experimental data from a levitated ethanol droplet at a
ventilation velocity of 1.67 m/s, corresponding to an orifice Reynolds number of 400. The temperature of the drying air
was 25°C with a relative humidity of 0.1%. The initial droplet volume was 1.3 µl at an initial effective SPL of
162.0 dB. (a) (rS 2 / rS 0 2 ) with evaporation time. (b) Comparison of the Sherwood numbers.
The influence of elevated temperatures was now investigated using either the levitation model at
ventilation velocities of about 1.0 m/s or the Ranz-Marshall correlation at larger velocities. All
experimental comparisons were performed at 40°C (Figure 5.38) and 60°C (Figure 5.39) with a
relative humidity of 0.1%.
Sherwood number
Sherwood number
10.0
8.0
6.0
4.0
2.0
(b)
12.0
10.0
8.0
6.0
4.0
(b)
Levitation model at 25.0°C
Experimental data ν air = 0.83 m/s
0 50 100 150
Evaporation time [s]
Ranz-Marshall correlation
Experimental data ν air = 1.67 m/s
Evaporation time [s]

128 RESULTS AND DISCUSSION
2 ) [-]
2 / rS 0
( r S
2 ) [-]
2 / rS 0
( r S
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
0.0
0 50 100 150 200
(a)
1.0
0.8
0.6
0.4
0.2
Diffusion-controlled model
Experimental data ν air = 0.0 m/s
Evaporation time [s]
0.0
0 50 100 150 200
(c)
1.0
0.8
0.6
0.4
0.2
Levitation model at 40°C
Experimental data ν air = 0.0 m/s
Evaporation time [s]
0.0
0 50 100 150 200
(e)
Levitation model at 40°C
Experimental data ν air =0.88 m/s
(Re orifice = 200)
Evaporation time [s]
0 50 100 150 200
Figure 5.38: Comparison of diffusion model (a-b) and levitation model (c-f) with experimental data from levitated pure
ethanol droplets at 40°C and 0.1% relative humidity. The initial droplet volume of all experiments was 1.6 µl at an
initial effective SPL of 163.0 dB. (a) Comparison of the radius-time course of the diffusion-controlled evaporation
model with experimental data in still air. (b) Comparison of the Sherwood numbers of the diffusion-controlled model
with experimental data in still air. (c) Comparison of the radius-time course of the levitation model with experimental
data in still air. (d) Comparison of the Sherwood numbers of the levitation model with experimental data in still air. (e)
Comparison of the radius-time course of the levitation model with experimental data at a ventilation velocity of
0.88 m/s. (f) Comparison of the Sherwood numbers of the levitation model with experimental data at a ventilation
velocity of 0.88 m/s.
Sherwood number
Sherwood number
Sherwood number
10.0
8.0
6.0
4.0
2.0
(b)
10.0
8.0
6.0
4.0
2.0
(d)
10.0
8.0
6.0
4.0
Diffusion-controlled model
Experimental data ν air = 0.0 m/s
Evaporation time [s]
Levitation model at 40°C
Experimental data ν air = 0.0 m/s
0 50 100 150 200
Evaporation time [s]
2.0
(Re = 200)
orifice
0 50 100 150 200
(f)
Levitation model at 40°C
Experimental data ν air =0.88 m/s
Evporation time [s]

CHAPTER 5 RESULTS AND DISCUSSION 129
2 ) [-]
2 / rS 0
( r S
2 ) [-]
2 / rS 0
( r S
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
Diffusion-controlled model at 60°C
Experimental data ν air = 0.00 m/s
0.0
0 20 40 60 80 100 120
(a)
1.0
0.8
0.6
0.4
0.2
Evaporation time [s]
0.0
0 20 40 60 80 100 120
(c)
1.0
0.8
0.6
0.4
0.2
Levitation model at 60°C
Experimental data ν air = 0.00 m/s
Evaporation time [s]
0.0
0 20 40 60 80 100 120
(e)
Levitation model at 60°C
Experimental data ν air = 0.99 m/s
Re orifice = 200
Evaporation time [s]
0 20 40 60 80 100 120
Figure 5.39: Comparison of diffusion model (a-b) and levitation model (c-f) with experimental data from levitated pure
ethanol droplets at 60°C and 0.1% relative humidity. The initial droplet volume of all experiments was 1.5 µl at an
initial effective SPL of 163.25 dB. (a) Comparison of the radius-time course of the diffusion-controlled evaporation
model with experimental data in still air. (b) Comparison of the Sherwood numbers of the diffusion-controlled model
with experimental data in still air. (c) Comparison of the radius-time course of the levitation model with experimental
data in still air. (d) Comparison of the Sherwood numbers of the levitation model with experimental data in still air. (e)
Comparison of the radius-time course of the levitation model with experimental data at a ventilation velocity of
0.99 m/s. (f) Comparison of the Sherwood numbers of the levitation model with experimental data at a ventilation
velocity of 0.99 m/s.
Sherwood number
Sherwood number
Sherwood number [-]
10.0
8.0
6.0
4.0
2.0
(b)
10.0
8.0
6.0
4.0
2.0
(d)
10.0
8.0
6.0
4.0
Diffusion-controlled model at 60°C
Experimental data ν air = 0.00 m/s
Evaporation time [s]
Levitation model at 60°C
Experimental data ν air = 0.00 m/s
0 20 40 60 80 100 120
Evaporation time [s]
2.0
Re = 200
orifice
0 20 40 60 80 100 120
(f)
Levitation model at 60°C
Experimental data ν air = 0.99 m/s
Evaporation time [s]

130 RESULTS AND DISCUSSION
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
0.0
0 50 100 150
(a)
Ranz-Marshall correlation
Experimental data ν air = 1.77 m/s
(Re orifice = 400)
Evaporation time [s]
2.0
0 50 100 150
Figure 5.40: Comparison of the Ranz-Marshall correlation with experimental data from a levitated pure ethanol droplet
at 40°C and 0.1% humidity. The ventilation velocity υair was 1.77 m/s (Reorifice = 400). The initial droplet volume was
1.6 µl at an initial effective SPL of 163.0 dB. (a) (rS 2 / rS 0 2 ) vs. evaporation time of the Ranz-Marshall correlation and
experimental data at υair = 1.77 m/s (b) Comparison of the Sherwood numbers between the Ranz-Marshall correlation
and experimental data at υair = 1.77 m/s.
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
0.0
0 20 40 60 80 100
(a)
Ranz-Marshall model at 60°C
Experimental data ν air = 1.98 m/s
(Re orifice = 200)
Evaporation time [s]
Figure 5.41: Comparison of the Ranz-Marshall correlation with experimental data from a levitated pure ethanol droplet
at 60°C and 0.1% humidity. The ventilation velocity νair was 1.98 m/s (Reorifice = 400). The initial droplet volume was
1.3 µl at an initial effective SPL of 163.25 dB. (a) (rS 2 / rS 0 2 ) vs. evaporation time of the Ranz-Marshall correlation and
experimental data at νair = 1.98 m/s (b) Comparison of the Sherwood numbers between the Ranz-Marshall correlation
and experimental data at νair = 1.98 m/s.
By considering the effects of inner and outer acoustic streaming, the radius-time course of an
evaporating pure ethanol droplet at temperatures of 40°C and 60°C with a ventilation velocity of
approximately 1.0 m/s can be accurately described using Equation 3.40 and Equation 3.34 (Figure
5.38, Figure 5.39). At larger ventilation velocities the Ranz-Marshall correlation according to
Equation 2.57 provides a suitable model to predict the radius-time course in the first part of droplet
evaporation (Figure 5.40; Figure 5.41). With decreasing droplet size a difference between predicted
Sherwood number
Sherwood number
14.0
12.0
10.0
8.0
6.0
4.0
(b)
12.0
10.0
8.0
6.0
4.0
Ranz-Marshall correlation
Experimental data ν air = 1.77 m/s
(Re orifice = 400)
Evaporation time [s]
Ranz-Marshall model at 60°C
Experimental data ν air = 1.98 m/s
2.0
(Re = 200)
orifice
0 20 40 60 80 100
(b)
Evaporation time [s]

CHAPTER 5 RESULTS AND DISCUSSION 131
radius-time course and experimental data occurs. This can be explained by looking at the Sherwood
numbers predicted by the levitation model and the Ranz-Marshall correlation. In the first part of
evaporation the Sherwood number calculated by the Ranz-Marshall equation exceeds the Sherwood
number caused by the inner acoustic streaming. With decreasing droplet size the Sherwood number
by Ranz-Marshall decreases also due to a decrease in the droplet Reynolds number. At 40°C, for
example, the Sherwood number decreases to values lower than 6.0. Figure 5.39 f shows that the
Sherwood number caused by the inner acoustic streaming is always larger than 6.0 during the whole
evaporation experiment. In the final evaporation phase the acoustic Sherwood number exceeds the
ventilation Sherwood number, leading to faster evaporation than predicted by the Ranz-Marshall
correlation.
An altered drying behaviour of ethanol droplets occurs with a relative humidity of the drying
air ≥ 5.0%. The radius-time course differs from the nearly linear style in dry air.
Figure 5.42 shows a comparison of the raw data at 50°C and relative humidity form 0.1 to 80%.
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
0.0
Drying temperature 50.0°C
0 50 100 150 200 250
2 2
( t / r ) [s/mm ]
S 0
Rel. humidity 0.1%
Rel. humidity 20.0%
Rel. humidity 40.0%
Rel. humidity 60.0%
Rel. humidity 80.0%
Figure 5.42: Raw data from the evaporation of ethanol droplets in still air at 50°C and different relative humidity. The
initial droplet size of all experiments was 1.5 µl at an initial effective SPL of 162.25 dB.
Two different evaporation stages occur for the pure ethanol droplets at higher relative humidity of
the drying air. An initial phase with a large evaporation rate is followed by a transition phase with a
constantly decreasing rate. Afterwards, a second phase with a lower evaporation rate compared to
the first is detected. The vaporisation of ethanol leads to a cooling of the droplet surface resulting in
attainment of the wet bulb temperature. If there is sufficient humidity in the air and the wet bulb
temperature falls below the dew point. There condensation of water vapour at the droplet surface

132 RESULTS AND DISCUSSION
occurs. Law et al. [1987] showed that the vaporization of pure volatile alcohols in humid air is
accompanied by the simultaneous condensation of water vapour on the droplet surface and its
subsequent diffusion into the droplet interior. In the first phase, the evaporation of pure ethanol
dominates. An increasing humidity results, however, in an increasing evaporation rate of the ethanol
droplets in this first part of evaporation. The associated heat release at the droplet surface due to the
condensation increases the initial evaporation rate of the ethanol. The mixture of ethanol and water
formed has a higher wet bulb temperature than pure ethanol, resulting in a larger evaporation rate.
Figure 5.43 a shows the values of calculated dew point temperature at the droplet surface with
increasing humidity of the drying air at 40°C, 50°C and 60°C. Figure 5.43 b shows the initial
evaporation rate of the ethanol droplets vaporizing in still air. Due to the effect of the condensed
water vapour on the surface temperature, the evaporation rate in the first phase increases not only
with increasing temperature but also with increasing humidity.
Calculated surface temperature [°C]
40
35
30
25
20
15
10
5
0
40°C drying air
50°C drying air
60°C drying air
0 10 20 30 40
Relative humidity of drying air [%]
0 20 40 60 80
Figure 5.43: Surface temperature and initial evaporation coefficient of ethanol droplets in still air without ventilation at
different temperature and humidity. The initial droplet size was 1.5 µl at an initial effective SPL of 162.25 dB. (a) Plot
of the calculated surface temperature of the ethanol droplets. (b) Initial evaporation coefficient with relative humidity
and temperature of the drying air.
After all of the ethanol has evaporated, the subsequent radius-time-course is dominated by the
evaporation of the condensed water vapour. The evaporation rate in this stage is equal to that of
pure water droplets under the same ambient conditions. Figure 5.44 shows the terminal evaporation
coefficient of the ethanol experiments at elevated humidity at the end of the second evaporation
phase. The evaporation coefficient was determined starting at 0.05 µl residual droplet volume to the
end of the evaporation process.
Initial evaporation rate β r [mm 2 /s]
0.016
0.012
0.008
0.004
0.000
40°C drying air
50°C drying air
60°C drying air
70°C drying air
Relative humidity of drying air [%]

CHAPTER 5 RESULTS AND DISCUSSION 133
Terminal evaporation rate β r [mm 2 /s]
0.0016
0.0012
0.0008
0.0004
0.0000
0 20 40 60 80
Relative humidity of drying air [%]
40°C
50°C
60°C
70°C
Figure 5.44: Terminal evaporation coefficient of the ethanol experiments at different humidity and temperature of the
drying air. The coefficients were determined in a range of 50 to 0 nl droplet volume at the end of each experiment. The
initial droplet volume was 1.5 µl at an initial effective SPL of 162.25 dB.
A comparison with the values from the pure water droplet experiments in the same size range and
still air under the same ambient conditions shows almost perfect match of the evaporation
coefficients at all tested temperatures. The data for 40°C and 60°C at different humidity is shown in
Figure 5.45. The experiments at 60°C were repeated with forced air flow. The evaporation
coefficient of each experiment was determined initially at a volume of 1.5 to 1.3 µl and in the end at
a volume of 50 nl to 0 nl. The radius-time course of the raw data can be seen in Figure 5.46.
Terminal evaporation constant β r [mm 2 /s]
0.0014
0.0012
0.0010
0.0008
0.0006
0.0004
0.0002
Condensed water vapour at 40°C
Water droplet at 40°C
Condensed water vapour at 60°C
Water droplet at 60°C
0.0000
0 20 40 60 80
Relative humidity of drying air [%]
Figure 5.45: Comparison between the terminal evaporation coefficient of ethanol droplets and the terminal evaporation
coefficient of pure water droplets with different humidity at 40°C and 60°C. The coefficients were determined in a
range of 50 to 0 nl of the droplet volume at the end of each experiment. The initial droplet volume was 1.5 µl at an
initial effective SPL of 162.25 dB

134 RESULTS AND DISCUSSION
0.0
0 50 100 150 200 250 300 350
Figure 5.46: Raw data of evaporation experiments of ethanol droplets at 60°C and different humidity of the drying air.
The ventilation velocity was 1.0 m/s and corresponded to an orifice Reynolds number of 200. The initial droplet volume
of each experiment was 1.5 µl at an initial effective SPL of 163.25 dB.
As before with elevated humidity in still air, the radius-time course with drying air velocity shows
two different evaporation stages. The fast size-change at the beginning is caused by the evaporation
of ethanol. Subsequently, the evaporation rate decreases to almost constant values in the second
evaporation stage. This stage is dominated by evaporation of the condensed water vapour at the
droplet surface. Figure 5.47 shows the initial evaporation coefficient as function of drying air
velocity at different temperature and humidity. As seen before in still air, the initial evaporation
coefficient increases with increasing humidity and temperature of the drying air.
Evaporation coefficient β r [mm 2 /s]
0.014
0.012
0.010
0.008
0.006
0.004
0.002
2 ) [-]
2 / rS 0
( r S
25°C; 0.1%
40°C; 0.1%
60°C; 0.1%
1.0
0.8
0.6
0.4
0.2
0.0 0.5 1.0 1.5 2.0
Drying air velocity ν air [m/s]
60.0°C; 0.1% rel. humidity
60.0°C; 5.0% rel. humidity
60.0°C; 20.0% rel. humidity
60.0°C; 40.0% rel. humidity
2 2
( t / r ) [s/mm ]
S 0
0.0 0.5 1.0 1.5 2.0
Figure 5.47: Initial evaporation coefficient of ethanol droplets as a function of drying air velocity at different
temperature and humidity of the drying air. The initial droplet volume of each experiment was 1.5 µl at an initial
effective SPL of 162.75 dB to 164.15. (a) Initial evaporation coefficient versus drying air velocity for different
temperatures. (b) Initial evaporation coefficient versus drying air velocity for different humidity.
Evaporation coefficient β r [mm 2 /s]
0.006
0.005
0.004
0.003
0.002
0.001
Drying temperature 60°C
Rel. humidity 0.1%
Rel. humidity 20%
Rel. humidity 40%
Drying air velocity ν air [m/s]

CHAPTER 5 RESULTS AND DISCUSSION 135
Figure 5.48 presents the initial and terminal evaporation coefficients at 60°C and 1.0 m/s ventilation
velocity, as well as a comparison of the terminal evaporation coefficient with values of pure water
under the same conditions. The terminal evaporation coefficient correlates to the values for pure
water under the same ambient conditions, and decreases with increasing humidity. A simple
analytical prediction of the evaporation process using Equation 3.45 is not possible, because a
rapid-mixing is used to describe the time-distribution of the two components. This assumes that all
transport processes of the components inside the droplet occur much faster than the change in
concentration at the droplet surface. This results in a homogeneous distribution of the components
over the radial axis of the droplet. In case of condensation of water vapour on the droplet surface,
however, rapid-mixing cannot describe this behaviour, because the condensed water vapour is
initially located only at the droplet surface [Kastner 2001].
Initial evaporation coefficient β r [mm 2 /s]
Terminal evaporation coefficient β r [mm 2 /s]
0.0260
0.0240
0.0220
0.0200
0.0180
0.0160
0.0140
0.0120
0.0100
(a)
0.0022
0.0020
0.0018
0.0016
0.0014
0.0012
0.0010
0.0008
0.0006
(b)
Initial β r of ethanol
Surface temperature
0 10 20 30 40
Relative humidity of drying air [%]
Terminal β r of water droplets
β r of condensed water vapour
0 10 20 30 40
Relative humidity of drying air [%]
Figure 5.48: Initial and terminal evaporation coefficient of ethanol droplets at 60°C and different humidity of the
drying air. The ventilation velocity was 1.0 m/s corresponding to an orifice Reynolds number of 200. The initial droplet
volume of each experiment was 1.5 µl at an initial effective SPL of 163.25 dB. (a) Initial evaporation coefficient and
droplet surface temperature with humidity. (b) Comparison of the terminal evaporation coefficient of ethanol droplet at
elevated humidity of the drying air and water droplets.
40
35
30
25
20
15
10
5
0
Calculated initial surface temperature [°C]

136 RESULTS AND DISCUSSION
5.2.4 Evaporation of ethanol-water mixtures
To investigate the evaporation behaviour of multi-component solvent droplets inside the acoustic
levitation system, different mixtures of ethanol and water were levitated and compared to the results
obtained from pure ethanol and pure water. Figure 5.49 shows the evaporation behaviour of the
mixture droplets in still air, neglecting the accumulation of solvent vapour in the toroidal vortices.
The decrease in the squared radius or diameter cannot be described by the d 2 -law. As with the
ethanol droplets at high humidity, the ethanol-water mixture shows a radius-time course that is split
into two parts. At the beginning both components evaporate simultaneously, with domination of the
more volatile one (EtOH). Then a transition period controlled by the evaporation of both
components in equal measure follows. Afterwards, the more volatile solvent has almost completely
evaporated, and the subsequent evaporation is dominated by the less volatile solvent (water)
[Kastner 2001].
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
40°C
0.0
0 200 400 600 800 1000
(a)
2 2
( t / r ) [s/mm ]
S 0
water:ethanol = 10:0
water:ethanol = 8:2
water:ethanol = 4:6
water:ethanol = 2:8
water:ethanol = 0:10
60°C
0.0
0 200 400 600
Figure 5.49: Evaporation of multi-component solvent droplets at different temperature and a humidity of 0.1%. The
initial droplet volume of all experiments was 1.5 µl at an initial effective SPL of 164.0 dB. (a) Radius-time course of
droplets at different water-ethanol ratio at 40°C. (b) Radius-time course of droplets with different water-ethanol ratio at
60°C.
The evaporation coefficients in the initial evaporation phase and at the end of each experiment were
calculated by using the first 5 data points in a size range between 1.5 µl and 1.3 µl and the last data
points starting from 0.05 µl. The results are compared to the values obtained form pure water and
ethanol droplets in the same size range and under the same ambient conditions. Figure 5.50 shows
increasing evaporation coefficients in the initial phase with increasing amount of ethanol in the
solvent mixture. The values for the mixtures are between the coefficients of pure water and pure
ethanol. In the terminal part, the evaporation coefficients show almost constant values independent
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
(b)
2 2
( t / r ) [s/mm ]
S 0
water:ethanol = 10:0
water:ethanol = 8:2
water:ethanol = 4:6
water:ethanol = 2:8
water:ethanol = 0:10

CHAPTER 5 RESULTS AND DISCUSSION 137
of the initial composition of the droplet. The comparison with pure water droplets shows good
agreement. This demonstrates again that the size change of the droplets in the second evaporation
phase is dominated by the evaporation of water. The experimental values in Figure 5.50 and also the
raw data at different temperature show that an increase in drying temperature leads to an increase in
the evaporation rate in every phase of evaporation. The different evaporation coefficients at the
beginning and end of pure water droplets are caused by the effects of inner acoustic streaming on
the shrinking droplet surface, as reported in detail in chapter 5.2.2.
Evaporation coefficient β r [mm 2 /s]
0.005
0.004
0.003
0.002
0.001
0.000
(a)
Initial phase at 40°C
Terminal phase at 40°C
10:0 8:2 6:4 4:6 2:8 0:10
Water : Ethanol [-]
10:0 8:2 6:4 4:6 2:8 0:10
Figure 5.50: Initial and terminal evaporation coefficients of mixture droplets of ethanol and water at 40°C and 60°C
drying temperature and a humidity of 0.1%. The initial droplet diameter of each experiment was 1.5 µl at an initial
effective SPL of 164.0 dB. (a) Evaporation coefficients at 40°C. (b) Evaporation coefficients at 60°C.
2 ) [-]
2 / rS 0
( r S
1.0
0.8
0.6
0.4
0.2
Drying temperature 25°C
Drying temperature 40°C
Drying temperature 60°C
0.0
Water : EtOH = 40 : 60
0 200 400 600 800 1000
2 2
( t / r ) [s/mm ]
S 0
Figure 5.51: Raw data, initial and terminal evaporation coefficients of ethanol-water mixture droplets at different
temperatures and 0.1% relative humidity. The initial droplet volume of each experiment was 1.5 µl at an effective initial
SPL of 164.0 dB. (a) Radius-time course of ethanol-water (6:4) droplets at different temperature. (b) Comparison of the
initial and terminal evaporation coefficients at different temperatures
Evaporation coefficient β r [mm 2 /s]
Evaporation coefficient β r [mm 2 /s]
0.010
0.008
0.006
0.004
0.002
0.000
0.010
0.008
0.006
0.004
0.002
0.000
(b)
Initial phase at 60°C
Terminal phase at 60°C
Initial β r at 40°C
Initial β r at 60°C
Water : Ethanol [-]
Terminal β r at 40°C
Terminal β r at 60°C
10:0 8:2 6:4 4:6 2:8 0:10
Water : Ethanol [-]

138 RESULTS AND DISCUSSION
5.3 Evaporation of solution droplets
5.3.1 Evaporation of maltodextrin solution droplets
Properties of maltodextrin
Maltodextrin is produced by controlled hydrolysis of starch using acids or enzymes with subsequent
purification and spray-drying. Different grades with a variable ratio of glucose, maltose and
polysaccharides are available [Burger 1998]. The use of maltodextrines as drying aids in spraydrying
has been practiced since the 1970s, mostly in the food industry [Adhikari et al. 2004;
Brennan et al. 1971]. In combination with gum Arabic and modified starch it serves a basis as a
wall material in micro-encapsulation processes of oils [Bhandari et al. 1992; Krishnan et al. 2005;
Soottitantawat et al. 2003], fatty acids [Minemoto et al. 2002], flavours and other volatile
substances [Bhandari et al. 1992; Buffo 2000]. In pharmaceutical research maltodextrin has been
used to produce model protein particles with BSA for the preparation of aerosol formulations by
spray-drying [Lucas et al. 1997]. As an additive to penicillium occitanis cellulases formulations, it
had a positive effect on enzyme stabilisation during spray-drying [Belghith et al. 2001]. For the
levitation experiments the liquid properties of four maltodextrin solutions with different solid
content were determined and shown in Table 5.3.
Table 5.3: Properties of maltodextrin solutions with different solid content.
Solid
content
Surface
tension γ
[ mg/ ml]
[ ]
Density
ρ liquid
3
mN/m [ ]
Maximum
diameter
Maximum
volume
Minimum
diameter
Minimum
volume
g/cm [ mm ] [ µl ] [ µm ] [ µl ]
50 72.8 ± 0.12 1.015 6.57 148.49 15 1.77⋅10 -6
100 73.2 ± 0.06 1.036 6.46 141.15 15 1.77⋅10 -6
200 73.6 ± 0.06 1.071 6.29 130.30 15 1.77⋅10 -6
400 74.5 ± 0.12 1.142 5.97 111.41 15 1.77⋅10 -6
Data analysis of maltodextrin experiments
Analysis of the drying data of solution droplets is divided into at least two different stages and
differs therefore from the analysis of pure solvent droplets. In the first stage, corresponding to the
constant rate period [Kastner et al. 2001; Masters 1991], the squared radius of the droplet decreases

CHAPTER 5 RESULTS AND DISCUSSION 139
linearly with evaporation time, similar to pure solvent droplets. The evaporation rate is determined
directly from the horizontal and vertical diameters of the levitated droplet. The data is analysed
according to Chapter 5.2.1 and the evaporation rate calculated using Equation 3.47. After the
critical point, which marks the transition from the first to the second drying stage, the volume of the
levitated droplet remains constant even though there is still evaporation of solvent from inside the
droplet [Kastner et al. 2001; Walton 1999]. Determination of the evaporation rate in this falling rate
period is performed from the rise of the droplet within the stationary ultrasonic field towards its
adjacent upper pressure node, and the evaporation rate calculated with Equation 3.49. To determine
the critical point the plot of the squared radius with time as well as the aspect ratio is used. The
effective SPL at the critical point necessary for calculation of the evaporation rate in the second
drying stage is determined levitating a water droplet with the same size and under the same
conditions as the solid particle at the critical point. This eliminates the effects of surface tension and
kinematic viscosity on the shape of the droplet. Figure 5.52 shows the raw data of a 200 mg/ml
solution droplet obtained by the imaging software versus evaporation time. Both, the rise in position
as well as the change in aspect ratio provide a useful tool to determine the critical point between the
first and second drying stages. The change in aspect ratio of the droplet / particle at the critical point
is caused by influences of the standing acoustic wave. While the horizontal diameter does not
change further due to the formation of a solid crust at the surface, the vertical diameter continues to
decrease after the critical point. The section is marked by the ellipse in Figure 5.52. This is caused
by the existing 5:1 ratio between axial and radial forces acting in the ultrasonic field [Lierke 1996].
The particle is thus flattened during this phase of drying, resulting in an increase in aspect ratio. The
deformation holds until the end of the drying process and can be seen in the front illumination
picture gallery taken during the drying process (Figure 5.53) as well as in SEM pictures of the final
particle. The flattening of the top of the droplet / particle during formation of a solid crust can be
seen clearly. The dry particle has a translucent glassy appearance.

140 RESULTS AND DISCUSSION
2 ) [-] Aspect ratio [-]
2 / rS 0
( r S
Diameter [µm]
1.4
1.2
1.0
0.8
0.6
Constant rate
Falling rate
0.4
0.2
Droplet / particle size
Aspect ratio
Vertical position
-300
0.0
-400
0 200 400 600 800 1000
1600
1400
1200
1000
Evaporation time [s]
100
0
-100
-200
800
600
Horizontal diameter
Vertical diameter
Aspect ratio
1.1
400
1.0
0 200 400 600 800 1000
Evaporation time [s]
Figure 5.52: Raw data form the levitation of a maltodextrin solution droplet with 200 mg/ml solid content without
ventilation. The drying air had a temperature of 40°C with 0.1% relative humidity. The initial droplet size was 1.6 µl at
an initial effective SPL of 164.5 dB.
The influences of SPL on the shape and the aspect ratio of particles are examined in drying
experiments under the same ambient conditions with various strengths of the ultrasonic field. The
aspect ratio at the beginning of the levitation experiment, at the critical point, and at the end of the
drying process is shown in Figure 5.54 for a maltodextrin solution with 200 mg/ml solid content.
With an increase in the effective SPL the aspect ratio increases at all determined points examined
during the drying process. This results in a greater flattening of the dry particle with increasing
effective SPL. Figure 5.54 a shows the different values of the aspect ratio with initial effective SPL.
The aspect ratio of the droplet decreases directly before the critical point. The formation of a solid
crust is influenced by the axial levitation force, resulting in the flattening of the particle already
1.4
1.3
1.2
Distance to adjacent pressure node [µm]
Aspect ratio [-]

CHAPTER 5 RESULTS AND DISCUSSION 141
mentioned. The increase in the aspect ratio starts at the critical point and is completed by the end of
the drying process. The initial effective SPL that determines the starting aspect ratio does therefore
influence the shape of the final particle (Figure 5.54 b).
Figure 5.53: Evaporation of a maltodextrin solution with 100 mg/ml solid content at 27°C and 23% relative humidity
without ventilation. Pictures were taken with the CCD camera every 20 seconds. The gallery starts 10 minutes after
injection of the droplet. The initial droplet volume was 2.0 µl at an effective SPL of 164.75 dB.
Aspect ratio [-]
2.2
2.0
1.8
1.6
1.4
1.2
Initial droplet
Critical point
Final praticle
1.0
163.0 164.0 165.0 166.0 167.0 168.0 169.0
(a)
Initial effective SPL [dB]
1.4
1.2
Experimental data
Linear fit ( R
1.0 1.2 1.4 1.6 1.8 2.0
2 = 0.98 )
Figure 5.54: Aspect ratio of levitated maltodextrin solution droplets with 200 mg/ml solid content and dried
maltodextrin particles at 60°C and 0.1% relative humidity. The initial droplet size was 1.8 µl at different initial effective
SPL. (a) Aspect ratio with initial effective SPL. (b) Correlation between initial aspect ratio of the droplet and the final
aspect ratio of the formed particle.
Aspect ratio of the final particle [-]
2.2
2.0
1.8
1.6
(b)
Aspect ratio of the initial droplet [-]

142 RESULTS AND DISCUSSION
There are a number of possibilities of plotting the evaporation rate of the maltodextrin solution
droplets, as already seen with the pure solvent droplets in Chapter 5.2.1. The first is to plot the
evaporation rate in mass per time unit on the y-axis versus the time on the x-axis (Figure 5.55 a). A
decreasing evaporation rate with time is seen due to both the decrease in surface area in the first
drying stage and the impeded solvent evaporation in the second stage. This plot shows different
values of evaporation rate with different initial volume of the droplet. This is normalised in a plot of
the evaporation rate in mass per time and surface area versus time divided by the squared initial
radius (Figure 5.55 b). The calculation of an average curve is now possible, if the influence of the
inner acoustic streaming on the droplet surface is neglected. Figure 5.55b shows an almost constant
evaporation rate in the first drying stage, a clear break at the critical point, and falling values
subsequently in the second drying stage.
Evaporation rate [mg/s]
6.0
5.0
4.0
3.0
2.0
1.0
0.0
0 200 400 600 800 1000
(a)
Evaporation time [s]
Initial volume 2.249 µl
Initial volume 1.815 µl
Initial volume 1.657 µl
Figure 5.55: Evaporation rate of maltodextrin droplets with 200 mg/ml solid content dried at 40°C and a relative
humidity of 0.1% without ventilation air stream. Initial droplet volume and initial effective SPL differed at the three
experiments. (a) Evaporation rate in evaporated mass per time unit with the evaporation time. (b) Evaporation rate in
evaporated mass per time unit and surface area with evaporation time divided by the squared initial radius.
The influence of the solid content on the radius-time course and the evaporation rate is shown in
Figure 5.56. With increasing solid concentration the evaporation time of the first drying stage
decreases leading to a shift in the critical point to earlier times. The 40% solution does not show a
clear transition between the two drying stages. The evaporation rate decreases also due to water
vapour pressure depression by the dissolved molecules. The decline in the evaporation rate in the
second drying stage becomes shallower with higher solid content. The duration of the second drying
stage increases therefore with higher solid content (Table 5.4).
Evaporation rate [mg/s/mm 2 ]
0.7
0.6
0.5
0.4
0.3
0.2
0.1 Constant Falling
0.0
rate rate
0 500 1000 1500 2000
(b)
Critical point
2 2
( t / r ) [s/mm ]
S 0
Initial volume 2.249 µl
Initial volume 1.815 µl
Initial volume 1.657 µl

CHAPTER 5 RESULTS AND DISCUSSION 143
Table 5.4: Constant and falling rate stages for 1.8 µl maltodextrin droplets with different solid content dried at a
temperature of 40°C and 0.1% relative humidity.
Solid content
[ ]
Evaporation rate in
constant rate period
−1 −2
mg/ml [ µg s ⋅ mm ]
⋅ [ ]
Critical point tcrit Duration of falling
rate period tcrit
s [] s
50 0.75-0.63 445.3 162.4
100 0.71-0.63 353.9 278.3
200 0.62-0.58 283.6 364.6
400 0.58-0.50 91.5 708.6
Evaporation rate [µg/s/mm 2 ]
0.8
0.6
0.4
0.2
0.0
0 500 1000 1500 2000
2 2
( t / r ) [s/mm ]
S 0
50 mg/ml
100 mg/ml
200 mg/ml
400 mg/ml
Figure 5.56: Evaporation rate of maltodextrin solutions with different solid content at 40°C and a relative humidity of
0.1% without ventilation air stream. The initial droplet volume of all experiments was 1.8 µl at an initial effective SPL
of 164.75 dB.
The temperature of the drying air has also an influence on the evaporation time and the evaporation
rate of solution droplets. Higher temperature leads to an increase in evaporation rate and a decrease
in evaporation time in the first drying stage Figure 5.57. The evaporation rate is almost constant in
this phase. The higher the temperature is, the earlier the critical point is reached and therefore the
formation of a solid crust leading to a decrease in the duration of the first and an increase in the
second drying stage Table 5.5. At 25°C the transition from constant to falling rate stage does not
result in a sharp point compared to 40°C and 60°C.

144 RESULTS AND DISCUSSION
Table 5.5: Duration of constant and falling rate for 1.8 µl maltodextrin droplets with 200 mg/ml solid content dried at a
different temperature and 0.1% relative humidity.
Drying temperature
[ ]
Constant rate period
⎡ µg ⎤
mg/ml ⎢ 2
⎣s⋅
mm ⎥
⎦
Critical point
tcrit
Duration of falling
rate period tcrit
[ s ]
[] s
25°C 0.39-0.36 502.5 628.0
40°C 0.62-0.58 283.6 364.6
60°C 1.22-1.19 111.7 333.9
Evaporation rate [mg/s/mm 2 ]
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0 500 1000 1500 2000
2 2
( t / r ) [s/mm ]
S 0
Drying temp. 25°C
Drying temp. 40°C
Drying temp. 60°C
Figure 5.57: Evaporation rate of maltodextrin solutions with 200 mg/ml solid content at different temperature and a
relative humidity of 0.1% without ventilation air stream. The initial droplet volume of all experiments was 1.8 µl at an
initial effective SPL of 164.75 dB.
The formed particles differ in size. Figure 5.58 shows that the particle size not only increases with
solid content of the maltodextrin solution (Figure 5.58 a), but also with the temperature of the
drying air (Figure 5.58 b). For a 1.8 µl droplet with 50 mg/ml solid content the volume of the
formed particle increases from 0.107 µl at 25°C to 0.129 µl at 40°C. A comparison of the final
particle densities shows decreasing density with higher drying temperature (Figure 5.58 c). The
density also slightly increases with greater solid content. The difference between the final particle
size and density values at 40°C and 60°C are, however, small compared to the values at 25°C. SEM
pictures of maltodextrin particles produced in the levitation system and in the Buchi spray dryer
with different solid content are shown in Figure 5.59. The maltodextrin solution was sprayed at

CHAPTER 5 RESULTS AND DISCUSSION 145
100°C inlet and 60°C outlet temperature. The levitated particles show a similar morphology
compared to the larger particles of the spray dried powder. The interior of the particles has a
massive solid structure without any holes. The surface is indented by small flat craters which are
not combined with capillaries in the interior.
2 ) [-]
( r S / r S 0
Particle density [g/cm 3 ]
1.0
0.8
0.6
0.4
0.2
50 mg/ml
100 mg/ml
200 mg/ml
0.0
400 mg/ml
0 500 1000 1500
1.0
0.9
0.8
0.7
[ Temp. 40°C - rel. humidity 0.1%]
2 2
( t / r ) [s/mm ]
S 0
Drying temp. 25°C
Drying temp. 40°C
Drying temp. 60°C
0.6
0 10 20 30 40
Maltodextrin solid content (m/V) [%]
0 10 20 30 40
Figure 5.58: Comparison of the resulting particle size and density of maltodextrin solutions with different solid content
dried at different temperature and 0.1% relative humidity. The initial droplet volume of all experiments was 1.8 µl at an
initial effective SPL between 164.0 and 164.75 dB. (a) Radius-time course of Maltodextrin solutions with different solid
content at 40°C. (b) Particle size compared to the initial droplet volume wit different solid content and temperature.
(c) Resulting particle density with different solid content and temperature.
Particle radius relativ to initial droplet radius [%]
90
80
70
60
50
40
Drying temp. 25°C
Drying temp. 40°C
Drying temp. 60°C
Maltodextrin solid content (m/V) [%]

146 RESULTS AND DISCUSSION
(a)
(b)
(c)
Figure 5.59: SEM pictures of maltodextrin particles from the levitation system and the Buchi B-191 Mini Spray Dryer.
(a-c) Maltodextrin particles from a solution with 100 mg/ml solid content dried at 60°C and 0.1% relative humidity.
Shown are pictures with a magnification of 75.5-times (a), 180-time (b) and 1000-times (c). (d-f) Spray-dried
maltodextrin particles from solutions with 100 mg/ml (d), 200 mg/ml (e) and 400 mg/ml (f) solid content (m/V) at an
inlet temperature of 100°C and an outlet temperature of 60°C. The pictures were taken with 2000-times magnification.
(d)
(e)
(f)

CHAPTER 5 RESULTS AND DISCUSSION 147
5.3.2 Evaporation of trehalose solution droplets
Properties of trehalose
Trehalose (α,α-trehalose) is a disaccharide formed by the 1,1-linkage of two D-glucose molecules
[Richards et al. 2002]. It has the molecular formula C12H22O11 and a molecular weight of
342.31 g/mol. Commercially and purified, it is usually found as dihydrate [Sigma 2005]. Trehalose
is a non-reducing sugar, that first melts at 97°C. Additional heat drives off the water of
crystallisation until the material resolidifies at 130°C. The anhydrous Trehalose melts at 203°C
[Richards et al. 2002]. The natural occurrence of α,α-trehalose is listed in over 80 different species
of plants, algae, fungi, yeasts, bacteria insects and other vertebrates. The biosynthesis of trehalose in
brewer’s yeast is catalysed by enzymes facilitating the reaction of UDP-D-glucose with D-
glucose 6-phosphate. The phosphate of the resulting α,α-trehalose 6-phosphate is enzymatically
removed leaving a trehalose molecule [Richards et al. 2002]. The role of trehalose in nature varies
from energy source during certain stages of development or the flight of insects to structural
component [Elbein 1974]. One very important observation is the participation of trehalose in
stabilisation of life processes in organisms that can survive either freezing or dehydration [Newman
et al. 1993]. It can stabilize the dehydrated form of biological structures and is able to restore them
functional as soon as the hydration and temperature conditions return to normal [Lins et al. 2004].
Two different stabilization levels are discussed [Lins et al. 2004]: one is the stabilization of
membranes and lipid assemblies at very low hydration [Hoekstra et al. 1997] and the other is the
stabilisation of biological macromolecules in the folded state under denaturation conditions [Xie
1997]. Due to the wide appearance in different biostructural classes, the protective mechanisms of
trehalose against stress by dehydration, heating or freezing is said to be a non-specific process
[Crowe et al. 1990]. Three main hypothesis are discussed describing the stabilizing mechanisms of
trehalose [Lins et al. 2004]. The first one is called the water-replacement hypothesis. It states
direct interactions between the disaccharide molecules and the protected biostructure through
hydrogen bonds [Arakawa et al. 2001]. The second mechanism is the water-layer hypothesis,
discussing a trapping of the water molecules close to the biomolecular surface layer [Gil et al.
1996]. The third and last is called mechanical entrapment hypothesis. It favours the entrapment of
a particular biomolecular confirmation in a high viscosity trehalose glass [Gil et al. 1996; Lins et al.
2004]. Among the various osmolytes in nature used to overcome deleterious environmental effects,
trehalose seems to be exceptional compared to other sugars and polyols [Kaushik 2003]. It is more
stable to wide ranges of pH and heat than most other sugars and its viscosity is relatively low with a

148 RESULTS AND DISCUSSION
40% solution being approximately 5.7 centipoises [Richards et al. 2002]. Recent studies by Kaushik
and Bhat [Kaushik 2003] stated that trehalose increases the transition temperature ( T )
Δ of proteins
to a maximal extent among the compatible osmolytes of the sugar and polyol series. They also
observed a decrease in the heat capacity of denaturation for all there tested proteins. This parameter
is said to reflect upon the subtle changes in protein-solvent interactions [Liu 1996]. Trehalose also
increases the surface tension of water to a larger extent than the other sugars and polyols. A linear
correlation between the increased surface tension and the increase in the transition temperature
( T )
Δ of protein was found by Kaushik and Bhat [Kaushik 2003]. It was also reported, that the
m
presence of trehalose leads to larger changes of the thermodynamic properties of water than for
other sugars, like the increase in partial molal heat capacity and volume. Trehalose is said to have a
larger hydrated volume compared to other disaccharides [Sola-Penna 1998]. These increased
parameters have been said to lead to stronger hydrogen bonding between hydroxyl groups of water
molecules and trehalose. In such a solution additional energy would be needed for protein
denaturation to accommodate its increased surface area [Kaushik 2003]. Additionally, there is also a
depletion of the surface tension increasing cosolvents at the protein-solvent interface leading to the
preferential hydration of the protein [Timasheff 2002].
For the levitation experiments four trehalose solutions with different solid content were
prepared and their liquid properties were determined before starting the experiments. The data is
shown in Table 5.6
Table 5.6: Liquid properties and levitation size range for trehalose solutions with different solid content.
Solid
content
Surface
tension γ
[ mg/ml ] [ ]
Density
ρ liquid
3
mN/m [ ]
Maximum
diameter
Maximum
volume
Minimum
diameter
m
Minimum
volume
g/cm [ mm ] [ µl ] [ µm ] [ µl ]
50.0 72.80 ± 0.14 1.015 6.56 148.1 15µm 1.77⋅10 -6
100.0 73.13 ± 0.08 1.032 6.49 142.8 15µm 1.77⋅10 -6
200.0 74.02 ± 0.20 1.068 6.33 133.4 15µm 1.77⋅10 -6
400.0 75.09 ± 0.20 1.140 6.02 114.5 15µm 1.77⋅10 -6

CHAPTER 5 RESULTS AND DISCUSSION 149
Data analysis of trehalose experiments
The analysis of the experimental data of the trehalose solution droplets has to be divided at least
into two different drying stages, similar to the maltodextrin analysis. The critical point between
constant and falling rate can be determined using the course of the aspect ratio with evaporation
time. The trehalose particles flattens during the formation of a solid crust due to the influence of the
standing acoustic wave and the 5:1 relation between axial and radial levitation force. While the
vertical diameter decreases under the influence of the axial levitation force after the critical point,
the horizontal diameter stays nearly constant. This leads to an increase in aspect ratio and therefore
provides a possibility to determine the duration of the first drying stage and the point of time of the
transition to the second drying stage. In all experiments the minimal effective SPL for a stable
levitation of the droplet / particle was chosen to keep the influence of the axial levitation force to a
minimum. Figure 5.60 shows the raw data of the drying of a trehalose solution with 100 mg/ml
solid content at 60°C and 5.0% relative humidity.
Figure 5.60 shows that there is a change in aspect ratio and a rise of the formed particle after
the critical point in the second drying stage. In contrast to maltodextrin, both diameters change
substantially after the critical point, whereas the influence of the axial levitation force on the
particle is much larger than the influence of the radial one resulting in an increasing aspect ratio and
a flattening of the particle during the falling rate. There is no sharp break in the curve of the squared
radius with time at the critical point according to the considerations of chapter 2.4.2 and literature
[Masters 1991]. Small size changes still occur in the second drying stage rounding the plotted
curve. The deformation of the particle holds up till the end of the drying process is achieved. The
gallery of photos taken from a levitated trehalose droplet with 200 mg/ml solid content with front
illumination shows the deformation of the droplet / particle during the drying process very clearly.
The impression of the top is not as for the maltodextrin droplets.
As with the maltodextrin solution, there are different ways to plot the evaporation rate
calculated from the experimental data. To compensate for different initial volumes of the droplets
the data is best plot as evaporated liquid mass per time and surface area with evaporation time
divided by the square of the initial radius. For trehalose solution droplets this is show in Figure
5.62. All trehalose experiments were performed at 60°C. The humidity of the drying air was varied
from 5.0% to a maximum of 40%. The influence of the drying air humidity for the trehalose
solutions with different solid content can be seen in Figure 5.63. An increasing humidity leads to an
increase in evaporation time and a shift of the critical point to later points of time in the drying
process.

150 RESULTS AND DISCUSSION
2 ) [-] Aspect ratio [-]
2 / rS 0
Diameter [µm]
( r S
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
Constant rate
Falling rate
Droplet / particle size
Aspect ratio
Vertical position
0.0
-200
0 200 400 600 800 1000
(a)
1600
1400
1200
1000
800
Evaporation time [s]
Figure 5.60: Raw data of the levitation of a trehalose solution droplet with 200 mg/ml solid content without ventilation.
The drying air had a temperature of 60°C and a relative humidity of 5.0%. The initial droplet size was 1.6 µl at an initial
effective SPL of 165.1 dB. The dashed red line marks the position of the critical point.
This is caused by a decrease of the water vapour pressure gradient between droplet surface and
environment. The evaporation rate in the first drying stage is almost constant for all humidities of
the drying air and all different solid concentrations, except for the trehalose solution with
400 mg/ml solid content. The decline in the evaporation rate after the critical point is steeper for
experiments at 5% and 10% relative humidity than for the experiments at 20% and 40%. The
trehalose solutions with 400 mg/ml solid content do not show a clear first drying stage any more.
The decrease of the evaporation rate occurred very early in the drying process due to high solid
concentration and the almost immediate crust formation after the injection of the droplet into the
acoustic levitation system.
50
0
-50
-100
-150
600
1.2
400
Horizontal diameter
200
Vertical diameter
Aspect ratio
1.1
0
1.0
0 200 400 600 800 1000
Evaporation time [s]
1.6
1.5
1.4
1.3
Distance to adjacent pressure node [µm]
Aspect ratio [-]

CHAPTER 5 RESULTS AND DISCUSSION 151
Figure 5.61: Evaporation of a trehalose solution droplet with 200 mg/ml solid content at 25°C and 26% relative
humidity in still air. Pictures were taken with the CCD-camera every 30 seconds. The gallery starts with the 5 minutes
after the injection of the droplet. The initial droplet volume was 2.1µl at an initial effective SPL of 164.28 dB.
Evaporation rate [µg/s]
10.0
9.0
Initial volume 1,663 µl
8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
Initial volume 2,123 µl
Initial volume 2,437 µl
0 200 400 600 800 1000
(a)
Evaporation time [s]
Figure 5.62: Different possibilities to plot the evaporation rate of trehalose solution droplets with 100 mg/ml solid
content at a drying temperature of 60°C and a relative humidity of 5%. Initial droplet volume and initial SPL differed
between the three experiments. (a) Evaporation rate as evaporated mass per time unit with evaporation time. (b)
Evaporation rate as evaporated mass per time unit and surface area with time divided by the squared initial droplet
radius.
Evaporation rate [µg/s/mm 2 ]
1.2
1.0
0.8
0.6
0.4
Critical point
2 2
( t / r ) [s/mm ]
S 0
Initial volume 1,667 µl
Initial volume 2,123 µl
Initial volume 2,437 µl
0.2
Constant Falling
0.0
rate rate
0 200 400 600 800 1000 1200 1400
(b)

152 RESULTS AND DISCUSSION
The influence of the solid content on the course of the evaporation rate with time at different
humidity of the drying air is shown in Figure 5.64. With increasing trehalose concentration the
evaporation rate in the first drying stage is decreasing due to the amount of dissolved molecules and
the related water vapour pressure depression. The evaporation rate shows almost constant values in
this phase, except for the solution with 400 mg/ml trehalose. The duration of the constant rate was
decreasing with increasing solid content, leading to a shift of the critical point to earlier point of
time in the drying curve. The decline of the evaporation rate after the crust formation is steeper for
lower concentrated trehalose solutions than for higher ones. Due to this effect, the duration of the
second drying stage is slightly increasing for increasing solid content of the trehalose solutions.
Table 5.7 gives an example comparison of the durations of the several drying stages and the
position of the critical point for trehalose solutions with different solid content dried at 60°C and
5.0% relative humidity of the drying air. The experiments with 200 mg/ml trehalose content had an
unexplainable course compared to all other experimental data.
Evaporation rate [µg/s/mm 2 ]
Evaporation rate [µg/s/mm 2 ]
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0 500 1000 1500 2000
(a)
1.2
1.0
0.8
0.6
0.4
0.2
Rel. humidity 5%
Rel. humidity 20%
Rel. humidity 40%
[Solid 50 mg/ml - 60°C]
2 2
( t / r ) [s/mm ]
0
0.0
0 500 1000 1500 2000
(c)
Rel. humidity 5%
Rel. humidity 20%
Rel. humidity 40%
[ Solid 200 mg/ml - 60°C
2 2
( t / r ) [s/mm ]
0
Evaporation rate [µg/s/mm 2 ]
Evaporation rate [µg/s/mm 2 ]
0.0
0 500 1000 1500 2000
Figure 5.63: Evaporation rate of trehalose solutions with different solid content at a drying temperature of 60°C and
different relative humidity. The initial droplet volume of the experiments was between 1.7 and 2.0 µl at an initial
effective SPL between 163.75 and 165.1 dB. (a) 50 mg/ml trehalose solid content. (b) 100 mg/ml trehalose solid
content. (c) 200 mg/ml trehalose solid content. (d) 400 mg/ml trehalose solid content.
1.2
1.0
0.8
0.6
0.4
0.2
(b)
1.2
1.0
0.8
0.6
0.4
0.2
Rel. humidity 5%
Rel. humidity 10%
Rel. humidity 20%
Rel. humidity 40%
[ Solid 100 mg/ml - 60°C]
2 2
( t / r ) [s/mm ]
0
Rel. humidity 5%
Rel. humidity 20%
Rel. humidity 40%
[ Solid 400 mg/ml - 60°C]
0.0
0 500 1000 1500 2000
(d)
2 2
( t / r ) [s/mm ]
0

CHAPTER 5 RESULTS AND DISCUSSION 153
Table 5.7: Duration of constant and falling rate for 1.8 µl trehalose droplets with different solid content dried at a
temperature of 60°C and a relative humidity of 5%. The initial effective SPL was between 163.8 and 165.1 dB.
Evaporation rate [µg/s/mm 2 ]
Evaporation rate [µg/s/mm 2 ]
1.2
1.0
0.8
0.6
0.4
0.2
1.2
1.0
0.8
0.6
0.4
0.2
Solid content
50 mg/ml
100 mg/ml
200 mg/ml
400 mg/ml
[60°C - rel. humidity 40%]
0.0
0 500 1000 1500 2000
(c)
[ ]
Constant rate period
⎡ µg ⎤
mg/ml ⎢ 2
⎣s⋅
mm ⎥
⎦
2 2
( t / r ) [s/mm ]
0
Critical point tcrit
Duration of detectable
falling rate period
[ s ]
[] s
50.0 1.20 – 1.10 274.5 234.0
100.0 1.06 – 1.03 261.1 344.2
200.0 1.06 – 1.03 - -
400.0 0.99 – 0.98 138.9 668.6
0.0
0 500 1000 1500 2000
(a)
2 2
( t / r ) [s/mm ]
0
50 mg/ml
100 mg/ml
200 mg/ml
400 mg/ml
[60°C - rel. humdity 5%]
Evaporation rate [µg/s/mm 2 ]
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0 500 1000 1500 2000
(b)
50 mg/ml
100 mg/ml
200 mg/ml
400 mg/ml
[60°C - rel. humidity 20%]
2 2
( t / r ) [s/mm ]
0
Figure 5.64: Evaporation rate of trehalose
solutions with different solid content at a drying
temperature of 60°C and different relative
humidity. The initial droplet volume of the
experiments was between 1.7 and 2.0 µl at an
initial effective SPL between 163.75 and
165.1 dB.
(a) Evaporation rate of trehalose solutions at 60°C
and 5% relative humidity.
(b) Evaporation rate of trehalose solutions at 60°C
and 20% relative humidity.
(c) Evaporation rate of trehalose solutions at 60°C
and 40% relative humidity.

154 RESULTS AND DISCUSSION
A comparison of the evaporation coefficient β r confirms the statement concluded from the
diagrams of the evaporation rate with time of Figure 5.63 and Figure 5.64. The evaporation
coefficient is determined using the droplet size in a range between 1.8 µl and 1.5 µl in the first
drying stage. The results are plotted in Figure 5.65 With increasing trehalose content and increasing
humidity a decrease in the evaporation coefficient can be determined. This shows again very clearly
the influence of the amount of dissolved molecules as well as the influence of the water vapour
pressure gradient between surface and ambience.
Evaporation coefficient β r [mm 2 /s]
0.0022
0.0020
0.0018
0.0016
0.0014
0.0012
0.0010
0.0008
0.0006
0.0004
Rel. humidity 5%
Rel. humidity 20%
Rel. humidity 40%
[Drying temp. 60°C]
0 100 200 300 400
Trehalose solid content [mg/ml]
Figure 5.65: Evaporation coefficient βr in the first drying stage of trehalose solutions as a function of trehalose solid
content at 60°C and different relative humidity in still air. The value are determined in a size range between 1.8 µl and
1.5 µl. The initial effective SPL was between 163.9 dB and 162.9 dB.
Investigations of the resulting particle size and particle density are carried out similar to the
maltodextrin solutions. The data is shown in Figure 5.66. An increasing solid content leads to an
increase in the particle size due to the higher solid concentration in the initial droplet. It can also be
seen that the particle radius in relation to the initial droplet radius shows the larges values for the
faster evaporation process at 60°C and 5% relative humidity and the smallest values at 60°C and
40% humidity. The density confirms this conclusion. Trehalose particles formed of solutions with
the same solid content but at different humidity of the drying air have an increasing resulting
particle density with increase in drying time, which is equal to an increasing humidity of the drying
air. The data shows that the density of the 400 mg/ml trehalose solution particles is lower compared
to the less concentrated samples under the same drying conditions. Figure 5.67 shows SEM pictures
of trehalose particles produced in the levitation system and in the Buchi Mini Spray-Dryer.
Trehalose particles from the levitation system show a folded structure on their top (Figure 5.67 b).

CHAPTER 5 RESULTS AND DISCUSSION 155
This effect can also be seen during the drying experiment itself using front light illumination. The
particles stay more spherical during the second drying stage than the maltodextrin ones. Structural
similarities to the spray-dried particles cannot be found at this magnification.
Particle radius relativ to initial droplet radius [%]
80
70
60
50
40
Rel. humidity 5%
Rel. humidity 20%
30
Rel. humidity 40%
0 100 200 300 400
(a)
Trehalose solution solid content [mg/ml]
0.9
0 100 200 300 400
Figure 5.66: Comparison of the resulting particle size and density of trehalose solutions with different solid content,
dried 60°C and different humidity without ventilation. The initial droplet volume of all experiments was between 1.7 µl
and 2.0 µl at an initial effective SPL of 163.8 dB to 165.1 dB. (a) Particle radius compared to the initial droplet radius
with different trehalose solution solid content at different humidity. (b) Resulting particle density with trehalose
solution solid content at different humidity.
To overcome the influence of the accumulation of solvent vapour in the toroidal vortices of
the outer acoustic streaming, a trehalose solution with 100 mg/ml solid content is tested under the
influence of different ventilation velocities. With increasing flow rate the droplet becomes more and
more unstable. This is most notable in the second drying stage after the formation of the solid crust,
when the mass of the particle is decreasing due to the proceeding evaporation of solvent. The
determination of the evaporation rate in this stage is very difficult and sometimes, if the oscillations
and the movement of the particle is too large, impossible. In contrast to the experiments in still air
neglecting the effects of the inner acoustic streaming on the Sherwood number, the experiments in
moving air cannot be plotted to compensate for the different initial droplet size. The droplet and
resulting particle size has a direct influence on the Reynolds number at the droplet / particle and
therefore a direct influence on the Sherwood number calculated by the Ranz-Marshall equation.
Because different initial droplet sizes result in different particle diameters under the same ambient
conditions, the Sherwood number and the mass transfer would be different in the second drying
stage. To compare experiments, it is necessary to inject solution droplets with the same initial
volume into a standing acoustic wave with a constant effective SPL. Figure 5.68 a shows the course
Particle density [g/cm 3 ]
1.3
1.2
1.1
1.0
(b)
Rel. humidity 5%
Rel. humidity 20%
Rel. humidity 40%
Trehalose solution solid content [mg/ml]

156 RESULTS AND DISCUSSION
of the Sherwood number at a ventilation velocity of 1.5 m/s ( Re = 300)
orifice calculated with the
Ranz-Marshall equation and the Sherwood number at a ventilation velocity of 1.0 m/s
( Re = 200)
orifice calculated with the levitation model. The influence of the ventilation on the
evaporation rate of a 1.7 µl droplet with 100 mg/ml trehalose content compared to experiments in
still air at 60°C and a relative humidity of 5% is plotted in Figure 5.68 b. With increasing flow rate
the evaporation rate in the first drying stage also increases. The formation of a solid crust appears
earlier at higher ventilation velocity than in still air, resulting in a decrease in evaporation time of
the constant rate. The decline of the evaporation rate after the critical point is steeper with
increasing ventilation. Increasing the humidity of the ventilation air stream leads to effects on the
evaporation rate equal to Figure 5.64 for the experiments in still air. At a velocity of 1.0 m/s and
increasing humidity the evaporation rate decreases leading to a increase in the evaporation time and
a shift of the critical point to later points of time in the evaporation process (Figure 5.68 c).
(a)
(b)
Figure 5.67: SEM pictures of trehalose particles from the levitation system and the Buchi B-191 Mini Spray Dryer.
(a-b) Trehalose particles from a solution with 200 mg/ml solid content dried at 60°C and 5% relative humidity. Shown
are pictures with a magnification of 75.5-times (a), 1000-times (b). (c-d) Spray-dried trehalose particles from solutions
with 100 mg/ml solid content at an inlet temperature of 100°C and an outlet temperature of 60°C. The pictures were
taken with 1000-times (c) and 2000-times (d) magnification.
(c)
(d)

CHAPTER 5 RESULTS AND DISCUSSION 157
Sherwood number [-]
Evaporation rate [µg/s/mm 2 ]
10.0
9.0
8.0
7.0
6.0
5.0
4.0
3.0
Levitation model at 166 dB
2.0
Ranz-Marshall correlation at 1.5 m/s
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
(a)
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0 200 400 600 800 1000
(b)
60°C
Droplet volume [µl]
Ventilation 0.0 m/s
Ventilation 1.0 m/s
Ventilation 1.5 m/s
[60°C - rel. humidity 5%]
2 2
( t / r ) [s/mm ]
S 0
Figure 5.68: (a) Sherwood number as a function of
droplet volume at 60°C and 0.1% relative humidity.
(b) Evaporation rate of trehalose solution droplets
with 100 mg/ml solid content at 60°C and 5%
relative humidity. The initial droplet volume of the
experiments was 1.7 µl at an initial effective SPL of
166.0 dB. The drying air velocity was varied from
still air to 1.5 m/s. (c) Evaporation rate of trehalose
solution droplets with 100 mg/ml solid content at
60°C and different relative humidity. All
experiments were carried out with a ventilation of
1.0 m/s. The initial droplet volume of the
experiments was 1.7 µl at an initial effective SPL
between 164.8 dB and 165.1 dB.
0.0
0 250 500 750 1000 1250 1500
The effects of the air flow rate on the particle formation and the particle morphology was examined.
With increasing ventilation the particle radius relative to the initial droplet radius increases, whereas
the density decreases. A drying of the particles at a relative humidity of 20% and 40% of the drying
air leads to a decrease of the particle size and an increase in density compared to the results from
the experimental data at 5% relative humidity. It seems that a decreasing evaporation time,
regardless of which is the causing factor, drying temperature, humidity of the drying air or
magnitude of the ventilation velocity, is leading to larger and less dense particles. The results can be
seen in Figure 5.69. A composition of SEM pictures of the resulting particles formed under a
ventilation velocity of 1.0 m/s and a humidity of 5% and 20% can be seen in Figure 5.70. It seems
that the fast drying process at 60°C, 1.0 m/s and 5% humidity causes a porous structure visible at
the particle surface by the small pores Figure 5.70 b. In contrast, the experiments with longer
evaporation time at 60°C, 1.0 m/s and 20% humidity show a smooth surface and the folded
structure (Figure 5.70 c / d) equal to the particles produces in still air (Figure 5.67 b).
Evaporation rate [µg/s/mm 2 ]
2.0
1.5
1.0
0.5
(c)
Rel. humidity 5%
Rel. humidity 20%
Rel. humidity 40%
[60°C - ventilation 1.0 m/s]
2 2
( t / r ) [s/mm ]
S 0

158 RESULTS AND DISCUSSION
Particle radius relative to initial droplet radius [%]
54.0
52.0
50.0
48.0
46.0
44.0
42.0
(a)
[Drying temp. 60°C]
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Ventilation velocity [m/s]
Rel. humidity 5%
Rel. humidity 20%
Rel. humidity 40%
Figure 5.69: Resulting particle size and density of trehalose solutions with 100 mg/ml solid content, dried 60°C and
different humidity at a ventilation velocity between 0.0 and 1.5 m/s. The initial droplet volume of all experiments was
between 1.7 µl and 2.0 µl at an initial effective SPL of 164.8 dB to 165.1 dB. (a) Particle size versus ventilation velocity
at different humidity. (b) Final particle density with ventilation velocity at different humidity.
(a) (b)
(c) (d)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Figure 5.70: SEM pictures of trehalose particles with 100 mg/ml solid content from the levitation system. (a-b)
Trehalose particles formed at 60°C and 5.0% relative humidity with a ventilation of 1.0 m/s. Shown are pictures with a
magnification of 100-times (a) and 1000-times (b). (c-d) Trehalose particles formed at 60°C and 20.0% relative
humidity with a ventilation of 1.0 m/s. Shown are pictures with a magnification of 100-times (c) and 1000-times (d)
Particle density [g/cm 3 ]
1.4
1.2
1.0
0.8
0.6
(b)
Rel. humidity 5%
Rel. humidity 20%
Rel. humidity 40%
[Drying temp. 60°C]
Ventilation velocity [m/s]

CHAPTER 5 RESULTS AND DISCUSSION 159
5.3.3 Evaporation of mannitol solution droplets
Properties of mannitol
Mannitol is a hexavalent sugar alcohol with the molecular formula C6H14O6 and a molecular weight
of 182.17 g/mol [Sigma 2005]. It melts at a temperature of 166-168°C [Windholz et al. 1983] and
has a maximum solubility of 182 mg/ml in water at 25°C [McEvoy 1992]. D-mannitol is a common
excipients in spray- and freeze-drying with a good chemical stability [Yu et al. 1998]. It does not
undergo hydrolysis at high or low pH. Even mannitol has the strong tendency to crystallize [Yu et
al. 1998] it also exists in fully and partially amorphous state in certain formulations [Bosquillon et
al. 2004; Costantino et al. 1998]. A crystalline state of excipients is detrimental for protein stability
because of phase separation and loss of excipients-protein interaction [Carpenter et al. 1997].
Constantino et al. [Costantino et al. 1998] stabilized recombinant humanized Anti-IgE using
mannitol and sodium phosphate. The presence of sodium phosphate was successful in inhibiting the
mannitol crystallization upon spray drying resulting in a significant lowering of solid state
aggregation. During long-term storage some crystallization in the spray-dried formulation was
observed [Costantino et al. 1998]. Spray-dried formulations of albumin together with mannitol and
dipalmitoylphosphatidylcholin also showed a fully amorphous structure of the produced particles
[Bosquillon et al. 2004].
A 100 mg/ml was prepared for single droplet drying experiments in the levitations system.
Experiments were carried out at 60°C and different humidity as well as at different ventilation
velocity. The liquid properties were determined before starting the levitation procedure. The data is
shown in Table 5.8.
Table 5.8: Liquid properties and levitation size range for mannitol solutions with different solid content.
Solid
content
Surface
tension γ
[ mg/ml ] [ ]
Density
ρ liquid
3
mN/m [ ]
Maximum
diameter
Maximum
volume
Minimum
diameter
Minimum
volume
g/cm [ mm ] [ µl ] [ µm ] [ µl ]
100.0 73.49 ± 0.08 1.030 6.53 145.8 15 1.77⋅10 -6

160 RESULTS AND DISCUSSION
Data analysis of mannitol solution experiments
The analysis of the experimental data of the mannitol solution droplets has to be divided into two
different drying stages. In contrast to maltodextrin and trehalose, the mannitol droplets behave
different at the transition between constant and falling rate. An immediate particle formation occurs
at the critical point resulting in a sharp break of the curve plotting the size versus evaporation time.
The horizontal and vertical diameters do not change any more in the second drying stage leading to
a constant aspect ratio and a constant size of the particle. The rise of the particle in the falling rate
can be determined without taking account of any impressions caused by the standing acoustic wave
after the initial particle formation. Even though an influence of the SPL on changes of the particle
shape within the second drying stage cannot be seen, the minimal value for a stable levitation was
chosen. In some experiments the immediate particle formation at the critical point leads to strong
oscillations of the new formed particle resulting in the impossibility to calculate the evaporation rate
in the second drying stage or even a drop-out of the particle of its pressure node. In contrast,
levitation experiments with stable droplet / particle position at the same drying conditions can also
be found. It seems that the shape of the resulting particle has an influence on the stability of the
formed particle at the critical point and within the second drying stage. Figure 5.71 shows the raw
data of the drying of a mannitol solution with 100 mg/ml solid content at 60°C and 10% relative
humidity with the stable behaviour of the particle at the transition from first to second drying stage.
The evaporation rate in the falling rate is again calculated using the rise of the particle in the
constant stationary ultrasonic field. The end of solvent evaporation is characterized by a constant
particle size and a constant particle position. A gallery of front illumination pictures of the drying
process for mannitol at room temperature can be seen in Figure 5.72. In contrast to maltodextrin and
trehalose that form glassy, almost transparent particles, the particles of mannitol are white and nontransparent.
A size reduction or a flattening of the particle due to influences of the ultrasonic field
cannot be seen in Figure 5.72. The final particles show a fragile structure. Low mechanic pressure
causes the break of the particle and the formation of a small amount of white powder.
A ventilation of 1.0 m/s at 60°C and 5% humidity of the drying air leads to an increase in
the evaporation rate from 1.4 µg/s/mm 2 to almost 2.4 µg/s/mm 2 . Therefore, a decrease in the
duration of the first drying stage is observed. As with still air, the evaporation rate in the first drying
stage gives higher values for mannitol than for trehalose. Experiments at a humidity of 20% and
40% and a ventilation velocity of 1.0 m/s do not show a second drying stage at all. The position of
the particle stays constant after the critical point and no tendency of a rise of the centre of mass

CHAPTER 5 RESULTS AND DISCUSSION 161
towards its adjacent upper pressure node can be observed. The raw data of mannitol experiments at
20% and 40% humidity are presented in Figure 5.71.
2 ) [-] Aspect ratio [-]
2 / rS 0
Droplet / particle diameter [µm]
( r S
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
Droplet / particle size
Aspect ratio
Vertical position
0.0
-100
0 200 400 600 800 1000
1400
1200
1000
800
600
Constant rate
Falling rate
Evaporation time [s]
Horizontal diameter
Vertical diameter
Aspect ratio
Figure 5.71: Raw data of the levitation of a mannitol solution droplet with 100 mg/ml solid content without ventilation.
The drying air had a temperature of 60°C and a relative humidity of 10%. The initial droplet size was 1.7 µl at an initial
effective SPL of 164.8 dB. The dashed red line marks the position of the critical point.
20
0
-20
-40
-60
-80
400
1.0
0 200 400 600 800 1000
Evaporation time [s]
1.5
1.4
1.3
1.2
1.1
Particle distance to adjacent node [µm]
Aspect ratio [-]

162 RESULTS AND DISCUSSION
Figure 5.72: Evaporation of a mannitol solution droplet with 100 mg/ml solid content at 25°C and 28% relative
humidity without ventilation. Pictures were taken with the CCD-camera every 20 seconds. The gallery starts with the
3.5 minutes after the injection of the droplet. The initial droplet volume was 1.7 µl at an initial effective SPL of
164.8 dB.
The evaporation rate of mannitol droplets with a solid content of 100 mg/ml at a temperature of
60°C and different relative humidity is determined using the method compensating the different
initial droplet volumes. The plot is presented in Figure 5.73. The evaporation rate in the first drying
stage decreased with increasing humidity of the drying air. This leads to an increase in duration of
the first drying stage equal to maltodextrin and trehalose. In contrast to the other two sugars,
mannitol shows a sharp break in the curve for the evaporation rate of all tested ambient conditions,
even at high humidity. Also interesting are the larger values of the evaporation rate for mannitol in
the first drying stage than for maltodextrin and trehalose. Even though a 100 mg/ml solution
contains more dissolved mannitol molecules than a trehalose solution with the same solid
concentration, the evaporation rate for mannitol is higher than for trehalose. This is observed at all
tested humidity conditions of the drying air.

CHAPTER 5 RESULTS AND DISCUSSION 163
Evaporation rate [µg/s/mm 2 ]
Figure 5.73: Evaporation rate of mannitol solutions with 100 mg/ml solid content at a drying temperature of 60°C and
different humidity. The initial droplet volume of the experiments was 1.7 µl at an initial effective SPL 164.8 dB.
Evaporation rate [µg/s/mm 2 ]
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0 500 1000 1500
2.5
2.0
1.5
1.0
0.5
Critical point
2 2
( t / r ) [s/mm ]
S 0
Rel. humidity 5%
Rel. humidity 10%
Rel. humidity 20%
Rel. humidity 40%
Ventilation 0.0 m/s
Ventilation 1.0 m/s
[60°C - rel. humidity 5%]
0.0
0 200 400 600 800
2 2
( t / r ) [s/mm ]
S 0
Figure 5.74: Comparison of the evaporation rate of mannitol solutions with 100 mg/ml solid content at a drying
temperature of 60°C and 5% humidity in still air and with ventilation of 1.0 m/s. The initial droplet volume of the
experiments was 1.7 µl at an initial effective SPL 164.8 dB.
In contrast to maltodextrin and trehalose, the ventilation of the mannitol particle with humid air
seems to prevent further drying. A comparison of the amount of solvent evaporated in the first
drying stage shows an increase from 63.4 ± 2.7% (n=3) at 5% humidity to 81.9 ± 1.3% (n=3) at
20% humidity to 92.9 ± 0.2% (n=3) at 40% humidity. Calculations of evaporated solvent for pure
water droplets at the same conditions do not show an additional evaporation of condensed water
vapour. Furthermore, the final particles also show a moist behaviour when trying to take SEM
pictures. According to the evaporated solvent in the first drying stage and the non-existence of a
second drying stage in the experimental data, the particles produced at 40% humidity have

164 RESULTS AND DISCUSSION
theoretically a lower residual humidity than the particles dried at 20% humidity. More probable is
that the rise of the particle is so minimal and at the same time the oscillations of the particle due to
the ventilation are that large, that the second drying stage cannot be detected. The particles are
affected very easily by the air stream in the second drying stage due to an unbalanced particle shape
causing turbulences in the area of the pressure node. The strong oscillations starting at the critical
point can be seen in Figure 5.75 marked by the ellipse. The higher the drying air velocity, the more
abstract the shape becomes. Additionally, the densities of the particles show the lowest values for
all examined sugars at drying air conditions 1.0 m/s and 60°C. Equal to maltodextrin and trehalose,
an increase in particle size and a decrease in particle density with decreasing humidity and
increasing ventilation can be observed.
2 ) [-] Aspect ratio [-]
2 / rS 0
( r S
Instable particle position after the critical point
1.6
1.4
1.2
1.0
0.8
0.6
0.4
Droplet / particle size
Aspect ratio
Vertical position
0.2
[60°C - humidity 20% - 1.0 m/s]
-200
0 150 300 450 600 750
(a)
Evaporation time [s]
Figure 5.75: Raw data mannitol solution droplets with 100 mg/ml solid content. The drying air had a temperature of
60°C and a ventilation velocity of 1.0 m/s. The dashed red line marks the position of the critical point.
(a) Relative humidity 20%. The initial droplet size was 1.4 µl at an initial effective SPL of 162.5 dB. (b) Relative
humidity 40%. The initial droplet size was 1.7 µl at an initial effective SPL of 166.6 dB.
Elversson and Millqvist-Fureby [Elversson 2005] determined the effective particle density of spray-
dried mannitol ( = 200 ° C; T = 90°
C; Liquid feed = 5ml/min)
T outlet
50
0
-50
-100
-150
Particle distance to adjacent node [µm]
2 ) [-] Aspect ratio [-]
2 / rS 0
( r S
Particle distance to adjacent node [µm]
Instable particle position after the critical point
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0 150
50
0
-50
Droplet / particle size
Aspect ratio
-100
Vertical position
-150
[60°C - humidity 40% - 1.0 m/s]
-200
300 450 600 750
Evaporation time [s]
inlet calculated from droplet-to-
particle measurements as 0.24 g/cm 3 for a 5% (w/w) solution and 0.30 g/cm 3 for a 15% (w/w)
solution. The calculated particle density of the dried mannitol solution droplets with 100 mg/ml at
60°C, 5% humidity and drying air velocity of 1.0 m/s in this work is 0.32 ± 0.01 g/cm 3 (n = 3).
They determined the apparent particle density using a gas pycnometer to 1.50 g/cm 3 for the
5% (w/w) solution and 1.49 g/cm 3 for the 15% (w/w). Due to blow holes in many of their mannitol
particles the measured density corresponded well to the true density of mannitol (1.51 g/cm 3 ). The
BET surface area of the spray-dried mannitol powder was determined as 4.63 m 2 /g at a particle size
of 4.00 µm (5% (w/w)) solution to 4.04 m 2 /g at a particles size of 5.01 µm (15% (w/w))
[Elversson 2005].
(b)

CHAPTER 5 RESULTS AND DISCUSSION 165
Particle radius relative to initial droplet radius [%]
70
65
60
55
50
Ventilation 0.0 m/s
Ventilation 1.0 m/s
0 5 10 15 20 25 30 35 40 45
Relative humidity of drying air at 60°C [%]
Figure 5.76: Comparison of the resulting particle size and density of mannitol solutions with 100 mg/ml solid content,
dried 60°C with different humidity and drying air velocity. The initial droplet volume of all experiments was between
1.5 µl and 2.0 µl at an initial effective SPL of 162.5 dB to 166.6 dB. (a) Particle radius compared to the initial droplet
radius with ventilation velocity at different humidity. (b) Final particle density with ventilation velocity at different
humidity.
The SEM pictures of the final particles show a mostly spicular shape of the particle surface
depending on the temperature, humidity and velocity of the drying air. The strongest distinctive
spicular morphology is observed for particles dried in still air at room temperature (Figure 5.77 a/b).
The particles are only partially spherical with protuberances at their surface.
(a) (b)
0.2
0 5 10 15 20 25 30 35 40 45
Figure 5.77: SEM pictures of mannitol particles with 100 mg/ml solid content from the levitation system dried at 25°C
and 20% relative humidity in still air. Shown are pictures with a magnification of 100-times (a) and 350-times (b).
Particle density [g/cm 3 ]
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
Ventilation 0.0 m/s
Ventilation 1.0 m/s
Relative humidity of drying air at 60°C [%]

166 RESULTS AND DISCUSSION
In literature [Elversson 2005] solid state characterization of spray-dried mannitol solutions
( = 200 ° C; T = 90°
C; Liquid feed = 5ml/min)
T outlet
inlet showed an 89 to 100% crystalline mannitol
fraction. This leads to the conclusion that sharp critical point in the evaporation curve of the
levitated droplets and the spicular surface morphology is caused by the crystallization of mannitol
during the drying process.
The levitation experiments with faster solvent evaporation at 60°C and 5% relative humidity
in still air (Figure 5.78) lead to particles with a smoother surface compared to the particles produced
at room temperature (Figure 5.77). Particles from different experiments all under the same drying
air conditions show different particle morphology (Figure 5.78 a and c). No two particles with the
same shape could be found. The investigated particles all differ in their protuberances but all show a
hollow interior with blow holes in their surface (Figure 5.78 c, Figure 5.79). A substantial influence
of the drying air humidity on the structure cannot be seen. It seems that the prolongation of the
drying time due in higher humidity environment increases the spicular particle morphology (Figure
5.80 and Figure 5.81). A constant particle shape at higher humidity cannot be found, either. A
comparison of the surface morphology with spray-dried mannitol is difficult due to the insufficient
magnification of the small particles of the spray-dried product (Figure 5.81). The SEM pictures of
spray-dried mannitol in largest magnification (Figure 5.81 b) show particles with a smooth surface.
A spicular surface structure cannot be determined. Equal to the levitated particles, hollow particle
interior and blow holes in the surface can be seen. Many fragments and broken particles can be
seen. Exceptional particles can be found when drying under drying air velocity conditions (Figure
5.82) at 60°C and 0.1% drying air humidity. The final particles have the structure of a bowl (Figure
5.82 a). The bottom side of the particle facing the air stream has an almost smooth whereas
protuberances are formed on the top side (Figure 5.82 d). The particles are flatter than under still air
conditions. An increase in drying air humidity and, therefore, an increase in drying time also seems
to lead to the development of more spicular surface structure than at 0.1% humidity (Figure 5.83).
Still the morphology of particles dried under the same drying air conditions varies in a way that a
clear influence of the ambient conditions cannot be seen.

CHAPTER 5 RESULTS AND DISCUSSION 167
(a) (b)
blow holes
(c) (d)
Figure 5.78: SEM pictures of mannitol particles with 100 mg/ml solid content from the levitation system dried at 60°C
and 5% humidity in still air. Shown are pictures of two different particles with a magnification of 100-times (a), 300times
(b), 100-times (c) and 350-times (d).
(a) (b)
hollow
interior
Figure 5.79: SEM pictures of mannitol particles with 100 mg/ml solid content from the levitation system dried at 60°C
and 10% relative humidity in still air. Shown are pictures with a magnification of 100-times (a) and 300-times (b).

168 RESULTS AND DISCUSSION
(a) (b)
(c) (d)
Figure 5.80: SEM pictures of mannitol particles with 100 mg/ml solid content from the levitation system dried at 60°C
and 20% relative humidity in still air. Shown are pictures with a magnification of 100-times (a), 600-times (b), 500times
(c) and 1000-times (d).
(a) (b)
Figure 5.81: SEM pictures of spray-dried mannitol particles with 100 mg/ml solid content in a Buchi-Mini-Spray-
Dryer B 190 with Tinlet = 100°C, Toutlet = 60°C and a liquid feed of 3 ml/min. Shown are pictures with a magnification of
1000-times (a) and 2500-times (b).

CHAPTER 5 RESULTS AND DISCUSSION 169
(a) (b)
(c) (d)
Figure 5.82: SEM pictures of mannitol particles with 100 mg/ml solid content from the levitation system dried at 60°C
and 0.% relative humidity with a drying air velocity of 1.0 m/s. Shown are pictures with a magnification of 80-times (a),
600-times (b), 150-times (c) and 500-times (d).
(a) (b)
Figure 5.83: SEM pictures of mannitol particles with 100 mg/ml solid content from the levitation system dried at 60°C
and 20% relative humidity in still air. Shown are pictures with a magnification of 60-times (a) and 1000-times (b).

170 RESULTS AND DISCUSSION
5.3.4 Evaporation of bSA solution droplets
Properties of bSA
The single-chain polypeptide bSA is often used as a model protein in, for example, processing
examinations and physical-state investigations in spray-drying [Adler et al. 2000; Bosquillon et al.
2004; Lucas et al. 1998; Witschi 1999], microencapsulation [Carrasquillo et al. 2001; Elversson
2005 b] and freeze-drying [Izutsu et al. 2004; Tattini et al. 2005]. Its structure and characteristics
are described in detail in Chapter 4.1.1. Lucas et al. [1998] co-processed bSA with maltodextrin to
produce model protein particles by spray-drying to prepare aerosol formulations and examined the
influence of fine particle multiplets as performance modifiers for protein deposition from dry
powder inhalers. The surface composition of spray-dried particles of bSA containing trehalose and
different surfactants was examined using electron spectroscopy for chemical analysis by Adler et al.
[2000]. They found that an increasing amount of polysorbate 80 in the spray-dried solution reduces
protein adsorption at the water/air-interface. Competitive protein absorption between bSA and β-
lactoglobulin during spray-drying was studied by Landstrom et al. [2000]. The powder surface was
examined using fluorescence quenching of pyrene labelled proteins. The surface analysis after
spray-drying of solutions with lower protein concentrations seemed independent of the other protein
present. The aerodynamic behaviour, surface composition and physical state of powder aerosols
containing albumin, dipalmitoylphosphatidylcholine and a protein stabilizer like lactose, trehalose
or mannitol and prepared by spray-drying was investigated by Bosquillon et. al [2004]. Witschi
[1999] prepared starch, chitosan or Carbopol © microspheres containing bSA by spray-drying. Their
particles in a size range between 2-4 µm were characterized by scanning electron mircroscopy and
laser diffraction. The protein release profiles were determined using an open-membrane system and
polarized Calu-3 cell sheets were taken to evaluate relative bioadhesion. Recent studies in the area
of protein encapsulation by spray-drying was done by Elversson and Millqvist-Fureby [Elversson
2005 b]. The aim was to examine to what extent an aqueous two-phase system could improve
protein stability during spray-drying by preventing interactions with the air-liquid interface. The
spray-dried solution contained bSA, polyvinylalcohol (PVA), dextran and in some experiments
trehalose. Their results showed that although bSA was well encapsulated by PVA, a partial loss of
native structure was observed. Other research in protein microencapsulation performed by
Carrasquillo et al. [2001] used excipients-stabilized spray-freeze dried BSA in a non-aqueous oil-inoil
encapsulation methodology for the development of sustained release microspheres. As wall
material poly(D,L-lactide-co-glycolide) (PLG) was used. FTIR analysis showed that bSA released

CHAPTER 5 RESULTS AND DISCUSSION 171
from the microspheres had similar monomer content and the same secondary structure as
unencapsuled BSA. In freeze drying bSA was used as model protein to examine the protective
effects of saccharides with different molecular weight against lyophilisation induced structural
perturbation [Izutsu et al. 2004]. A decreasing structure stabilizing effect of the saccharides with
increasing number of the ssaccharide units was found. Recently, PEGylated bSA was chosen by
Tattini et al. [2005] to investigate the influence of lyophilisation on structure and phase changes.
A 100 mg/ml pure bSA solution and a 100 mg/ml bSA-Trehalose (1:1) mixture were
prepared for single droplet drying experiments in the levitations system. Experiments were carried
out at 60°C and different humidity as well as at different drying air velocity. The liquid properties
were determined before starting the levitation procedure. The data are shown in Table 5.9.
Table 5.9: Liquid properties and levitation size range for bSA and bSA-Trehalose solutions with 100 mg/ml solid
content.
Solid
content
100 mg/ml
Surface
tension
[ ]
Density
ρ liquid
3
mN/m [ ]
Maximum
diameter
Maximum
volume
Minimum
diameter
Minimum
volume
g/cm [ mm ] [ µl ] [ µm ] [ µl ]
bSA 58.1 1.023 5.20 73.5 15 1.77⋅10 -6
bSA-
Trehalose
58.5 1.027 5.21 74.2 15 1.77⋅10 -6
Data analysis of bSA solution experiments
The data analysis of pure bSA droplets / particles is more difficult than the analysis of the sugar
data. As seen with maltodextrin, trehalose and mannitol, the drying process of a pure bSA solution
can be divided into constant and falling rates. The evaporation rate in the first drying stage is
calculated using the decrease in droplet volume [Frohn 2000; Kastner et al. 2001], whereas the
evaporation in the second drying stage after the crust formation is calculated using the rise of the
particle within the constant stationary ultrasonic field. In contrast to the saccharides, the
droplet / particle behaviour shortly after the critical point differs from the experiments reported so
far. In almost all experiments, the new formed particle starts to oscillate after the formation of a
solid crust at the droplet surface. The amplitude of the oscillations increases such that the standing
acoustic wave cannot stabilize the particle any more and it drops out of its levitation position.
Additionally, breaking of the particle within the falling rate can sometimes be seen in the photo
stream taken by the imaging software. The results of pure bSA presented are therefore calculated

172 RESULTS AND DISCUSSION
from the few experiments with a stable droplet / particle levitation. Figure 5.84 presents the raw
data of a bSA solution with 100 mg/ml solid content dried at 60°C and 5% relative humidity in still
air. It can be seen that change in aspect ratio after the formation of the solid crust can be used to
determine the critical point and the transition between first and second drying stages.
2 ) Aspect ratio
2 / rS 0
( r S
Diameter [µm]
Constant rate Falling rate
1.6
100
1.4
0
Distance
1.2
to
1.0
-100
Particle size
0.8
Aspect ratio
adjacent
Vertical position -200
0.6
pressure
-300
0.4
node
0.2
-400
0 100 200 300 400 500 600
[µm]
1200
1100
1000
900
800
700
600
500
Evaporation time [s]
1500 Horizontal diameter
1400
Vertical diameter
1300
Aspect ratio
Change in both diameters
after critical point
400
1.0
0 100 200 300 400 500 600
Evaporation time [s]
Figure 5.84: Raw data of the levitation of a pure bSA solution droplet with 100 mg/ml solid content in still air. The
drying air had a temperature of 60°C and a relative humidity of 5%. The initial droplet size was 1.1 µl at an initial
effective SPL of 166.25 dB. The dashed red line marks the position of the critical point.
1.6
1.5
1.4
1.3
1.2
1.1
Aspect ratio

CHAPTER 5 RESULTS AND DISCUSSION 173
There is a substantial change in vertical as well as in horizontal diameter after the critical point.
Since the effective SPL depends on the particle size, and calculation of the evaporation rate in the
second drying stage requires a constant SPL, the determination of the evaporation coefficient is not
possible. Calculation of the SPL at the critical point and at the end of the size change of the particle
in the falling rate using the method of Yarin et al. [1998] shows a difference of 0.025 from the
maximum of 0.10 dB. This small difference has no substantial influence on the calculated
evaporation rate data and can therefore be neglected. Figure 5.85 shows front illumination pictures
of a levitation experiment of pure bSA solution at 60°C and 5% humidity in still air. As with
maltodextrin, the particle flattens within the second drying stage. The line of breakage of the
particle after the critical point can also be seen and is marked by the white arrows in Figure 5.86.
Figure 5.85: Evaporation of a pure bSA solution droplet with 100 mg/ml solid content at 60°C and 10% relative
humidity without drying air stream. Pictures were taken with the CCD-camera every 10 seconds. The initial droplet
volume was 1.9 µl at an initial effective SPL of 164.2 dB.

174 RESULTS AND DISCUSSION
before breakage after breakage
(a) (b) line of breakage
Figure 5.86: Front illumination pictures of pure bSA particles with 100 mg/ml solid content dried at 60°C and 10%
relative humidity in still air. Shown are pictures directly before (a) and after (b) breakage of the particle.
hole in the
particle top
(a) (b)
Figure 5.87: SEM pictures of pure bSA particles with 100 mg/ml solid content dried at 60°C and 10% relative
humidity in still air. Shown are pictures with a magnification of 100-times (a) and 250-times (b).
Figure 5.87 shows SEM pictures of the broken particle from the front illumination experiment of
Figure 5.85. It can be seen that the drying of the pure bSA solutions forms a hollow particle with a
massive solid crust. The crust does not show any capillary structure. The half of a large hole (“blow
hole”) can be seen in the top side of the bSA particle, whereas the bottom side is intact. Two
different ways of particle formation of the pure bSA solution can be observed. The first way is the
(Figure 5.87) already presented formation of holes in the particle surface during the second drying
stage with a occasional breakage of the particle into two parts. The second way is the formation of
an elliptical to almost spherical particle with intact surface and also a massive crust, that always
breaks in the second drying stage. Particles obtained from the second way of particle formation are
presented in Figure 5.88.

CHAPTER 5 RESULTS AND DISCUSSION 175
(a) (b)
Figure 5.88: SEM pictures of pure BSA particles with 100 mg/ml solid content dried at 60°C and 10% relative
humidity in still air. Shown are pictures with a magnification of 100-times (a) and 500-times (b).
Both the breakage of the particle as well as the formation of a large hole in the particle crust leading
to the formation of an “interior surface” have an influence on the results and the calculation of the
evaporation rate. In the first case, breakage of the particle can result in complete disintegration and
drop-out of the remaining halves out of the standing acoustic wave. A determination of the
evaporation rate within the falling rate is then impossible. If the particle breaks, but the two parts
stick together, water vapour from the inside can easily reach the exterior without having to penetrate
the crust of solid bSA. In the second case, the formation of a hole in the crust and the development
of an interior surface enlarges the surface area of the particle, which results in higher evaporation
rates [Frohn 2000]. Neither of the two cases can be unequivocally recorded by the imaging-software
during the progression of the levitation experiment. The back light illumination produces only a
shadow image of the droplet / particle. Use of front light illumination is difficult, due to the poor
contrast between droplet and background. Therefore, the pictures must be taken with back light
illumination and the evaporation rate calculated as with maltodextrin, trehalose or mannitol. The
evaporation rate of pure bSA solutions with 100 mg/ml solid content at 60°C and different relative
humidity in still air can be seen in Figure 5.89. Increasing drying air humidity results in an increase
in the duration of the first drying stage and a shift of the critical point (Figure 5.89). The
evaporation rate in the second drying stage does not decrease with evaporation time continuously.
An increase in the evaporation rate within the falling rate period occurs. The starting evaporation
rate increase is concurrent to the rupture or break of the particle. The easier solvent evaporation
through holes and the enlarged surface area leads to the increase in the curve in Figure 5.89. The
maximum in the evaporation rate in the falling rate period occurs later with increasing drying air
humidity.

176 RESULTS AND DISCUSSION
Evaporation rate [µg/s/mm 2 ]
1.4
1.2
1.0
0.8
0.6
Critical point
0.4
Rel. humidity 5%
0.2
Rel. humidity 10%
Rel. humidity 20%
0.0
[Drying temperature 60°C]
0 200 400 600 800 1000
2 2
t / r [s/mm ]
S 0
Evaporation rate
increase in
falling rate period
Figure 5.89: Evaporation rate of pure BSA solutions with 100 mg/ml solid content at a drying temperature of 60°C and
different relative humidity. The initial droplet volume of the experiments was between 1.5 and 2.0 µl at an initial
effective SPL between 163.75 and 165.1 dB.
Analysing the SEM pictures of the broken pure bSA particles, the thickness of the solid crust is
determined to 31.75% of the particle radius. Therefore, a spherical particle with a radius of 500 µm
has an apparent volume of 0.524 µl and a void volume of 0.166 µl. The outer surface area of the
particle of 3.14 mm 2 is enlarged by an interior surface of 1.46 mm 2 to an overall surface area of
4.60 mm 2 during the second drying stage. Blow holes in the surface are neglected in these
considerations. No statements about the temporal development of the interior surface can be made
analysing the back light illuminated photo stream of the bSA droplet drying experiment. A
correction of the surface in the falling rate period is not possible. Pictures of the front light
illuminated single droplet drying experiments of the mixture of 50 mg/ml bSA and 50 mg/ml
trehalose can be seen in Figure 5.90. The molar ratio between bSA and trehalose is approximately
1:194. The drying behaviour of the mixture is different to the pure bSA droplets. There is no change
in the horizontal particle diameter after the critical point but small changes in the vertical diameter
(Figure 5.91). Therefore, a small flattening of the particle in the second drying stage can be seen
from the aspect ratio and the live pictures. In contrast to the pure bSA solution, an increase in the
evaporation rate within the second drying stage is not determined for the mixture with trehalose.
With increasing evaporation time in the falling rate, the values of the evaporated mass per time and
surface area get continuously smaller until the end of the drying process. The plot of the
evaporation rate versus time at 60°C and different relative humidity in still air is shown in Figure

CHAPTER 5 RESULTS AND DISCUSSION 177
5.92. As with all other tested substances, an increase in drying air humidity leads to an increase in
duration of the first drying stage.
Figure 5.90: Evaporation of a mixture bSA-trehalose (1:1) solution droplet with 100 mg/ml solid content at Room
temperature and 27% relative humidity without drying air stream. Pictures were taken with the CCD-camera every 30
seconds. The initial droplet volume was 2.0 µl at an initial effective SPL of 164.4 dB. The gallery starts 15 minutes
after droplet injection.
The droplets / particles of the bSA-trehalose (1:1) mixture show more stable levitation behaviour
during the evaporation experiments than pure bSA. Oscillations associated with the particle
formation at the critical point cannot be determined. Considering the course of the evaporation rate
versus time, Figure 5.91 emphasizes this statement. The SEM pictures of the final bSA-trehalose
particles show slightly flattened particle shape with a folded top side (Figure 5.93 a, b). A breakage
of the particles into two or more parts cannot be seen. Instead of that, many small cracks appeared
on the bottom side of the surface (Figure 5.93 c, e and f). It is obvious that those cracks do not have
the same influence on the evaporation rate in the second drying stage than the breakage of the pure
bSA particles has (Figure 5.92). The particle surface itself is rougher for the mixture particles than
for any other of the tested substances (Figure 5.93 d). Destruction of the particles shows a massive
particle interior. Blow holes cannot be found. Therefore, no additional interior surface has to be
taken into account when analysing the evaporation rate versus time. An influence of the drying air
humidity on the particle morphology cannot be seen.

178 RESULTS AND DISCUSSION
(r / r 0 ) 2 Aspect ratio
1.6
1.4
1.2
1.0
0.8
0.6
0.4
Droplet / particle size
Aspect ratio
Vertical position
0.2
-250
0 500 1000 1500
Evaporation time [s]
Figure 5.91: Raw data of the levitation of bSA-Trehalose (1:1) mixture solution droplet with 100 mg/ml solid content
without ventilation. The drying air had a temperature of 60°C and a relative humidity of 5%. The initial droplet size was
2.8 µl at an initial effective SPL of 166.4 dB. The dashed red line marks the position of the critical point.
Evaporation rate [µg/s/mm 2 ]
1.0
0.8
0.6
0.4
0.2
Diameter [µm]
2200
2000
1800
1600
1400
1200
1000
800
Constant rate Falling rate
Horizontal diameter
Vertical diameter
Aspect ratio
constant horizontal diameter
50
0
-50
-100
-150
-200
600
0 500 1000
1.0
1500
Evaporation time [s]
Rel. humidity 5%
Rel. humidity 10%
Rel. humidity 20%
Rel. humidity 40%
[Drying air temp. 60°C]
0.0
0 500 1000 1500
2 2
t / r [s/mm ]
0
1.6
1.5
1.4
1.3
1.2
1.1
Distance to adjecent pressure node [mm]
Aspect ratio
Figure 5.92: Evaporation rate of bSA-
Trehalose (1:1) mixture solutions with
100 mg/ml solid content at a drying
temperature of 60°C and different relative
humidity. The initial droplet volume of
the experiments was between 1.5 and
2.0 µl at an initial effective SPL between
163.8 and 165.9 dB.

CHAPTER 5 RESULTS AND DISCUSSION 179
(a) (b)
(c) (d)
(e) (f)
Figure 5.93: SEM pictures of BSA-Trehalose (1:1) particles with 100 mg/ml solid content dried at 60°C and 5%
relative humidity (a-b) or 20% humidity (c-f) in still air. Shown are pictures with a magnification of 100-times (a,c),
250-times (e), 1000-times (b, d) and 2000-times (f).

180 RESULTS AND DISCUSSION
The comparison of the evaporation rate of single droplets of pure bSA, the mixture of bSAtrehalose
(1:1) and pure trehalose at 60°C and 10% relative humidity in still air is shown in Figure
5.94. The evaporation rate of bSA has larger values in the first drying stage than the mixture and the
pure trehalose due to the lowest amount of dissolved molecules. A 100 mg/ml bSA solution has a
molar concentration of 1.51 x 10 -3 mol/l, whereas the pure trehalose has a molar concentration of
0.29 mol/l. The mixture of bSA and trehalose has a molar concentration of approximately
0.15 mol/l. The first drying stage increases with addition of trehalose to the solution under the same
drying conditions and with the same initial droplet size. The critical point shifts to later points of
time in the drying process. The decline in the evaporation rate in the falling rate period is shallower
for the pure trehalose than for the mixture. In contrary, the values of the evaporation rate after the
decline are larger in the pure trehalose experiments than in the pure bSA or mixture runs. The
percentage of solvent evaporated in the first drying stage at 60°C in still air is listed in Table 5.10.
65.1% of solvent are evaporated in the constant rate of pure bSA solutions, whereas 87.8% of
solvent are evaporated form the bSA-trehalose (1:1) mixture at 5% relative humidity of the drying
air. The values for the bSA-trehalose (1:1) mixture and the pure trehalose solution are almost
identical. No influence of the drying air humidity in the range between 5% and 20% on the amount
of evaporated solvent can be seen either for these to system. The calculated values at 40% are larger
than at lower humidity caused by the difficulty to determine the exact critical point due to the slow
drying process. The standard deviation at 40% humidity is larger than at all other drying air
humidities. The pure bSA solution shows a decrease in the amount of evaporated solvent in the
constant rate with increasing drying air humidity.
Table 5.10: Percentage of evaporated solvent in the first drying stage at 60°C and different relative humidity in still air.
Relative humidity Percentage of evaporated solvent in the first drying stage (n=3)
of drying air bSA bSA-Trehalose (1:1) Trehalose
mg/ml
mg/ml
100 mg/ml
[ % ]
[ 100 ]
[ 100 ]
[ ]
5 65.1 ± 1.9 87.8 ± 0.7 85.6 ± 1.8
10 64.3 ± 1.1 87.6 ± 0.7 87.8 ± 1.7
20 61.3 ± 1.8 87.9 ± 0.5 86.5 ± 1.9
40 - 92.2 ± 2.5 91.6 ± 3.1

CHAPTER 5 RESULTS AND DISCUSSION 181
Evaporation rate [mg/s/mm 2 ]
1.4
1.2
1.0
0.8
0.6
0.4
0.2
Figure 5.94: Comparison of the evaporation rate of pure bSA, bSA-trehalose (1:1) mixture and pure trehalose solutions
with 100 mg/ml solid content at a drying temperature of 60°C and 10% relative humidity in still air. The initial droplet
volume of the experiments was 1.5 µl an initial effective SPL between 164.1 and 164.5 dB. Due to the different density
of the solutions, the initial effective SPL differed at constant initial droplet volume. This effect is neglected in the
considerations of the experiment.
For comparison with the spray-dried product, bSA and bSA-trehalose (1:1) solutions with a solid
content of 100 mg/ml are spray-dried using the Buchi Mini Spray Dryer B-191. The SEM pictures
of the final powders are presented in Figure 5.95 and compared to the spray-dried pure trehalose
particles of Figure 5.67. bSA shows particles with a smooth surface and a donut-like shape with
dimples and holes. In contrast to this result, Maa et al. [1997] found a wrinkled or raisin-like surface
morphology for spray-dried pure bSA, produced under similar process conditions
[Tinlet = 90°
C, Toutlet
= 53°
C, Liquid feed =
Critical point and end of first drying stage
0.0
0 250 500 750 1000 1250 1500 1750 2000
2 2
( t / r ) [s/mm ]
S 0
5ml/min]
bSA pure
bSA-Trehalose (1:1)
Trehalose pure
larger evaporation rate
with increasing
trehalose content
. The addition of trehalose to the bSA solution
changed the appearance of the spray-dried particles. As found for rhGH [Maa et al. 1997] and
granulocyte stimulation factor [Niven et al. 1993], the particles of the formulated protein show a
wrinkled surface shape. The spray-dried pure trehalose particles are mostly spherical with a smooth
surface (Figure 5.67). The change in surface morphology from the smooth and spherical trehalose to
the raisin-like structure of the bSA-trehalose mixture is an effect of the addition on an high
molecular weight substance, which alters the balance of surface-to-viscous forces controlling the
droplet shape during the drying process [Alexander 1978]. ESCA (Electron Spectroscopy for
Chemical Analysis) of spray-dried pure bSA, pure trehalose and bSA-trehalose (5:95) mixture
particles performed by Adler et al. [2000] gave an approximately 9 times higher N-level for the
mixture than expected from a homogeneous distribution of bSA within the trehalose particles. They

182 RESULTS AND DISCUSSION
attributed this increase to the adsorption of bSA to the liquid-air interface of the atomized droplets
before they dry.
(a) (b)
Figure 5.95: (a) SEM picture of spray-dried bSA particles with 100 mg/ml solid content in a Buchi-Mini-Spray-Dryer
B 190 with Tinlet = 100°C, Toutlet = 60°C and a liquid feed of 3 ml/min. Shown is a picture with a magnification of
3000-times (b) SEM picture of spray-dried bSA-trehalose (1:1) mixture particles with 100 mg/ml solid content in a
Buchi-Mini-Spray-Dryer B 190 with Tinlet = 100°C, Toutlet = 60°C and a liquid feed of 3 ml/min. Shown is a pictures
with a magnification of 2000-times.
The influence of trehalose on the size and density of the final particles resulting from the levitated
solutions at 60°C and different relative humidity in still air can be seen in Figure 5.96. As with all
other tested substances before, the particle size of bSA and the bSA-trehalose (1:1) mixture
decreases with increasing drying air humidity and increasing drying time. The final particle density,
however, increases with increasing drying air humidity. The final particle density of the bSA
particles is smaller at the same ambient conditions than the density of the bSA-trehalose (1:1)
mixture. At 60°C and 5% relative humidity drying conditions the bSA particles have a density of
averaged 0.62 g/cm 3 , whereas the mixture particles with trehalose have a density of 0.95 g/cm 3 .
Figure 5.96 presents that the drying of the bSA-trehalose (1:1) mixture and the pure trehalose yields
almost the same particle size and density. The pure trehalose particles are only marginally smaller
in size and only marginally larger in density than the bSA-trehalose (1:1) mixture. The course of the
density as a function of evaporation time for all three formulations at 60°C and 5% relative
humidity in still air can be seen in Figure 5.97. All curves start at approximately the same point
because of their similar liquid density. After an initial increase in density due to an increasing solid
content and a decrease in droplet volume, the density decreases as soon as a constant droplet
volume is reached due to evaporation of liquid from inside the particle. Using this plot it can be
seen that there are still changes in volume after the critical point, because of a further increase in
density within the second drying stage. The maximum values of the density during the drying

CHAPTER 5 RESULTS AND DISCUSSION 183
experiments are determined to 1.064 g/cm 3 for pure bSA solution, 1.244 g/cm 3 for the bSAtrehalose
(1:1) mixture and 1.451 g/cm 3 for the pure trehalose solution. The final particle densities
are equal to the data of Figure 5.96.
Particle radius relative to initial droplet radius [%]
56.0
54.0
52.0
50.0
48.0
46.0
44.0
42.0
0 10 20 30 40
(a)
Pure bSA (100 mg/ml)
bSA-Trehalose (100 mg/ml)
Pure trehalose (100 mg/ml)
Relative humidity of drying air [%]
0 10 20 30 40
Figure 5.96: Comparison of the resulting particle size and density of pure bSA, bSA-trehalose (1:1) and pure trehalose
solutions with 100 mg/ml solid content, dried 60°C with different humidity in still air. The initial droplet volume of all
experiments was between 1.5 µl and 2.0 µl at an initial effective SPL of 163.1 dB to 165.9 dB. (a) Particle radius
compared to the initial droplet radius versus drying air humidity. (b) Final particle density versus drying air humidity.
Droplet / particle density [g/cm 3 ]
1.6
1.4
1.2
1.0
0.8
0.6
[60°C - 5% rel.humidity]
Figure 5.97: Droplet / particle density as a function of (t / rS 0 2 ) for pure bSA, bSA-trehalose (1:1) mixture and pure
trehalose solutions with a solid content of 100 mg/ml at 60°C and 5% relative humidity in still air. The initial droplet
volume of the experiments was 1.5 µl an initial effective SPL between 164.1 and 164.5 dB.
Final particle density [g/cm 3 ]
1.2
1.1
1.0
0.9
0.8
0.7
0.6
(b)
0 500 1000 1500 2000
2 2
( t / r ) [s/mm ]
S 0
Pure bSA (100 mg/ml)
bSA-Trehalose (100 mg/ml)
Pure trehalose (100 mg/ml)
Relative humidity of drying air [%]
pure trehalose
bSA-trehalose
pure bSA

184 RESULTS AND DISCUSSION
Levitation experiments with drying air velocity cannot be performed for the pure bSA solution. As
with the experiments in still air, the droplet / particle shows an instable behaviour after the
formation of a solid crust. In combination with the stress related to the direct air streaming the
droplet is blown out of the standing acoustic wave into the environment in almost every experiment.
In case that the particle stays levitated the droplet oscillations are so strong that a determination of
the evaporation rate in the second drying stage using the rise of the centre of mass of the particle to
its next adjacent pressure node is not possible. The particles of these experiments are only used for
taking SEM pictures (Figure 5.98). As with the particles obtained under still air conditions, the pure
bSA particles show a hollow interior, whereas the mixture of bSA and trehalose has a massive
particle structure. Analysing the SEM picture of a pure bSA particle dried at 60°C and 5% relative
humidity in a drying air velocity of 1.0 m/s, the solid crust has a thickness of 22.34% of the particle
radius. This is much smaller than the 31.75% obtained in still air. Assuming a spherical particle
with a radius of 500 µm, the void volume inside the particle would be 0.245 µl at a total volume of
0.524 µl. With increasing drying air humidity and increasing drying time, the solid crust of the
hollow bSA particle seems to get larger in relation to the particle radius. A large magnification of
the solid particle crust enables to see two to three different shell areas. The top level shell looks like
a thin particle coating skin with small circular slots on the surface. Persisting capillaries cannot be
seen. The next level is a porous area with lots of very small cavities. This thickness of this area is
increasing with increasing drying air humidity. It is not found at 5% drying air humidity.
(a)
Figure 5.98: SEM pictures of pure bSA particles with 100 mg/ml solid content dried at 60°C and 5% relative humidity
at a drying air velocity of 1.0 m/s. Shown are pictures with a magnification of 70-times (a) and 4000-times.
(b)

CHAPTER 5 RESULTS AND DISCUSSION 185
The innermost and also largest shell area appears massive and uniform on the SEM pictures. It does
not show any holes, capillaries or inhomogeneity in its structure. The appearance of this area in
Figure 5.99 d is associated to a bad waste edge. The discussed overall structure of the particle shell
area is only seen at the outer surface of the particle and not at the inner surface developing during
the drying process. The inner surface is formed by the third massive shell area.
(a) (b)
(c) (d)
Figure 5.99: SEM pictures of pure bSA particles with 100 mg/ml solid content dried at 60°C and 1.0 m/s drying air
velocity in 20% relative humidity (a-b) or 40% humidity (c-d). Shown are pictures with a magnification of 125-times
(a), 1000-times (b), 100-times (c) and 500-times (d).

186 RESULTS AND DISCUSSION
Interfacial behaviour and surface excess of bSA
To investigate the earlier critical point of the pure bSA solutions and the smaller amount of solvent
evaporated in the first stage of the drying process in comparison to the pure trehalose and the bSAtrehalose
solution, the surface activities of the different substances were analysed using a bubble
pressure tensiometer. Due to their dual hydrophobic / hydrophilic nature, dissolved proteins tend to
orient themselves so that the exposure of the hydrophobic parts of the protein to the aqueous
solution is minimized [Randolph 2002]. In systems with air / water interfaces, proteins tend to
accumulate at these interfaces exposing their hydrophilic portion to water. This kind of orientation
and surface adsorption can also occur at solid / water interfaces, such as those found during the
drying process between the solid crust at the droplet /particle surface and the liquid interior
[Fuhrling 2004; Randolph 2002]. If according to classical thermodynamics, the surface tension of
the interface exceeds the internal tension of the protein, the surface area of the protein must increase
for example by unfolding, until the two values are equal [Verger et al. 1973]. If only an equilibrium
monolayer would be formed by surface adsorption and unfolding of the protein, the amount of
adsorbed protein would be small [Randolph 2002; Verger et al. 1973]. However, additional
processes like gas-to-liquid surface transitions, surface precipitation and the formation of surface
sublayers can occur, depending on the degree of hydrophobicity and the characteristics of the
protein. According to de Jongh et al. [2004], the events describing the adsorption process of
proteins at air-liquid interfaces are firstly bulk diffusion that is determined by the molecular size.
Secondly, net adsorption, which is related to the kinetic barrier determining the ratio of sticking to
or bouncing from the interface. Thirdly, conformational changes that are determined by the
activation energy required to disrupt part of the protein’s globular stability. Fourthly, protein
networking, determined by the chemical reactivity or physiochemical activity of side chains that are
related to local system conditions like the dielectric constant. Fifthly, response to externally applied
shear conditions. Additionally, the orientation of protein molecules in the adsorbed phase must be
considered because of their non-uniformity in properties or structure across their exterior surface.
Adsorbed proteins are not free to rotate, because of multiple bonding between protein and adsorbed
surface and therefore a fixed array of exterior amino acids residues of the protein is exposed to the
bulk phase [Horbett 1992]. The driving force of protein adsorption at interfaces is a decrease in
entropy of the water molecules that are ordered around the protein’s hydrophobic parts when the
protein is in bulk solution. It is determined not only by the hydrophobicity but also by the flexibility
of the protein. A flexible protein can expose addition non-polar residues, leading to an increase in
strength of the binding to the surface [Tripp 1995]. Adsorption and unfolding of the protein can lead
to nearly a complete loss of native activity [Randolph 2002; Verger et al. 1973]. In contrast, a gain

CHAPTER 5 RESULTS AND DISCUSSION 187
of structure, for example by an increase in α-helical content, is reported in literature for some
proteins [Caessens et al. 1999]. When proteins are adsorbed at interfaces, the interfacial tension will
decrease dynamically from the value of the pure solvent to the lower equilibrium value. Tripp and
Magda [Tripp 1995] divide this process into three different dynamic interfacial kinetic regimes.
First, the induction time with little or no apparent decrease in the interfacial tension. Secondly, a
rapid interfacial tension decrease when approximately 50% of the monolayer surface coverage is
reached. Thirdly, the meso-equilibrium interfacial tension that results in the steady-state interfacial
tension when the protein molecules have achieved their equilibrium confirmation and surface
concentration at the interface.
Figure 5.100 shows the air / water interfacial tension versus log time isotherms obtained
with bSA solutions with concentrations varied from 0.1 to 4.0 mmol for a solution volume of 10 ml
in a bubble pressure tensiometer. Even after an interfacial lifetime of only 1 ms (log t = -3.0) the
values for the dynamic interfacial tension are lower than that of 72.8 mN/m measured for pure
water. For low bSA concentration (0.1 mmol) the values after this time lies only marginally below
pure water. With increasing solid concentration and increasing interfacial lifetime the interfacial
tension decreases. Because protein adsorption and rearrangement extends over long time of a few
hours to some days before equilibrium is reached and long-time approximation is regarded more
accurate than short-time, recent studies on proteins dynamic interfacial tension have measured at
interfacial lifetimes ≥ 1 s and applied long-time approximation to describe the interfacial tension
versus time [Chen et al. 1998; Tripp 1995]. In spray-drying however, the relevant time scale for
atomisation and droplet drying is < 1 s [Nurnberg 1980], in which it is expected that short time
approximation is valid. The time range of a single droplet drying experiment in the acoustic
levitation system at 60°C is from seconds to a few minutes depending on the drying air humidity
and velocity.
The Ward and Tordai Equation considers diffusion-controlled adsorption to the surface of
a protein or surfactant solution in equilibrium with its bulk which is suddenly expanded or
compressed. They integrated the diffusion equation using Green’s function with the boundary
condition for conservation of mass at the surface and the boundary conditions far away from the
surface [Joos 1999].

188 RESULTS AND DISCUSSION
Dynamic interfacial tension [mN/m]
74.0
72.0
70.0
68.0
66.0
64.0
bSA solution
0.1 mmol
62.0
0.5 mmol
1.0 mmol
60.0
2.0 mmol
58.0
4.0 mmol
0.0 1.0 2.0 3.0 4.0 5.0
Effective time [s]
Figure 5.100: Dynamic air / water interfacial tension as a function of time of bSA solutions with concentration of
minimum 0.1 mmol to 4.0 mmol measured at 25°C.
1/
2
t
⎛ D ⎞ ⎡
⎤
Equation 5.8 Γ () t = Γ0
+ 2⎜ ⎟ ⋅ ⎢c0
t − ∫ cS
⋅ ( t −υ
) ⋅ d υ ⎥
⎝ π ⎠ ⎢⎣
0
⎥⎦
Γ is the surface excess concentration, D the diffusion coefficient, c the concentration and υ the
relaxation. In case that Γ 0 , then at early times the diffusion-controlled process 0 ≈ c and the
0 =
convolution integral of Ward and Tordai can be neglected, resulting in a “short-time”
approximation [Joos 1999]
⎛ D ⋅ t ⎞
Equation 5.9 Γ () t = 2 ⋅ c0
⋅ ⎜ ⎟
⎝ π ⎠
1/
2
In terms of surface pressure, Π () t γ − γ ( t)
= Γ ( t)RT
⎛ D ⋅ t ⎞
Equation 5.10 Π () t = γ 0 − γ () t = 2 RTc0⎜
⎟
⎝ π ⎠
= 0 , this can be rearranged to
The measured dynamic surface pressure, Π ( t)
, should therefore increase linearly with t in the
early times of the adsorption process [Joos 1999].
For a “long-time” approximation the Ward and Tordai equation is reformed as
1/
2 t
⎛ D ⎞
= ⎜ ⎟
S
⎝ π ∫ with Δ cS = cS
− c0
⎠ 0
Equation 5.11 Γ () t −2
⋅ Δ c ( t −υ
) d t
Dynamic interfacial tenion [mN/m]
74.0
72.0
70.0
68.0
66.0
64.0
62.0
60.0
58.0
bSA solution
0.1 mmol
0.5 mmol
1.0 mmol
2.0 mmol
4.0 mmol
-3.0 -2.0 -1.0 0.0 1.0
Log of time in seconds [-]
S

CHAPTER 5 RESULTS AND DISCUSSION 189
Over the interval at large times, Δ cS
changes little and Equation 5.11 can be given by
1/
2
⎛ 4Dt
⎞
Equation 5.12 Γ () t = ⎜ ⎟ ( c0
− cS
)
⎝ π ⎠
If the change in concentration is linearized with respect to the interfacial tension, γ () t , and if the
Gibbs equation dγ = −RT
⋅ Γ ⋅ dc / c0
is used, the “long-time” approximation to Ward and Tordai
becomes
Equation 5.13 γ () t
γ
− ∞
0
1/
2
2
RT ⋅ Γ ⎛ π ⎞
= ⋅ ⎜ ⎟
c ⎝ 4Dt
⎠
Figure 5.101 shows the relationship between surface pressure and interfacial tension, to convert the
above equations to representations of surface pressure. At low concentrations, when
Π () t / Π ≤ 0.
1 the short-time approximation is valid [Joos 1999]. The long-time approximation
∞
describes bulk-to-surface diffusion as single adsorption mechanism [Fuhrling 2004]. For short-time
approximation the plot of Π () t / Π ∞ versus t should be linear, whereas for long-time
approximation the plot of Π ∞ () t / Π ∞ versus 1 / t should be linear.
Π (t) Π∞ (t)
γ 0 γ (t) γ∞
Π∞
Figure 5.101: Relationship between surface pressure and interfacial tension [Fuhrling 2004].
In Figure 5.102, Π () t / Π ∞ is plotted versus t for the bSA solutions for diffusion –controlled
adsorption. The values of Π ∞ were determined by equilibrium ring tensiometry after an
equilibration time of 3 hours and corrected using the method by Harkins and Jordan [Harkins 1930].
The results are shown in Table 5.11. In comparison to data published by Tripp [1995] who found an
meso-equilibrium interfacial tension of 52.7 mN/m for an aqueous 0.015 mmol bSA solution at

190 RESULTS AND DISCUSSION
25°C and recently by Wen [2001], who found an equilibrium interfacial tension of 50 mN/m for an
aqueous bSA solution of the same concentration, the experimental values in this work are higher.
Table 5.11: Values for equilibrium interfacial tension after 3 hours for aqueous bSA solutions at 25°C ambient
temperature using ring tensiometry.
Concentration of
bSA solution
Equilibrium
interfacial tension
[ mmol ] 0.1 0.5 1.0 2.0 4.0
[ mN/m ] 57.4 56.5 56.1 54.9 54.4
Π (t) / Π ∞
Figure 5.102: Π (t) / Π ∞ as a function of time ½ of bSA solutions with different molar concentration at 25°C measured
with bubble pressure tensiometry.
In Figure 5.102 the plot of the short-time approximation shows a biphasic behaviour with two
almost linear ranges separated by a clear break point at approximately 500 ms ( t = 0.
7 ). The
slopes of the initial section at t ≤ 500 ms increase with higher protein concentration, but are almost
equal for the three most concentrated bSA solutions. The linearity occurs at longer adsorption times
than that of Π () t / Π ≤ 0.
1 stated by Joos [1999]. The slopes in the second linear section for
∞
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
4.0 mmol
2.0 mmol
1.0 mmol
0.5 mmol
0.1 mmol
0.0
[bSA solution at 25°C]
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Time 1/2 [s 1/2 ]
t ≥ 500 ms are equal for all bSA concentrations. Π ( t ) / Π ∞ increases much slower than in the slope
in the initial section. Thus, the diffusional adsorption is evidently reduced in rate at the latter points
in the curves of Figure 5.102. According to Fuhrling [2004], it seems that a barrier to adsorption is
formed.

CHAPTER 5 RESULTS AND DISCUSSION 191
Figure 5.103 presents a plot of the dynamic interfacial tension versus the total molarity of
the bSA solution at increasing time. The values decrease with increasing concentration of bSA and
increasing time. Only the 1 ms curve shows tendency of a levelling-out at approximately 2 mmol/l.
The curves at 10 ms, 100 ms and 1000 ms show a further decrease in interfacial tension with
increasing solution molarity of bSA.
Figure 5.103: Dynamic air / water interfacial tension as a function of solution molarity of bSA solutions at different
times.
The total interfacial excess concentration of bSA is calculated using the Gibbs equation.
Transformation of the original equation leads to a form that shows that the slope of the plot of the
dynamic interfacial tension versus ln c defines the interfacial excess of a solute [Hiemenz 1986].
Equation 5.14
Dynamic interfacial tension [mN/m]
74.0
72.0
70.0
68.0
66.0
64.0
62.0
60.0
[bSA solutions at 25°C]
0.0 1.0 2.0 3.0 4.0 5.0
1 ⎛ dγ
⎞
Γ = − ⋅ ⎜ ⎟
RT ⎝ d ln c ⎠
Solution molarity [mmol/l]
T
10 ms
100 ms
1000 ms
Figure 5.104 shows the calculated surface excess concentration plotted versus solution molarity of
the bSA solutions for different interfacial lifetime. As expected, an increase in Γ (t)
can be seen
with increasing protein concentration. The formation of a plateau with increasing bSA
concentration cannot be seen from Figure 5.104. Additionally to the plots of the surface tension
with time or concentration, the curve for the extrapolated values at 10 s lifetime is also shown. After
1 s interfacial lifetime the surface excess value increases up to 0.00132 mmol/m 2 for a 4.0 mmol/l
bSA solution. After 10 s the surface excess is increased to 0.00146 mmol/m 2 . These values are
equivalent to 88 mg/m 2 – 97 mg/m 2 . Chen et al. [1998] determined a long time equilibrium surface
excess value for bSA of approximately 12 mg/m 2 using the Gibbs equation. They noted that this
1 ms

192 RESULTS AND DISCUSSION
value corresponds to a close-packed monolayer of the protein. The values in this work are seven
times larger than that of Chen et al.. Repeated measurement of the bSA solutions using a different
batch of lyophilized bSA produced the same results. Figure 5.105 presents the surface excess
concentration versus interfacial lifetime with different solid concentration. In the time range
between 1 s and 10 s a further increase in surface excess concentration can be seen for all bSA
concentrations.
Surface excess [mmol/m 2 ]
0.0016
0.0014
0.0012
0.0010
0.0008
0.0006
0.0004
0.0002
0.0000
10000 ms
0.000 0.001 0.002 0.003 0.004 0.005
Solution molarity [mmol/m 3 ]
1000 ms
100 ms
10 ms
Figure 5.104: Surface excess concentration Γ (t) as a function of bSA solution molarity at 25°C for different lifetimes.
Surface excess [mmol/m 2 ]
0.0016
0.0014
0.0012
0.0010
0.0008
0.0006
0.0004
0.0002
0.0000
Figure 5.105: Surface excess concentration as a function of time of bSA solutions at various concentration at 25°C.
1 ms
[bSA solution at 25°C]
4.0 mmol
2.0 mmol
1.0 mmol
0.5 mmol
0.0 1.0 2.0 9.0 10.0 11.0 12.0
Time [s]
0.1 mmol
[bSA solution at 25°C]

CHAPTER 5 RESULTS AND DISCUSSION 193
A comparison of the surface excess concentration of bSA solutions with other protein solutions is
presented in Figure 5.106. Trypsinogen from bovine pancreas with molecular weight of 23.7 kDa
[Sigma 2005] and salmon calcitonin with a molecular weight of 3.43 kDa [Sigma 2005] were
examined by Fuhrling [2004]. The plots show the surface excess concentration of a 4.0 mmol/l
solution versus time for all three proteins and the surface excess concentration with solution
molarity for a lifetime of 1 s.
Surface excess [mmol/m 2 ]
0.0014
0.0012
0.0010
0.0008
0.0006
0.0004
0.0002
bSA (this work)
0.0000
Trypsinogen [Fuhrling 2004]
Calcitonin [Fuhrling 2004]
0.000 0.001 0.002 0.003 0.004
(a)
[Lifetime 1s at 25°C]
Solution molarity [mmol/m 3 ]
0.0014
0.0012
0.0010
0.0008
0.0006
0.0004
0.0002
0.0000
Figure 5.106: Surface excess concentration of bSA, trypsinogen, and salmon calcitonin. (a) Surface excess versus
solution molarity at 1 s lifetime. (b) Surface excess verusus time for a 4.0 mmol/l solution.
At an interfacial lifetime of 1 s the surface excess values of trypsinogen increase to
0.0006 mmol/m 2 for 1 mmol/kg, and 0.0008 mmol/m 2 for 8 mmol/kg. These values are equivalent
to 14 mg/m 2 – 19mg/m 2 [Fuhrling 2004]. According to Figure 5.106 and influence of the molecular
weight of the protein on the surface excess cannot be seen, because bSA with a higher molecular
weight than trypsinogen as well as calcitonin with a lower molecular weight than trypsinogen show
a larger surface excess concentration.
Interfacial behaviour and surface excess of Pluconic F 127
0.0 0.2 0.4 0.6 0.8 1.0
To assess the potential of interfacial activity of the bSA solutions, Pluronic F 127 solutions with the
same solution molarity are prepared and tested in a bubble pressure tensiometer the same way as the
bSA solutions before. Pluronic F 127 is chosen due to its polymeric character with a molecular
weight of 12.6 kDa [Seth 2005]. Figure 5.107 shows the surface tension versus log time (Figure
5.107 a) and solution molarity (Figure 5.107 b). The equilibrium interfacial tension values measured
by ring tensiometry are listed in Table 5.12.
Surface excess [mmol/m 2 ]
(b)
bSA (this work)
Trypsinogen [Fuhrling 2004]
Calcitonin [Fuhrling 2004]
[Solution molarity 4.0mmol at 25°C]
Time [s]

194 RESULTS AND DISCUSSION
Table 5.12: Values for equilibrium interfacial tension after 3 hours for aqueous Pluronic F 127 solutions at 25°C
ambient temperature using ring tensiometry.
Concentration of
Pluronic solution
Equilibrium
interfacial tension
[ mmol ] 0.1 0.5 1.0 2.0 4.0
[ mN/m ] 50.1 43.9 41.0 38.3 37.0
The Pluronic F 127 solutions show a higher surface activity at equivalent concentrations than does
the bSA. In all plots the interfacial tension decreases continually as seen in Figure 5.107 a. At
lifetimes ≥ 1 s the slope of the plot, γ / d logt
, tends to increase with decreasing surfactant
d C
concentration. With increasing solution molarity and lifetime the interfacial tension decreases,
indicating a higher amount of surface coverage. Due to the higher degree of surface coverage at
larger Pluronic concentration, the adsorption rate is reduced.
Dynamic interfacial tension [mN/m]
65.0
60.0
55.0
50.0
45.0
40.0
(a)
0.1 mmol
0.5 mmol
1.0 mmol
2.0 mmol
4.0 mmol
[Pluronic F 127 solutions at 25°C]
-3 -2 -1 0 1
Log time in seconds [-]
35.0
0.0 1.0 2.0 3.0 4.0 5.0
Solution molarity [mmol/l]
Figure 5.107: Dynamic interfacial tension of Pluronic F 127 solutions at 25°C. (a) Dynamic interfacial versus log time
in seconds for different Pluronic concentrations. (b) Dynamic interfacial tension versus solution molarity at different
lifetime.
The plots of the calculated surface excess concentration versus solution molarity of the
Pluronic F 127 solution and interfacial lifetime are presented in Figure 5.108. The Pluronic curves
show a greater surface excess concentration with increasing solution molarity and increasing
interfacial lifetime. The experimental results are smaller than those published by Fuhrling [2004]
for equivalent concentration of the solution. The surface excess values for Pluronic F 127 are larger
than the bSA ones with the same molar concentration.
Dynamic interfacial tension [mN/m]
75.0
70.0
65.0
60.0
55.0
50.0
45.0
40.0
(b)
[Pluronic F 127 solutions at 25°C]
1 ms
10 ms
100 ms
1000 ms

CHAPTER 5 RESULTS AND DISCUSSION 195
Surface excess [mmol/m 2 ]
0.0025
0.0020
0.0015
0.0010
0.0005
100 ms
10 ms
1 ms
0.0000
[Pluronic F 127 solutions at 25°C]
0.000 0.001 0.002 0.003 0.004 0.005
(a)
Solution molarity [mmol/m 3 ]
1000 ms
Figure 5.108: Surface excess concentration of Pluronic F 127 solutions at 25°C. (a) Surface excess concentration
versus solution molarity at different interfacial lifetimes. (b) Surface excess concentration versus interfacial lifetime for
different solid concentrations.
Influence of trehalose on the interfacial behaviour of bSA
Surface excess [mmol/m 2 ]
0.0025 4.0 mmol
2.0 mmol
1.0 mmol
0.0020
0.5 mmol
0.0015
0.0010
0.0005
0.0000
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Time [s]
0.1 mmol
[Pluronic F 127 solutions at 25°C]
The effect of trehalose on the surface tension and other physico-chemical properties of water has
been studied and discussed in detail by Kaushik and Bhat [Kaushik 2003]. It has been observed, that
trehalose increases the surface tension of water by a larger amount than other sugars and polyols do.
The thermodynamic properties of water like partial molal heat capacity and volume show a
markable increase in the presence of trehalose [Kaushik 2003]. A larger hydrated volume compared
to other sugars [Sola-Penna 1998] and a linear correlation of the M T Δ ( T M = midpoint of thermal
denaturation) with increasing surface tension due to trehalose has also been reported
[Kaushik 2003]. Other effects of trehalose on the stabilisation of proteins have already been
discussed in Chapter 5.3.2. Fuhrling [2004] showed an increase in the dynamic air / water
interfacial tension with increasing solid concentration. For a 50 mg/ml solution he found an
interfacial tension of averaged 73.1 mN/m increasing to approximately 73.8 mN/m for a 400 mg/ml
solution. Due to this increase in surface tension with increasing solid content, the calculated surface
excess was negative (-0.002 mmol/m 2 ) for a trehalose solution with 100 mg/ml solid content at an
interfacial lifetime of 1 s. The results of pure trehalose solutions with a solid content of 50 mg/ml,
100 mg/ml, 200 mg/ml and 400 mg/ml are presented in Table 5.13. The values of the equivalent
solutions are larger than the above. To investigate the influence of trehalose on the interfacial
tension of bSA solutions within this work, the same molar concentration of bSA with 200 mg/ml
trehalose were prepared and tested equal to the pure bSA and Pluronic F 127. Therefore, the density
of the 1 mmol/l bSA solution increased from 1.01 g/cm 3 without trehalose to 1.09 g/cm 3 with
(b)

196 RESULTS AND DISCUSSION
trehalose. Figure 5.109 shows the influence of trehalose on the dynamic interfacial tension of bSA
solutions as a function of solution molarity for an interfacial lifetime of 0.1 s and 1.0 s as well as the
dynamic interfacial tension as a function of interfacial lifetime for a solution molarity of 2.0 mmol/l
and 4.0 mmol/l.
Table 5.13: Equilibrium interfacial tension of trehalose solutions with different solid content measured with bubble
pressure tensiometry at 25°C.
Concentration of
trehalose solution
Average interfacial
tension (n = 3)
Dynamic interfacial tension [mN/m]
Dynamic interfacial tension [mN/m]
76.0
74.0
72.0
70.0
68.0
66.0
64.0
62.0
(a)
74.0
72.0
70.0
68.0
66.0
64.0
62.0
(c)
[ mg/ml ]
50 100 200 400
[ mN/m ] 72.80 ± 0.14 73.13 ± 0.08 74.02 ± 0.20 75.09 ± 0.20
Interfacial lifetime 100 ms
bSA solution
bSA solution + 200 mg/ml trehalose
0.0 1.0 2.0 3.0 4.0
bSA solution molarity [mmol/l]
Solution bSA molarity 2.0 mmol/l
bSA solution
bSA solution + 200 mg/ml trehalose
0.0 0.2 0.4 0.6 0.8 1.0
Time [s]
0.0 1.0 2.0 3.0 4.0
Figure 5.109: Dynamic interfacial tension of bSA solution and bSA solution with 200 mg/ml trehalose content a
function of solution molarity and interfacial lifetime. (a) Dynamic interfacial tension versus solution molarity for an
interfacial lifetime of 100 ms. (b) Dynamic interfacial tension versus solution molarity for an interfacial lifetime of
1000 ms. (c) Dynamic interfacial tension versus interfacial lifetime for a bSA solution molarity of 2.0 mmol/l. (d)
Dynamic interfacial tension versus interfacial lifetime for a bSA solution molarity of 4.0 mmol/l.
Dynamic interfacial tension [mN/m]
Dynamic interfacial tension [mN/m]
76.0
74.0
72.0
70.0
68.0
66.0
64.0
62.0
(b)
74.0
72.0
70.0
68.0
66.0
64.0
62.0
(d)
bSA solution
bSA solution + 200 mg/ml Trehalose
Interfacial lifetime 1000 ms
bSA solution molarity [mmol/l]
bSA solution
bSA solution + 200 mg/ml trehalose
Solution bSA molarity 4.0 mmol/l
0.0 0.2 0.4 0.6 0.8 1.0
Time [s]

CHAPTER 5 RESULTS AND DISCUSSION 197
The presence of trehalose reduces the adsorption of bSA to the surface. After an interfacial lifetime
of 1 s an increase in the dynamic interfacial tension of 3.67 mN/m for the 2.0 mmol/l bSA solution
and of 4.42 mN/m for the 4.0 mmol/l bSA solution can be detected. Similar results are obtained
plotting the dynamic interfacial tension as a function of bSA solution molarity. Trehalose increases
the slope d γ () t / dc of the plots for interfacial lifetimes of 100 ms and 1 s. Figure 5.110 presents the
surface excess concentration versus bSA solution molarity and interfacial lifetime for bSA solutions
and the bSA-trehalose mixture with a trehalose content of 200 mg/ml. Trehalose decreases the
surface excess of bSA for every solution molarity at interfacial lifetimes of 100 ms and 1 s. For a
4.0 mmol/l solution the addition of trehalose reduces the surface excess of bSA to 41% of the value
of pure bSA. The plot of the surface excess versus interfacial lifetime in Figure 5.110 c and d shows
a decrease in slope d Γ () t / dt with addition of trehalose at equivalent bSA concentration. This leads
to a reduction of bSA at the surface from 87 mg/m 2 for the pure 4.0 mmol/l bSA solution at an
interfacial lifetime of 1 s to 36 mg/m 2 for the mixture with 200 mg/ml trehalose. The values at 10 s
are extrapolated from the experimental data. The role of the surface tension in the stabilization of
RNase A with trehalose was investigated by Lin and Timasheff [Lin 1996] and the preferential
interactions of trehalose and ribonuclease as well as the thermal unfolding of the protein was
examined by Xie and Timasheff [Xie 1997]. Preferential interaction measurements demonstrated
that trehalose unlike other sugars is totally excluded from the first hydration shell of the protein
[Lin 1996]. On a scale comparing the preferential interactions of co-solvents published by
Timasheff [2002], trehalose shows the most preferential hydration of the protein with the highest
amount of preferential exclusion. The results were supported by Wyman linkage analysis done by
Kaushik [2003]. The negative values of the Wyman slope of the tangent from -7 to -4 for various
proteins at 1.5 M trehalose concentration indicated the preferential exclusion of trehalose from the
hydration shell of the protein upon denaturation. Lins et al. [2004] set-up a model for proteintrehalose
interactions in aqueous solution on the nanosecond timescale. Initially, trehalose is
distributed homogeneously in solution. The presence of a protein induces clustering of trehalose
molecules and the trapping of a thin water-layer at the proteins surface leading to preferential
hydration. The trehalose molecules in the coating layer then compete with the protein for forming
hydrogen bonds with the water molecules in the trapped layer. Recapitulating, preferential
hydration of the protein in a triphasic system of water, protein and co-solvent postulates, that the cosolvent
(e.g. a sugar) is excluded from vicinal water that composes the solvation layer of the
protein. The protein then becomes preferentially hydrated with a decrease in radius of the salvation
layer and the apparent volume of the protein [Sola-Penna 1998]. This leads to more stable protein
confirmation and enhances the maintenance of the native state, since the unfolded state becomes

198 RESULTS AND DISCUSSION
thermodynamically even less favourable [Lee 1981]. This mechanism would increase the free
energy of adsorption of the protein to the interface and hence reduces its extend of adsorption
[Fuhrling 2004]. A reduced extend or slower rate of adsorption of the protein to the air / water
interface could be a possible explanation for the increase in the amount evaporated in the first
drying stage and the shift of the critical point in the single droplet drying experiment of pure bSA,
bSA-trehalose (1:1) and pure trehalose, as presented in Figure 5.94.
Surface excess [mmol/m 2 ]
Surface excess [mmol/m 2 ]
0.0016
0.0014
0.0012
0.0010
0.0008
0.0006
0.0004
0.0002
0.0000
(a)
0.0016
0.0014
0.0012
0.0010
0.0008
0.0006
0.0004
0.0002
0.0000
0.000 0.001 0.002 0.003 0.004 0.005
(c)
Interfacial lifetime 100 ms
bSA solution
bSA solution + 200 mg/ml trehalose
bSA solution molarity [mmol/m 3 ]
bSA solution molarity 0.002 mmol/m 3
bSA solution
bSA solution + 200 mg/ml trehalose
0.0 0.5 1.0 9.0 10.0
Time [s]
Surface excess [mmol/m 2 ]
Surface excess [mmol/m 2 ]
0.0016
0.0014
0.0012
0.0010
0.0008
0.0006
0.0004
0.0002
0.0000
Interfacial lifetime 1000 ms
bSA solution
bSA solution + 200 mg/ml trehalose
0.000 0.001 0.002 0.003 0.004 0.005
bSA solution molarity [mmol/m 3 ]
Figure 5.110: Surface excess concentration of bSA solution and bSA solution with 200 mg/ml trehalose content a
function of solution molarity and interfacial lifetime. (a) Surface excess concentration versus solution molarity for an
interfacial lifetime of 100 ms. (b) Surface excess concentration versus solution molarity for an interfacial lifetime of
1000 ms. (c) Surface excess concentration versus interfacial lifetime for a bSA solution molarity of 0.002 mmol/m 3 .
(d) Surface excess concentration versus interfacial lifetime for a bSA solution molarity of 0.004 mmol/m 3 .
(b)
0.0016
0.0014
0.0012
0.0010
0.0008
0.0006
0.0004
0.0002
0.0000
(d)
bSA solution molarity 0.004 mmol/m 3
bSA solution
bSA solution + 200 mg/ml trehalose
0.0 0.5 1.0 9.0 10.0
Time [s]

CHAPTER 5 RESULTS AND DISCUSSION 199
Determination of bSA monolayer
A monomolecular layer, monolayer, of an air / water interfacial active substance can slow down the
evaporation of the droplet solvent [Tuckermann 2002]. The formation and the characteristics of
such monolayers are usually investigated using a film balance. The determination via acoustical
levitation of droplets was first described by Frost and Seaver [Frost 1993] and experimentally
studied and discussed in detail for 1-octadecanol, stearic acid and stearylamin by Tuckermann
[2002]. The addition of an interfacial active substance to a levitated pure solvent droplet results in a
decrease in surface tension and a stronger deformation of the droplet. The aspect ratio increases due
to the larger vertical than horizontal levitation forces. The process of monolayer formation of
surfactant molecules is described by Hiemenz [1986] and shown in Figure 5.111 a to e. In the first
and second state, the so called gaseous state and the liquid-expanded state, the surfactant molecules
are too far away from each other and consequently the surface tension does not decrease very much
(Figure 5.111, regions G and L1-G). With the evaporation of solvent of a droplet containing
interfacial active substances and, therefore, a decrease in droplet volume and surface area, the
surfactant molecules draw nearer causing a strong decrease in surface tension. This state is called
the liquid condensed state (L1) and the solid state (L2, S) (Figure 5.111). Between the two states
there is a break, known as the intermediate or transition state, and indicated by the capital I. Further
evaporation of solvent and further compression leads to a collapse of the monolayer (Figure
5.111 e). The pressure at which this occurs is somewhere in the vicinity of the equilibrium
spreading pressure [Hiemenz 1986].
Figure 5.111: Phases of the formation of monolayers of interfacial active substances on the surface of a levitated
droplet. (left) Sketch of the surfactant orientation on the droplet surface. (right) States of the surfactant at the droplet
surface as a function of molecule area [Hiemenz 1986].

200 RESULTS AND DISCUSSION
The surface tension of the droplet cannot be measured directly in the acoustic levitation system. But
the transition from the gaseous to the liquid condensed state and the decrease in surface tension can
be determined monitoring the aspect ratio and the surface temperature of the levitated droplet
[Tuckermann 2002]. Additionally, the evaporation rate decreases due to an evaporation repressing
effect of the monolayer.
Within this work, the formation of the liquid-condensed state of monolayers is examined
only be monitoring the course of the aspect ratio of the levitated droplet with time. To examine if
the determination of the point of formation is also possible without IR-thermocamera, 1octadecanol
and stearic acid were examined and compared to the results published by Tuckermann
[2002]. Therefore, a 1-octadecanol solution in hexane with a concentration of 0.143 g/l was
prepared and dispersed in water in a relation of water to 1-octadecanol as 46.2 to 1. Stearic acid was
also dissolved in hexane in a concentration of 0.l g/l and dispersed in water in a relation of water to
Stearic acid as 22 to 1. The results and the comparison to literature are given in Table 5.14. A very
good correlation is found so that a determination of the limiting area per molecule in a droplet
surface monolayer at the transition to the liquid-condensed phase can only be determined from the
course of the aspect ratio with time.
Table 5.14: Literature and experimental values for the limiting area per molecule in a droplet surface monolayer at the
formation of the liquid-condensed state L1.
Interfacial active
substance
Langmuir
film balance
[Stosch 2000]
Langmuir
film balance
[Mingotaud et al. 1993]
Acoustic
levitator
[Tuckermann 2002]
Acoustic
levitator
(this work, n = 3)
1-octadecanol - 0.21 nm 2 0.22 ± 0.03 nm 2 0,21 ± 0,02 nm 2
Stearic acid 0.25 nm 2 0.25 nm 2 0.21 ± 0.03 nm 2 0.23 ± 0.04 nm 2
To determine the area per bSA molecule at the formation of the liquid-condensed state of a bSA
monolayer, a dilution row of bSA solutions is prepared and tested by evaporating the bSA solution
droplet at room temperature and 0.3% humidity, and monitoring the size and aspect ratio of the
levitated droplets. When evaporating a droplet with an initial bSA concentration of 0.02 nmol/l and
an initial volume of 2.8 µl, an aspect ratio profile similar to the profile shown in Figure 5.111 for
the change in surface tension versus molecule area is obtained. The plot is presented in Figure
5.112. First, with decreasing droplet size, the aspect ratio decreases until the bSA molecules on the
droplet surface draw that close that the liquid-condensed state is reached and the surface tension
decreases. This results in an increase in aspect ratio due to the force distribution in the acoustic
levitator. Equal to Figure 5.111 the plot of the aspect ratio versus drying time shows an increase in

CHAPTER 5 RESULTS AND DISCUSSION 201
slope until a maximum is reached. After the maximum, the value of the aspect ratio decreases
rapidly to almost 1.0. This decrease could possibly be caused by the collapse of the monolayer
reported by Hiemenz [1986]. A decrease of the evaporation coefficient β r can also be seen in
Figure 5.112 marked by the two red lines. The value determined for β r before the formation of the
bSA monolayer in a size range from 1.0 µl to 0.5 µl is 0.000518 mm 2 /s which corresponds to the
values of the pure water droplet experiments at 25°C and 0.1% relative humidity in still air. The
decrease in β r is not associated with the formation of the liquid-condensed state, but with the
transition form the liquid-condensed state to the solid state. β r decreases to 0.000273 mm 2 /s. If the
aspect ratio is plotted versus the surface area per molecule, Figure 5.112 b is obtained. If the
transition from gaseous state G to liquid-condensed state L1 is taken for the determination of the
area per bSA molecule in the monolayer on the droplet surface, a value of approximately 100 nm
per bSA molecule is obtained (Figure 5.112 a). Comparison with literature shows a very good
correlation of the data [MacRitchie 1986].
( r S / r S 0 ) 2 [-]
1.0
0.8
0.6
0.4
[bSA solution 0.02 nmol/l]
0.2
Droplet size
Aspect ratio
1.1
0.0
1.0
0 200 400 600 800 1000 1200 1400
(a)
Evaporation time [s]
1.6
1.5
1.4
1.3
1.2
Figure 5.112: (a) Droplet size (rS /rS 0) 2 and droplet aspect ratio as a function of evaporation time for a 0.02 nmol/l
aqueous bSA solution at 25°C and 0.3% relative humidity in still air. The initial droplet size was 2.8 µl at an initial
effective SPL of 165.38 dB. (b) Aspect ratio of the levitated 0.02 nmol/l aqueous bSA solution as a function of surface
area per bSA molecule. The experiment was performed at 25°C and 0.3% relative humidity in still air. The initial
droplet volume was 2.8 µl at an initial effective SPL of 165.38 dB.
Aspect ratio [-]
Aspect ratio [-]
1.6
1.5
1.4
1.3
1.2
1.1
[bSA solution 0.02 nmol/l]
1.0
300 250 200 150 100 50 0
Surface area per bSA molecule [nm 2 (b)
]
G
L 1
L 2
S

202 RESULTS AND DISCUSSION
5.3.5 Evaporation of catalase solution droplets
Properties of catalase solutions
The tetramer catalase consist of four equal sub-unit, each with 506 amino acids and an overall
molecular weight of 250 kDa [Sigma 2005]. Catalase is poorly soluble in water, but soluble to
1 mg/ml in 50 mM potassium phosphate buffer at pH 7.0 [Sigma 2005]. In this work a 50 mM tris
buffer at pH 8.0 was used to prepare solutions with a solid content of 200 mg/ml. Only few
publications are found on the spray-drying of catalase. One recent study was done by Liao et al.
[2005] who investigated the physical stability of spray-dried proteins (lysozyme and catalase)
within surfactant-free hydrofluoroalkane (HFA) pressurized metered dose inhalers (pMDIs). Their
model proteins were spray-dried, stabilized in the presence of excipients and suspended within
HFA. Catalase activity was determined equal to the method described in Chapter 4.2.6. Forbes et al.
[1998] performed water vapour sorption studies on the physical stability of spray-dried
protein / sugar powders using catalase, insulin and ribonuclease A as model proteins. The proteins
were spray-dried pure and formulated with lactose or mannitol in a Buchi Mini Spray-Dryer at
T = 200° C and T = 90° C with an air flow of 800 l/h. Powder X-ray diffraction characterized
inlet
outlet
the extent of cristallinity in the spray-dried product. The pure spray-dried proteins and the
protein / lactose-mixtures showed no presence of cristallinity, whereas the same proteins co-spraydried
with mannitol showed evidence of mannitol component cristallinity except of the
RNase/mannitol mixture. When exposed to humidity most of their powders showed a transition
from amorphous to crystalline state. However, catalase appeared to inhibit lactose crystallisation
from the amorphous matrix to a greater extend than insulin in short-term humidity exposure test.
Using freeze-drying, Liao et al. [2002] investigated the influence of type and amount of small
molecular excipients (glycerol, sorbitol, sucrose and trehalose) on the preservation of the native
protein structure and the biological activity of catalase and lysozyme. Catalase activity was
determined equal to the method of Chapter 4.2.6 and FTIR-spectroscopy was used to examine
secondary structure of the protein in the dry state. The native secondary structure of catalase
determined in the dry state by FTIR had a weaker correlation with the residual catalase activity than
the degree of retained native structure in solution determined by circular dichroism (CD). Jiang and
Nail [Jiang 1998] used catalase as well as β-galactosidase and lactate dehydrogenase (LDH) to
investigate the maximization of recovery of protein activity after freeze-drying by manipulating of
freeze-dry process condition in the absence of protecting co-solutes.

CHAPTER 5 RESULTS AND DISCUSSION 203
Pure catalase solutions as well as mixtures of catalase and trehalose were prepared in
50 mM tris buffer at pH 8.0. All solutions had an overall solid content of 100 mg/ml. Experiments
were carried out at 60°C and different relative humidity of the drying air. The liquid properties were
determined before starting the levitation procedure. The data are shown in Table 5.9.
Table 5.15: Liquid properties and levitation size range for a pure catalase solution with 100 mg/ml solid content at
25°C.
Solid
content
100 mg/ml
Surface
tension
[ ]
Density
ρ liquid
3
mN/m [ ]
Maximum
diameter
Maximum
volume
Minimum
diameter
Minimum
volume
g/cm [ mm ] [ µl ] [ µm ] [ µl ]
Catalase 48.6 1.028 4.33 42.4 15 1.77⋅10 -6
Figure 5.113 presents the liquid density of catalase solutions in a concentration range from
0.05 mmol/l to 1.0 mmol/l with different amount of trehalose.
Liquid density [g/cm 3 ]
1.08
1.07
1.06
1.05
1.04
1.03
1.02
1.01
1.00
Pure catalase solutions at 25°C
in 50 mM tris buffer pH 8.0
50 mg/ml
25 mg/ml
12,5 mg/ml
100 mg/ml
250 mg/ml
0.99
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Catalase concentration [mmol/l]
(a)
0 100 200 300 400
Figure 5.113: Liquid density of catalase solution at 25°C. Catalase was dissolved in 50 mM tris buffer at pH 8.0.
(a) Liquid density of pure catalase solutions as a function of molar concentration. (b) Liquid density of catalasetrehalose
mixtures as a function of trehalose content for different molar catalase concentrations.
Liquid density [g/cm 3 ]
1.18
1.16
1.14
1.12
1.10
1.08
1.06
1.04
1.02
1.00
(b)
Catalase-trehalose solutions at 25°C
in 50 mM tris buffer pH 8.0
Trehalose content [mg/ml]
Catalase 0.05 mmol/l
Catalase 0.1 mmol/l
Catalase 0.2 mmol/l
Catalase 0.4 mmol/l
Catalase 1.0 mmol/l

204 RESULTS AND DISCUSSION
Data analysis of catalase solution experiments
The data analysis of the pure catalase droplets / particles is different to the pure sugar solutions. The
evaporation process can be divided into two different stages. The constant rate, where the
evaporation rate is determined using the decrease in droplet volume with time [Frohn 2000; Kastner
et al. 2001] and the falling rate, where the evaporation rate is calculated using the rise of the centre
of mass of the particle towards its adjacent upper pressure node [Kastner et al. 2001]. The raw data
for a levitation experiment of a pure catalase solution with a solid content of 100 mg/ml at 60°C and
5% relative humidity in still air can be seen in Figure 5.114. The behaviour of the pure catalase
solutions is as with the pure bSA solutions with the same initial concentration. After the formation
of a solid crust at the droplet surface, the particles start oscillating what leads to difficulties in
determination of the evaporation rate in the second drying stage or even to a drop-out of the particle
out of the standing acoustic wave. The disturbed particle position can be seen from fluctuation in
the curve of the aspect ratio versus drying time shortly after the critical point (Figure 5.114). Even a
breakage of the levitated particles into two parts can be observed during the experiments. The pure
catalase results in this work are calculated from the few experiments with stable droplet / particle
levitation. There are substantial size changes in horizontal and vertical diameter after the critical
point. The critical point itself is determined using the increase in aspect ratio of the
droplet / particle. As discussed in chapter 3.2.3, size changes of the levitated droplet or particle lead
to changes in the values of the effective SPL. Using the method by Kastner et al. [2001] to
determine the evaporation rate, a constant effective SPL in the second drying stage is necessary.
The difference of the effective SPL at the critical point and at the end of the size change was
maximum 0.17 dB. The effective SPL is calculated using the method by Yarin et al. [1998]. The
small difference in SPL is neglected when calculating the evaporation rate in the second drying
stage. Particles resulting form the drying of pure catalase solution are shown in Figure 5.115. It
seems that the particle formation of catalase is more strongly influenced by the magnitude of the
effective SPL than the particle formation of any other of the tested substance. A high effective SPL
of 166.5 dB leads to very flat particles with a donut like shape (Figure 5.115 a), whereas an
effective SPL of approximately 164.6 dB leads to particles with a more spherical shape but with a
hollow interior (Figure 5.115 b-d). The more spherical particles are almost similar to the pure bSA
particles with a slightly impressed particle top. They show a hole in their top side and an
undamaged bottom side. When destroying the final particles a hollow interior was found.

CHAPTER 5 RESULTS AND DISCUSSION 205
2 ) Aspect ratio
2 / rS 0
( r S
Diameter [µm]
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
Droplet / particle size
Aspect ratio
Vertical position
0.2
-400
0 100 200 300 400 500 600 700
(a)
Constant rate Falling rate
Evaporation time [s]
1800 Horizontal diameter
Vertical diameter
1600
Aspect ratio
1400
1200
1000
800
Figure 5.114: Raw data of a levitated pure catalase solution droplet with 100 mg/ml solid content in 50 mM tris buffer
pH 8.0 dried at 60°C and 5% relative humidity in still air. The initial droplet size was 1.8 µl at an initial effective SPL
of 166.5 dB. (a) Aspect ratio, (rS 2 /rS 0 2 ) and position as a function of evaporation time. (b) Horizontal diameter, vertical
diameter and aspect ratio as a function of evaporation time.
The surface holes have a mean diameter of 45.1 ± 4.3% (n = 3) of the horizontal particle diameter.
The solid crust has a thickness of approximately 18.3% of the final particle radius. Assuming a
spherical particle with a radius of 500 µm the overall volume would be 0.524 µl with a void volume
of 0.286 µl. Neglecting any holes in the surface, the surface area of the internal void sphere would
be calculated to 2.10 mm 2 , the outer surface area of the spherical particle to 3.14 mm 2 . A
comparison to the spray-dried pure catalase product dried in the Buchi Mini Spray-Dryer is
presented in Figure 5.116 and shows very good correlation. The spray-dried particles seem to have
100
0
-100
-200
-300
600
1.0
0 100 200 300 400 500 600 700
(b)
Evaporation time [s]
2.0
1.8
1.6
1.4
1.2
Distance to adjacent pressure node [µm]
Aspect ratio [-]

206 RESULTS AND DISCUSSION
impressed surfaces with one ore multiple holes in it, too. Additionally, undamaged particles as well
as particle fragments can be found.
(a) (b)
(c) (d)
Figure 5.115: SEM pictures of pure catalase particles with 100 mg/ml solid content in 50 mM tris buffer pH 8.0 dried
at 60°C and 5% relative humidity in still air. (a) Pure catalase particle levitated at an initial effective SPL of 166.5 dB.
(b-d) Pure catalase particles levitated at an initial effective SPL of 164.6 dB. Shown are pictures with a magnification of
75-times (a), 45-times (b), 80-times (c) and 100-times (d).
Figure 5.116: SEM pictures of spray-dried pure catalase
particles with 100 mg/ml solid content in 50 mM tris
buffer pH 8.0. Tinlet = 100°C, Toutlet = 60°C, liquid feed
3 ml/min. The picture shown has a magnification of
3000-times.

CHAPTER 5 RESULTS AND DISCUSSION 207
Due to the similar behaviour of the pure catalase solution droplet during the drying process in the
acoustic levitator compared to the pure bSA solution and the similar way of particle formation and
surface morphology, the plot of the evaporation rate as a function of time is expected to be similar
to that of pure bSA. The obtained results proved this assumption and are presented in Figure 5.117.
With increasing relative humidity of the drying air, the values of the evaporation rate in the first
drying stage decrease from 0.93 µg/s/mm 2 at 5% humidity to 0.41 µg/s/mm 2 at 40% humidity. In
return, the duration of the first drying stage increases leading to a shift of the critical point. After a
first decrease of the evaporation rate in the falling rate, an increase in the evaporation rate can be
determined resulting in values almost as large as at the end of the constant rate period, equal to
bSA. This increase in evaporation rate is synchronous with the formation of the hole in the surface
on the top side of the particle. After the maximum in the second drying stage is reached, the
evaporation rate decreases to very low values. The decline in evaporation rate is shallower at 40%
relative humidity of the drying air than at 5%.
Evaporation rate [µg/s/mm 2 ]
1.0
0.8
0.6
0.4
0.2
Critical point
0.0
[Drying temp. 60°C]
0 200 400 600 800 1000 1200 1400
2 2
t / r [s/mm ]
S 0
Rel. humidity 5%
Rel. humidity 20%
Rel. humidity 40%
Evaporation rate
increase in falling
rate period
Figure 5.117: Evaporation rate in mass per time and surface area of pure catalase solutions as a function of (t /rS 0 2 ) at
60°C and different relative humidity in still air. The initial droplet volume of the experiments was between 1.5 and
2.0 ml at an initial effective SPL of 164.6 dB to 166.5 dB.
A mixture series of catalase and trehalose is prepared in 50 mM tris buffer at pH 8.0. The overall
solid content of 100 mg/ml is kept constant. The weight ratio and the molar ratio of the different
catalase-trehalose mixtures are listed in Table 5.16.

208 RESULTS AND DISCUSSION
Table 5.16: Weight ratio and molar ratio of mixtures with different content of catalase and trehalose.
Catalase-trehalose [ mg/ml ]
Weight ratio
80:20
4:1
60:40
3:2
40:60
2:3
20:80
Molar ratio 1:183 1:487 1:1096 1:2921
The results of the evaporation rate as a function of time for the mixture series at a drying air of
60°C and 5% relative humidity are presented in Figure 5.118. An analysis of a diagram containing
the plots of the evaporation rates of all tested catalase-trehalose mixtures is difficult. Therefore,
only the pure catalase, the catalase-trehalose (6:4) and the catalase-trehalose (2:8) mixture at 5%
and 20% humidity are plotted. Due to the longer evaporation time at increased humidity, the events
of the drying process are protracted and better detectable. A tendency of decreasing values of the
evaporation rate in the first drying stage with increasing trehalose content can be seen. An increase
in trehalose leads to an increase in the overall amount of dissolved molecules. As with bSA and
bSA-trehalose (1:1) mixtures, the duration of the first drying stage increases with increasing
trehalose content. The catalase-trehalose (6:4) mixture at 60°C and 5% humidity shows an outlier
behaviour compared to all other results. The shift of the critical point due to the increasing trehalose
content becomes more obvious when analysing the results at increased drying air humidity. As with
the pure catalase solutions, the increase of the evaporation rate in the second drying stage due to the
formation of holes in the particle surface can still be seen for the catalase-trehalose (8:2) mixture. A
further increase in trehalose content leads to disappearance of this behaviour and to a continuously
falling evaporation rate in the second drying stage without maximum. The SEM pictures of the final
particles confirm these results. As the catalase-trehalose (8:2) mixture particles still show holes in
their surface, the final particles of the catalase-trehalose (6:4) solution show an undamaged surface
with a massive particle interior. If the trehalose content is increased further, the particle morphology
adapts to that of the pure trehalose particles shown in Figure 5.67.
Similar to the effect of increasing drying air humidity seen in Figure 5.117, increasing
trehalose content leads to a shallower decline of the evaporation rate in the falling rate period. Only
marginal differences in the evaporation rate curves of the mixtures with a catalase-trehalose ratio of
4:6 and 2:8 and the pure trehalose curve can be seen (not shown).
1:4

CHAPTER 5 RESULTS AND DISCUSSION 209
Evaporation rate [µg/s/mm 2 ]
1.0
0.8
0.6
0.4
0.2
0.0
Drying temp. 60°C
Rel. humidity 5%
0 250 500 750 1000 1250 1500
Figure 5.118: Evaporation rate of pure catalase and catalase-trehalose mixtures in 50 mM tris buffer pH 8.0 as a
function of (t /rS 0 2 ) at 60°C and different relative humidity in still air. The initial droplet volume of the experiments was
between 1.5 and 2.0 µl at an initial effective SPL of 164.6 and 167.2 dB. (a) Drying conditions 60°C and 5% relative
humidity in still air. (b) Drying conditions 60°C and 20% relative humidity in still air.
The values of the catalase-trehalose (2:8) curve in Figure 5.118 are much lower and the evaporation
time is much longer than for pure trehalose shown in Figure 5.63 and Figure 5.64. This is caused by
different solvents. In the experiments of Figure 5.118 all formulations are dissolved in 50 mM tris
buffer at pH 8.0 due to the poor solubility of catalase in water, whereas in Figure 5.63 and Figure
5.64 trehalose is in aqueous solution without any additives. Due to the increase in dissolved
molecules caused by the buffer, the evaporation rate values of Figure 5.118 are lower and the
evaporation time is longer. The values of the evaporation rate at later points in second drying stage
are larger with increasing trehalose content. A comparison of the AUCs of the different experiments
show the largest values for the pure trehalose and the lowest values for the pure catalase, implying a
more efficient drying with increasing trehalose content. Because a determination of the residual
water content of the single particles was not possible, the pure substances and the formulations
presented in Table 5.16 are spray-dried in the Buchi Mini Spray-Dryer at T = 100° C ,
T = 60° C and a liquid feed of 3 ml/min and the residual water content of the product was
outlet
Critical point
Rupture of the
pure catalase
particle
2 2
( t / r ) [s/mm ]
S 0
Catalase-trehalose (10:0)
Catalase-trehalose (6:4)
Catalase-trehalose (2:8)
Larger values
with increasing
trehalose content
1.0
Critical point
Catalase-trehalose (10:0)
Catalase-trehalose (6:4)
0.9
Catalase-trehalose (2:8)
0.8
0.7
0.6
Rupture of the
pure catalase particle
0.5
0.4
Larger values
with increasing
0.3
0.2
trehalose content
0.1 Drying temp. 60°C
0.0
Rel. humidity 20%
0 250 500 750 1000 1250 1500
analysed via Karl-Fischer titration. The results are shown in Figure 5.119. The relative humidity of
the spray-dryer environment is additionally plotted. A clear decrease of the residual moisture
content with increasing trehalose and decreasing catalase content in the formulation cannot be seen.
All values are within a range of 0.3%. The lowest residual moisture content is found for the pure
trehalose powder. However, the laboratory humidity which also has an substantial influence on the
residual moisture of spray-dried products [Fitzner 2003; Masters 1991] has been lowest in this
Evaporation rate [µg/s/mm 2 ]
2 2
( t / r ) [s/mm ]
S 0
inlet

210 RESULTS AND DISCUSSION
experiment. Further investigations with spray-drying in conditioned environment or with
conditioned drying air has to be done to examine influences of formulation variables on the residual
moisture more detailed. References on the moisture content of spray-dried catalase-trehalose
formulations could not be found. Tzannis and Prestrelski [1999] investigated the moisture effects of
sucrose when spray-drying trypsinogen. They found decreasing residual moisture values with
decreasing sucrose content. Their optimum formulation in terms of lowest moisture content had
equal mass of sucrose and trypsinogen.
Residual moisture content [%]
6.0
5.8
5.6
5.4
5.2
5.0
4.8
(n = 3)
lab humidity
0 20 40 60 80 100
Trehalose content in formulation [% solid]
Figure 5.119: Residual water content of spray-dried catalase-trehalose solutions in 50 mM tris buffer at pH 8.0 as a
function of trehalose solid content of formulation. The residual water content was determined via Karl-Fischer titration.
The final particle size and density of the catalase-trehalose formulations and the pure solutions are
presented in Figure 5.120. As with bSA and its mixtures with trehalose, the final particle size
relative to the initial droplet size decreases with increasing trehalose content and increasing
humidity of the drying air. In return, the particles get denser with increasing trehalose content and
increasing drying air humidity. This behaviour is caused by the different length of the first drying
stage and the shift of the critical point in Figure 5.118. The longer the first drying stage and the later
the formation of the solid crust at the droplet surface, the smaller and denser the final particles
become. The effect has been seen for all tested substances and formulations. With increasing
trehalose content, an increase in duration of the first drying stage and in the amount of water
evaporated can be detected. The data are listed in Table 5.17. Only 61.9% of solvent is evaporated
in the first drying stage from the pure catalase solution droplets. This portion increases to 85.9%
solvent for the pure trehalose solution. The values at 20% relative humidity of the drying air are in
average 1.7% larger than at 5% humidity. A decrease in the percentage of solvent evaporated from
28.0
26.0
24.0
22.0
20.0
18.0
16.0
Relative humidity of spray-drying environment

CHAPTER 5 RESULTS AND DISCUSSION 211
the pure catalase solution in the constant rate period with increasing humidity, as seen from the bSA
results, cannot be detected. Both of the pure protein solutions show approximately the same values.
The values of the pure trehalose solution in 50 mM tris buffer at pH 8.0 differ only marginally form
the aqueous trehalose solution.
Particle size relative to initial droplet size [%]
65
60
55
50
45
40
(a)
Figure 5.120: Particle size and final particle density as a function of trehalose solid content in the formulation at 60°C
and different relative humidity in still air. The ignition droplet volume of the experiments was between 1.5 µl and 2.0 µl
at an initial effective SPL between 164.6 dB to 167.2 dB. (a) Particle size relative to initial droplet size versus trehalose
content in formulation. (b) Final particle density versus trehalose content in formulation.
Table 5.17: Percentage of evaporated solvent in the first drying stage depending on a change of trehalose content and
relative humidity of the drying air. The experiments were performed at 60°C in still air.
Relative humidity Percentage of evaporated solvent in the first drying stage (n=3)
of drying air catalase : trehalose ratio (50 mM tris buffer pH 8.0)
[ % ]
Rel. humidity 5%
Rel. humidity 20%
Rel. humidity 40%
0 20 40 60 80 100
10:0
Drying temp. 60°C
Trehalose content in formulation [% solid]
8:2
6:4
0 20 40 60 80 100
4:6
2:8
0:10
5 61.9 ± 2.8 64.6 ± 3.0 71.2 ± 2.9 76.7 ± 1.8 85.5 ± 2.8 85.9 ± 0.7
20 63.2 ± 4.0 68.4 ± 0.7 72.3 ± 2.1 78.1 ± 1.9 87.1 ± 1.8 87.0 ± 2.8
In Figure 5.121 and Figure 5.122 the final particles of the catalase-trehalose (6:4) mixture from
spray-drying and levitation can be seen. With increasing trehalose content the holes and impressions
in the particle surface get less and the particles become more spherical. Almost ideal spheres are
obtained for pure trehalose, whereas the catalase-trehalose (4:6) and (2:8) formulation show the
raisin like morphology often mentioned in literature [Maa et al. 1997]. The levitated catalasetrehalose
(6:4) particles have a broken surface similar to the bSA-trehalose (1:1) mixture. A folded
surface morphology on the top side of the particle cannot be seen in that degree as with bSAtrehalose
solutions. Destruction showed a massive internal particle structure volume.
Particle density [g/cm 3 ]
1.2
1.0
0.8
0.6
0.4
(b)
Rel. humidity 5%
Rel. humidity 20%
Rel. humidity 40%
Drying temp. 60°C
Trehalose content in formulation [% solid]

212 RESULTS AND DISCUSSION
(a) (b) (c)
(d) (e) (f)
Figure 5.121: SEM pictures of spray-dried pure catalase-trehalose solutions with 100 mg/ml solid content from a Buchi
Mini Spray-Dryer B-191 with Tinlet=100°C, Toutlet=60°C and a liquid feed of 3 ml/min. All pictures have a 3500-times
magnification. (a) Pure catalase. (b) Catalase-trehalose (8:2). (c) Catalase-trehalose (6:4). (d) Catalase-trehalose (4:6).
(e) Catalase-trehalose (2:8). (f) Pure trehalose.
(a) (b)
(c) (d)
Figure 5.122: SEM pictures of final particles from levitated catalase-trehalose (6:4) solutions with 100 mg/ml solid
content in 50 mM tris buffer pH 8.0 dried at 60°C and 5% relative humidity in still air. Shown are pictures with a
magnification of 100-times (a), 1000-times (b), 100-times (c) and 200-times (d).

CHAPTER 5 RESULTS AND DISCUSSION 213
Interfacial behaviour and surface excess of catalase
The interfacial behaviour and the surface excess of catalase are tested to investigate the earlier
critical point in the drying process of the pure catalase solution compared to the mixtures of catalase
and trehalose. The pure 50 mM tris buffer at pH 8.0 has no influence on the surface tension of
water. Due to the much larger molecular weight of catalase the solution molarity chosen is in a
range between 0.01 mmol/l and 1.0 mmol/l. A solution with a molar catalase concentration of
0.4 mmol/l is equal to 100 mg/ml. Figure 5.123 a shows the air / water interfacial tension versus log
time in seconds obtained for pure catalase solutions at 25°C using a bubble pressure tensiometer.
Figure 5.123 b presents the plot of Π () t / Π ∞ versus t according to the short-time approximation
of the Ward and Tordai Equation. After an interfacial lifetime of only 1 ms ( log = −3.
0)
t the values
for the dynamic interfacial tension are lower than 72.8 mN/m measured for the pure buffer solution.
For low catalase concentration (0.05 mmol) the value after 1 ms lies only marginally below pure
water. For the 0.01 mmol/l solution no difference to water at 1 ms can be detected. With increasing
solid concentration and increasing interfacial lifetime the interfacial tension decreases. For the
1.0 mmol/l solution a surface tension of 47.5 mN/m is found after an interfacial tension of 1 s.
Dynamic interfacial tension [mN/m]
75.0
70.0
65.0
60.0
55.0
50.0
45.0
(a)
Catalase solutions in
50mM tris buffer pH 8.0 at 25°C
0.05 mmol
0.1 mmol
0.2 mmol
0.4 mmol
1.0 mmol
-3 -2 -1 0 1 2
log time in seconds
0.01 mmol
0.2
0.0
Catalase solutions in
50mM tris buffer pH 8.0 at 25°C
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Figure 5.123: (a) Dynamic air / water interfacial tension as a function of time of different catalase solutions in 50 mM
tris buffer at pH 8.0 with concentration of minimum 0.01 mmol to a maximum of 1.0 mmol/l measured at 25°C. (b)
Π (t) / Π ∞ as a function of time ½ of catalase solutions in 50mM tris buffer pH 8.0 with different molar concentration at
25°C measured with bubble pressure tensiometry.
In Figure 5.123 b Π () t / Π ∞ is plotted versus t for the catalase solutions for diffusion–controlled
Π t / Π ∞
adsorption. The values of Π ∞ were determined by equilibrium ring tensiometry after an
equilibration time of 3 hours and corrected using the method by Harkins and Jordan [1930]. The
results are shown in Table 5.18. Clarkson et al. [1999] found a surface tension of 57.0 mN/m for a
1.0
0.8
0.6
0.4
(b)
Time 1/2 [s 1/2 ]
1.0 mmol
0.4 mmol
0.2 mmol
0.1 mmol
0.05 mmol
0.01 mmol

214 RESULTS AND DISCUSSION
0.01 mmol/l catalase solution in 0.1 mM phosphate buffer at pH 7.5 using ring tensiometry. For a
0.04 mmol/l catalase solution in the same solvent they found a value of 54.5mN/m.
Table 5.18: Values for equilibrium interfacial tension after 3 hours for catalase solutions in 50 mM tris buffer pH 8.0 at
25°C ambient temperature using ring tensiometry.
Concentration of
catalase solution
Equilibrium
interfacial tension
[ mmol ] 0.01 0.05 0.1 0.2 0.4 1.0
[ mN/m ] 55.0 51.1 50.4 48.6 47.0 45.7
The plot of the short-time approximation in Figure 5.123 b shows biphasic behaviour. In contrast to
bSA, the catalase solutions do not show a linear shape of the plot in the fist part and a clear break to
separate the two phases. It seems that the break point is equal to bSA at approximately 500 ms
( t = 0.
7 ). The slopes of the initial section for t ≤ 500 ms increase with higher protein
concentration. The slopes in the second linear section for t ≥ 500 ms are equal for all catalase
concentrations. Π () t / Π ∞ increases much slower in the second phase than in the initial one. Thus,
the diffusional adsorption is evidently reduced in rate at the later points in the curves of Figure
5.123 b. According to Fuhrling [2004],it seems that a barrier to adsorption is formed.
Dynamic interfacial tension [mN/m]
75.0
72.5
70.0
67.5
65.0
62.5
60.0
57.5
55.0
52.5
50.0
47.5
Catalase solutions in
50 mM tris buffer at pH 8.0
10 ms
100 ms
1000 ms
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Catalase concentration [mmol/l]
Figure 5.124: Dynamic air / water interfacial tension as a function of solution molarity of catalase solutions in 50 mM
tris buffer at pH 8.0 at different times.
1 ms

CHAPTER 5 RESULTS AND DISCUSSION 215
Figure 5.124 presents the plot of the dynamic interfacial tension versus the total molarity of the
catalase solution at different lifetime. The values decrease with increasing concentration of catalase
and increasing lifetime. None of the curves shows tendency of a levelling-out. The interfacial
tension of all curves decreases further with increasing solution molarity of catalase.
The total interfacial excess concentration of catalase is calculated using the Gibbs Equation
5.14 [Hiemenz 1986]. Figure 5.125 a shows the calculated surface excess concentration plotted
versus solution molarity for the catalase solutions at different interfacial lifetime. As expected, an
increase in Γ (t)
is found with increasing protein concentration. The formation of a plateau with
increasing catalase concentration cannot be seen. After 1 s interfacial lifetime the surface excess
values increase to 0.00226 mmol/m 2 for a 0.04 mmol/l catalase solution and to 0.00268 mmol/m 2
for a 0.1 mmol/l catalase solution. These values are equivalent to 565 mg/m 2 – 670 mg/m 2 . In
comparison, a pure bSA solution with a concentration of 0.1 mmol/l has a surface excess
concentration of 0.00113 mmol/m 2 equivalent to 75.1 mg/m 2 at an interfacial lifetime of 1 s. This
means, that catalase has a more than twice as large surface excess concentration based on the
amount of molecules than bSA resulting in an almost nine times larger mass per area unit.
Reference values from literature approving the experimental catalase values could not be found.
Figure 5.125 b presents the surface excess concentration versus interfacial lifetime with different
solid concentration. With increasing catalase content the slope of the plots in a time range between
100 ms and 1 s increases. A levelling-out in this time range can only be seen for the 0.01 mmol/l
catalase solution.
Surface excess [mmol/m 2 ]
0.0030
Catalase solutions in
50 mM tris buffer pH 8.0
0.0025
0.0020
0.0015
0.0010
0.0005
100 ms
10 ms
1 ms
0.0000
0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012
(a)
Solution molarity [mmo/m 3 ]
1000 ms
0.0030
0.0025
0.0020
0.0015
0.0010
0.0005
0.0000
0.4 mmol
0.2 mmol
0.1 mmol
0.05 mmol
0.01 mmol
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Figure 5.125: (a) Surface excess concentration Γ (t) as a function of catalase solution molarity in 50 mM tris buffer at
pH 8.0 at 25°C for different lifetimes. (b) Surface excess concentration as a function of time of catalase solutions in
50 mM tris buffer at pH 8.0 at various concentration at 25°C.
Surface excess [mmol/m 2 ]
(b)
Catalase solutions in
50 mM tris buffer pH 8.0
Time [s]
1.0 mmol

216 RESULTS AND DISCUSSION
Influence of trehalose on the interfacial behaviour of catalase
To investigate the influence of trehalose on the interfacial tension of catalase solutions, the above
molar concentration of catalase were prepared with different amounts of trehalose. The density of a
0.04 mmol/l catalase solution increases from 1.03 g/cm 3 without trehalose to 1.09 g/cm 3 with
200 mg/ml trehalose. Figure 5.126 shows the influence of trehalose on the dynamic interfacial
tension of catalase solutions with a catalase concentration of 0.04 mmol/l equivalent to 100 mg/ml
as a function of log time. The surface tension at an interfacial lifetime increases from 55.9 mN/m
for the pure catalase to 59.8 mN/m for catalase with 200 mg/ml trehalose and to 64.4 mN/m with
400 mg/ml trehalose. Figure 5.127 presents the dynamic interfacial tension of catalase solutions
with different amount of trehalose as a function of solution molarity (a, b) and interfacial lifetime
(c, d). The addition of 400 mg/ml trehalose to a 1.0 mmol/l catalase solution increases the dynamic
interfacial tension by 7.47 mN/m at an interfacial lifetime of 100 ms and by 8.27 mN/m at an
interfacial lifetime of 1000 ms. With increasing solution molarity a decrease in the dynamic
interfacial tension is determined for all tested formulations.
Dynamic interfacial tension [mN/m]
75.0
70.0
65.0
60.0
55.0
50.0
at 25°C in
50 mM tris buffer at pH 8.0
-3 -2 -1 0 1
log time in seconds
Catalase 0,40 mmol (pure)
Catalase 0,40 mmol + 100mg/ml Trehalose
Catalase 0,40 mmol + 200mg/ml Trehalose
Catalase 0,40 mmol + 400mg/ml Trehalose
Figure 5.126: Dynamic interfacial tension of 0.04 mmol/l catalase solutions in 50 mM tris buffer at pH 8.0 with
different trehalose content as a function of log time in seconds at 25°C.
Increasing trehalose content leads to a slight increase in the slope d γ ( t)
/ dc . The plot of the
dynamic interfacial tension versus interfacial lifetime does not show a levelling-out at larger
interfacial lifetime for the catalase solutions even at the highest trehalose content of 400 mg/ml. It
seems that there is a slight increase in d γ ( t)
/ dt with increasing trehalose concentration in the range

CHAPTER 5 RESULTS AND DISCUSSION 217
between 100 ms and 1000 ms. The interactions between proteins and trehalose are discussed in
detail in Chapter 5.3.4.
Figure 5.128 presents the surface excess concentration of catalase solutions with a
concentration of 0.4 mmol/l and 1.0 mmol/l and different trehalose content versus interfacial
lifetime. Trehalose decreases the surface excess of catalase for both solution molarities at interfacial
lifetimes of 100 ms and 1000 ms. For a 0.4 mmol/l solution the addition of 200 mg/ml trehalose
reduces the surface excess of pure catalase from 0.0023 mmol/m 2 to 0.0016 mmol/m 2 and the
addition of 400 mg/ml trehalose results in a surface excess decrease to 0.0015 mmol/m 2 at an
interfacial lifetime of 1000 ms. That is equivalent with a decrease in catalase concentration at the
surface from 575 mg/m 2 to 375–400 mg/m 2 .
Dynamic interfacial tension [mN/m]
Dynamic interfacial tension [mN/m]
75.0
70.0
65.0
60.0
55.0
50.0
75.0
70.0
65.0
60.0
55.0
50.0
Catalase + trehalose at 25°C
Interfacial lifetime 100 ms
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Catalase solution molarity [mmol/l]
+ 400 mg/ml
+ 200 mg/ml
+ 100 mg/ml
pure
Catalase solution molarity 0.4 mmol/l
Catalase + trehalose at 25°C
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Time [s]
+ 400 mg/ml
+ 200 mg/ml
+ 100 mg/ml
pure
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Catalase solution molarity [mmol/l]
Figure 5.127: Dynamic interfacial tension of catalase solution in 50 mM tris buffer at pH 8.0 with different amount of
trehalose as a function of solution molarity and interfacial lifetime. (a) Dynamic interfacial tension versus solution
molarity for an interfacial lifetime of 100 ms. (b) Dynamic interfacial tension versus solution molarity for an interfacial
lifetime of 1000 ms. (c) Dynamic interfacial tension versus interfacial lifetime for a catalase solution molarity of
0.4 mmol/l. (d) Dynamic interfacial tension versus interfacial lifetime for a catalase solution molarity of 1.0 mmol/l.
Dynamic interfacial tension [mN/m]
Dynamic interfacial tension [mN/m]
75.0
70.0
65.0
60.0
55.0
50.0
75.0
70.0
65.0
60.0
55.0
50.0
Interfacial lifetime 1000 ms
Catalase + trehalose at 25°C
+ 400 mg/ml
+ 200 mg/ml
+ 100 mg/ml
pure
Catalase solution molarity 1.0 mmol/l
Catalase + trehalose at 25°C
+ 400 mg/ml
+ 200 mg/ml
+ 100 mg/ml
pure
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Time [s]

218 RESULTS AND DISCUSSION
The plots of the surface excess versus interfacial lifetime show almost similar values for the three
different trehalose formulations. At a catalase solution molarity of 0.4 mmol/l they are within a
range of 0.0015 mmol/m 2 to 0.0017 mmol/m 2 . For the 1.0 mmol/l Catalase solution, equivalent to
250 mg/ml, the addition of 200 mg/ml or 400 mg/ml trehalose reduces the surface excess of catalase
from 0.00268 mmol/m 2 to approximately 0.0017 mmol/m 2 . Therefore the amount of catalase at the
surface decreases from 670 mg/m 2 to 425 mg/m 2 . The slope d ( t)
/ dt
Γ of the plots between 100 ms
and 1000 ms at 0.4 mmol/l catalase solution molarity as well as at 1.0 mmol/l catalase solution
molarity decreases with increasing trehalose content.
Surface excess [mmol/m 2 ]
0.0030
0.0025
0.0020
0.0015
0.0010
0.0005
0.0000
Catalase solution molarity 0.0004 mmol/m 3
Catalase pure
Catalase + 100 mg/ml trehalose
Catalase + 200 mg/ml trehalose
Catalase + 400 mg/ml trehalose
0.0 0.2 0.4 0.6 0.8 1.0
Time [s]
Figure 5.128: Surface excess concentration of catalase solutions in 50 mM tris buffer at pH 8.0 with different trehalose
content as a function of interfacial lifetime at 25°C. (a) Surface excess concentration versus interfacial lifetime for a
0.4mmol/l catalase solution. (b) Surface excess concentration versus interfacial lifetime for a 1.0 mmol/l catalase
solution.
Comparison of surface tension and surface excess of bSA and catalase
0.0030 Catalase solution molarity 0.001 mmol/m 3
0.0025
0.0020
0.0015
0.0010
0.0005
0.0000
0.0 0.2 0.4 0.6 0.8 1.0
To compare the bSA and catalase results only the surface tension and the surface excess of the
1.0 mmol/l protein solutions are presented in Figure 5.130. At an interfacial lifetime of 1.0 s the
dynamic interfacial tensions of the pure catalase and the catalase with 200 mg/ml trehalose have
lower values than the bSA solutions. The slopes d γ / dt of both catalase plots between 100 ms and
1000 ms are smaller than for bSA. The same results are obtained for the surface excess of the two
proteins. Catalase and the catalase-trehalose formulation show a larger surface excess at any
interfacial lifetime than bSA. The slopes d Γ / dt of the plots between 100 ms and 1000 ms are
larger for pure catalase than for pure bSA. The same behaviour can be observed for the protein-
trehalose formulations. The slope d Γ / dt between 100 ms and 1000 ms is lager for catalase with
200 mg/ml trehalose than for bSA solution with the same trehalose concentration. The 1.0 mmol/l
Surface excess [mmol/m 2 ]
Catalase pure
Catalase + 100 mg/ml trehalose
Catalase + 200 mg/ml trehalose
Catalase + 400 mg/ml trehalose
Time [s]

CHAPTER 5 RESULTS AND DISCUSSION 219
catalase solution has a surface excess concentration of 0.00268 mmol/m 2 at an interfacial lifetime of
1.0 s, what is equivalent to 670 mg/m 2 . In contrast, bSA has a surface excess concentration of
0.00113 mmol/m 2 at an interfacial lifetime of 1.0 s what is equivalent to 75.1 mg/m 2 . Catalase has a
more than twice as large surface excess concentration based on the amount of molecules than bSA
resulting in an almost nine times larger mass per area unit. Although catalase has an approximately
3.8-times larger molecular weight, it shows a more than two times larger surface excess
concentration than bSA at any interfacial lifetime.
Dynamic interfacial tension [mN/m]
75.0
70.0
65.0
60.0
55.0
50.0
bSA pure
bSA + 200 mg/ml trehalose
Catalase pure
Catalase + 200 mg/ml trehalose
Protein solution molarity 1.0 mmol/l
0.0 0.2 0.4 0.6 0.8 1.0
Time [s]
Figure 5.129: (a) Dynamic interfacial tension of aqueous bSA solutions and catalase solutions in 50 mM tris buffer at
pH 8.0 as a function of interfacial lifetime for a protein concentration of 1.0 mmol/l without and with 200 mg/ml
trehalose. (b) Surface excess concentration of aqueous bSA solutions and catalase solutions in 50 mM tris buffer at
pH 8.0 as a function of interfacial lifetime for a protein concentration of 1.0 mmol/l without and with 200 mg/ml
trehalose.
Enzyme activity of levitated catalase solution droplets
Surface excess [mmol/m 2 ]
0.0030
0.0025
0.0020
0.0015
0.0010
0.0005
0.0000
bSA pure
bSA + 200 mg/ml trehalose
Catalase pure
Catalase + 200 mg/ml trehalose
Protein solution molarity 0.001 mmol/m 3
0.0 0.2 0.4 0.6 0.8 1.0
Time [s]
To investigate influences of the drying conditions and the ultrasonic levitation system on the
activity of catalase, the solutions of the mixture series of catalase and trehalose with an overall solid
content of 100 mg/ml are levitated at 60°C and different relative humidity in still air and the
residual enzyme activity of the final particles is determined. Therefore, the formulations are freshly
prepared in ice-cooled 50 mM tris buffer at pH 8.0 and divided into two portions. One is frozen at -
80°C and used to determine the initial enzyme activity. The other portion is put on ice and directly
used for the levitation experiments. The final particles are taken out of the standing acoustic wave
as soon as no more changes in volume and vertical position can be determined for 30 seconds. The
particles are also frozen at -80°C for later determination of the residual enzyme activity. Due to the
low particle mass and the lack of accuracy when weighing the particles, the amount of catalase is

220 RESULTS AND DISCUSSION
determined using the volume of the initial droplet calculated from the back illumination pictures
taken by the CCD-camera and the density of the liquid solution, assuming a particle with no
residual moisture content. To determine the catalase activity, the rate of disappearance of H2O2 was
followed by monitoring the decrease in absorbance at 240 nm in 50 mM phosphate buffer at pH 7.0
at 25°C. The method is described in detail in Chapter 4.2.6. The experiments are compared to the
results obtained from spray-dried catalase formulations. 20 ml solutions are prepared the same way
as for the levitation experiments and divided into 5 ml for the determination of the initial enzyme
activity and to 15 ml for the spray-drying experiments in the Buchi Mini Spray-Dryer B-191 at
T = 100° C , T = 60° C and a liquid feed of 3 ml/min. After the experiment the product is
inlet
outlet
divided into two portions, one to determine the residual moisture content via Karl-Fischer titration
and the other to determine the residual enzyme activity. All results are presented in Figure 5.130.
Regarding the spray-drying results, the pure trehalose looses 2.9% enzyme activity. Compared to
lactate dehydrogenase (LDH) which looses approximately 11% when spray-dried at T = 90° C
and T = 60° C [Adler 1999] the loss in enzyme activity of catalase is very low under these
outlet
conditions. Formulating catalase with trehalose increases the activity of catalase. The addition of
20% trehalose based on the solid content is sufficient to achieve a residual activity of 99.1%.
Further increase in trehalose content has no significant influence. In contrast, the residual activity of
the levitated particles at drying air conditions of 60°C and 5% relative humidity is determined to
87.7%. As for spray-drying, the residual catalase activity increases with the addition of trehalose to
the catalase formulation. 20% trehalose based on the solid content is sufficient to achieve a residual
activity of 95.5% under the same drying conditions. Further increase in the trehalose content has no
additional influence on the activity. An increase in drying air humidity results in a decrease in
catalase activity. The residual enzyme activity determined for the pure catalase particles decreases
to 81.2% at drying air humidity of 20% and to 77.2% at drying air humidity of 40%. The increased
humidity increases the droplet surface temperature from 24.9°C at 60°C and 5% humidity to 43.2°C
at 60°C and 40% humidity. As for the other results before, the addition of 20% trehalose based on
the solid content increases the residual catalase activity to 92.2% at 20% relative humidity and to
91.0% at 40% relative humidity. Under these conditions a further increase in trehalose content
seems to result in a slight increase in residual enzyme activity. Although examinations on the
determination of enzyme kinetics in levitated water droplets state, that an influence of the standing
acoustic wave and the ultrasonic field on the residual activity can be excluded [Weis 2005], the
values for catalase dried in the levitator are lower than for all spray-dried solutions. The larger loss
in activity using the levitation system can be caused by the longer handling and drying time
compared to spray-drying. A slight decrease in residual catalase activity by averaged 2.4% (n = 3)
inlet

CHAPTER 5 RESULTS AND DISCUSSION 221
can be detected with an increase in effective initial SPL from 164.9 dB to 166.2 dB. Untreated
dissolved catalase shows a 15% loss in activity in 2 hours at 20°C. Further investigations on
enzyme activity of more sensitive proteins, for example LDH, have to be done to obtain a better
comparison of the two drying processes. Altogether a stabilizing effect of trehalose on the protein
can be seen for both drying techniques. The protein-sugar interactions as well as the effects and the
exceptional role of trehalose in protein stabilization have been discussed in detail in Chapter 5.3.2
and Chapter 5.3.4.
Residual catalase activity [%]
100.0
95.0
90.0
85.0
80.0
75.0
Spray-dried T in / T out = 100 / 60°C
Levitated at 60°C and 5% humidity
Levitated at 60°C and 20% humidity
Levitated at 60°C and 40% humidity
0.0 20.0 40.0 60.0 80.0
Trehalose content [% solid]
Figure 5.130: Residual catalase activity as a function of trehalose solid content in the formulation with catalase. Shown
are results from spray-drying experiments at Tinlet=100°C, Toutlet=60°C and a liquid feed of 3 ml/min as well as from
levitation experiments at 60°C and different relative humidity in still air. The initial droplet volume was 1.5 µl at an
initial effective SPL between 164.6 dB and 165.1 dB.

CHAPTER 6 CONCLUSIONS 222
6 Conclusions
The present thesis deals with the set-up of an acoustic levitation system to examine pharmaceutical
spray-drying formulations of peptides and proteins. Spray-drying is a well known, rapid and easy
method to transform peptide and protein solutions into dry powders for pulmonary and parenteral
application. However, there are effects reported in literature with regard to protein stability, which
limit the overall applicability of spray-drying. To investigate the influence of the formulation
excipients and the drying conditions on the drying kinetics and the particle formation, single droplet
drying methods have been studied in the last couple of years. Acoustic levitation is the containerless
processing of small liquid or solid samples in the pressure nodes of a standing acoustic wave
between an ultrasonic transducer and a reflector. The characteristics of the acoustic levitator enable
the determination of the single droplet drying kinetics within the constant rate and the falling rate.
The goal of this work was first of all to set up an acoustic levitation system for single droplet drying
experiments under varying drying conditions. Secondly, the evaporation behaviour of single
droplets of pure solvents or solvent mixtures should be investigate and influences of the levitation
system on the droplet drying kinetics should be taken into account. The experimental results had to
be compared to simple gas-phase models and data from the literature. Furthermore, the evaporation
behaviour of single solution droplets containing sugars, peptides or proteins and complex protein
formulations had to be investigated and compared to data form spray-drying experiments and
literature.
In the first part of the thesis a single-walled acoustic levitator with a flat-flat transducerreflector
design was set up into a self-constructed acrylic glass container. A mass flow and liquid
flow controller in combination with a controlled evaporation mixer and an additional heater were
introduced to the system to set predefined and accurate drying conditions. Thus, experiments in a
temperature range from room temperature up to 70°C with a relative humidity from a few ppm to
almost 100% were possible. Different connection possibilities of the drying air supply enabled
evaporation in still air as well as under relative velocity conditions up to approximately 3.0 m/s. A
variable positioning of the CCD-camera and the light source offered further possibility of taking
back light and front light illumination pictures to get a better understanding of the drying process
and the particle formation. Comparison of levitated Migliol N812 droplets with rigid polypropylene
spheres showed a deformation of the Migliol N812 droplet to an oblate ellipsoid caused by the
different values of axial and radial levitation forces. Furthermore, internal droplet oscillations
occurring in vertical direction resulted in a larger standard deviation of the mean vertical diameter

CHAPTER 6 CONCLUSIONS 223
of the droplet than of the rigid sphere. Due to the deformation of liquid samples the calculation of
droplet volume could not be performed assuming a spherical geometry. Experiments comparing the
injected to the calculated volume showed the best correlation for an oblate rotational ellipsoid. An
increasing effective sound pressure level (SPL) had a strong influence on the deformation of the
droplet and leading to an increasing aspect ratio. Vibrations, air flow or a not ideal adjusted
standing acoustic sound wave could lead to a deflection of the sample out of its rest position
resulting in unstable droplet behaviour. Levitation capabilities could be improved by using a curved
reflector and enlarging its section as to levitate dense materials or liquids under large ventilation air
streams. The semi-confocal set-up with a reflector having a radius of curvature of twice the distance
between transducer and reflector was the least problematic. Experiments at 60°C and 20% relative
humidity in still air and with a drying air velocity of 2.0 m/s confirmed the superior and more stable
droplet levitation of the semi-confocal set-up than the flat-flat one.
In the second part of this thesis the evaporation of pure water and ethanol droplets and
binary mixtures of both was analysed in the acoustic levitator and the results were compared to
different mathematical single droplet drying models. The plot of
2
rS rS
0
2 / versus
2
t rS
0
/ was the most
suitable for data analysis, because it compensated different initial droplet volumes. The slope was
defined as evaporation coefficient β r and characterized the evaporation process for a given pure
solvent droplet under conditions valid for the d 2 -law. Experiments with water droplets at 25°C in
still air showed a faster evaporation than predicted by the diffusion-controlled evaporation model
and a slower evaporation than predicted by the levitation model. Influence of the standing acoustic
wave affected the evaporation process. The inner acoustic streaming led to an increased evaporation
due to shear stress at the droplet surface, whereas the accumulation of solvent vapour in the toroidal
vortices of the outer acoustic streaming had a hindering effect on the solvent evaporation. A force
drying air stream of 1.0 m/s was determined to be suitable to remove the solvent vapour out of the
vortices completely. Experimental results obtained at 25°C and under a drying air velocity of
1.0 m/s matched perfectly with the levitation model. The Sherwood number was determined to 5.3
for an initial droplet volume of 2.0 µl. The same correlation with levitation model was obtained at
40°C and 60°C with a drying air humidity of 0.1%. The initial Sherwood number at 40°C and 0.1%
humidity was found to be 8.0 for an initial droplet volume of 2.0 µl. Drying air velocities > 1.0 m/s
resulted in an additional convective influence on the droplet surface and could not be described by
the levitation model any more. The Ranz-Marshall correlation provided a suitable equation to
predict the existing Sherwood numbers and therefore the radius-time course of the drying
experiment. The plot of the evaporation coefficient in still air showed increasing values with

CHAPTER 6 CONCLUSIONS 224
increasing temperature and decreasing drying air humidity. Under relative velocity conditions the
evaporation coefficient determined in a diameter range between 1200 µm and 800 µm increased
from 0.00193 mm 2 /s at 60°C and 0.1% humidity in still air to 0.00458 mm 2 /s under the same
conditions but with a drying air velocity of 1.98 m/s. At the same time the evaporation time of a
1.0 µl droplet was reduced from 225 s to approximately 80 s. Increasing drying air velocity and
decreasing humidity led to increasing values of the evaporation coefficient β r under relative
velocity conditions.
The evaporation of pure ethanol droplets resulted in a faster evaporation and larger β r
values than water due to the higher vapour pressure of ethanol at equal temperature. At 60°C and
0.1% humidity in still air, the evaporation coefficient of ethanol was determined to 0.00542 mm 2 /s.
Influences of inner and outer acoustic streaming were as with pure water droplets. The levitation
model and the Ranz-Marshall correlation could also be used to determine the radius-time course at
different temperatures and humidities ≤ 3.0%. With an increase in drying air humidity biphasic
evaporation behaviour of the ethanol droplet evaporation could be seen. The vaporization of pure
volatile alcohols in humid air was accompanied by the simultaneous condensation of water vapour
on the droplet surface and its subsequent diffusion into the droplet interior. In the first phase, the
evaporation of pure ethanol dominated. An increasing humidity resulted, however, in an increasing
evaporation rate of the ethanol droplets in this first part of evaporation. The associated heat release
at the droplet surface due to the condensation increased the initial evaporation rate of the ethanol.
The mixture of ethanol and water formed had a higher wet bulb temperature than pure ethanol,
resulting in a larger evaporation rate. The wet bulb temperature of ethanol droplets at 60°C drying
temperature increased from 13.3°C at 0.1% humidity to 32.6°C at 40% humidity. This effect led to
increased evaporation coefficients for ethanol experiments not only with temperature but also with
drying air humidity. After all of the ethanol was evaporated, the subsequent radius-time-course was
dominated by the evaporation of the condensed water vapour. It could be shown, that the
evaporation coefficient in this stage was equal to that of pure water droplets under the same ambient
conditions. Under relative velocity conditions an increase in drying air velocity resulted in an
increase in evaporation coefficient. At 60°C and 0.1% humidity the evaporation coefficient
increased to 0.01308 mm 2 /s resulting in a decrease of evaporation time for a 1.0 µl droplet from
83.0 s in still air to 27.3 s at a velocity of 1.7 m/s.
The binary mixture of water-ethanol also showed biphasic behaviour. The results obtained at
60°C and 0.1% humidity showed increasing evaporation coefficients in the initial phase with
increasing amount of ethanol in the solvent mixture. The values for the mixtures were between the

CHAPTER 6 CONCLUSIONS 225
coefficients of pure water and pure ethanol under same ambient conditions. In the terminal part, the
evaporation coefficients showed almost constant values independent of the initial composition of
the droplet. The comparison with pure water droplets gave a good agreement.
The third part of this thesis describes the application of the acoustic levitation system to
determine the single droplet drying kinetics of solution droplets. The drying behaviour and particle
formation of sugar solutions relevant in spray-drying (maltodextrin, trehalose and mannitol), protein
solution (bSA and catalase) and protein-sugar formulations were investigated. Experiments
performed with maltodextrin solutions showed a strong influence of the effective SPL on the shape
of the resulting particle. With increasing effective SPL the initial aspect ratio of the levitated
solution droplets and the final particles increased. The initial droplet aspect ratio and the final
particle aspect ratio showed a linear relationship (R 2 = 0.98). Maltodextrin solutions showed clear
transition from constant to falling rate. Only small size changes of the vertical diameter could be
determined in the second drying stage, resulting in flatting of the particle. Different initial droplet
sizes in still air experiments could be compensated by plotting the evaporation rate in evaporated
mass per time and surface area versus
2
t rS
0
/ . Increased maltodextrin solid content resulted in a
decrease in the duration of the first drying stage and a shallower decline of the evaporation rate in
the second drying stage. For a 1.8 µl droplet dried at 40°C and 0.1% relative humidity in still air,
the constant rate decreased from 445.3 s at 50 mg/ml solid content to 91.5 s at 400 mg/ml solid
content whereas the falling rate period increased from 162.4 s to 708.6 s. Due to the different
amount of dissolved molecules the evaporation rate in the first drying stage decreased from
0.75 µg/s/mm 2 to 0.58 µg/s/mm 2 . Particle size analysis showed an increasing particle size with
increasing solid content. The final particle density of the experiments at 25°C gave almost constant
density values of approximately 0.85 g/cm 3 with increasing maltodextrin concentration, whereas a
slight increase in particle density from approximately 0.7 g/cm 3 to 0.75 g/cm 3 could be determined
at 40°C and 60°C drying temperature. SEM pictures of the final levitator particles showed a particle
surface indented by small craters which were not combined with capillaries in the interior. The
interior had a massive solid structure without any holes. The levitated particles showed a similar
morphology compared to the larger particles of the spray dried powder.
For trehalose solution droplets no sharp transition from constant to falling rate could be seen
form the graph of the volume as a function of evaporation time. The critical point could only be
detected using the plot of the aspect ratio versus time. A flattening as for maltodextrin particles
could not be seen. With increasing solid content an increase in the first and a decrease in the second
drying stage could be determined. For an initially 1.8 µl droplet dried at 60°C and 5% relative

CHAPTER 6 CONCLUSIONS 226
humidity in still air, the critical point appeared after 274.4 s for a 50 mg/ml solution and after
138.9 s for a 400 mg/ml solution. The detectable falling rate period increased from 234.0 s to
668.6 s. With increasing solid content and increasing drying air humidity the decline of the
evaporation rate after the critical point became shallower. For a 400 mg/ml trehalose solution
droplet at 60°C and 40% humidity, no transition between first and second drying stage could be
detected any more. The final particle size in relation to the initial droplet size increased from 37.4%
for a 50 mg/ml trehalose solution (60°C; 5% humidity; still air) with increasing solid content to
75.5% for a 400 mg/ml solution. Increasing humidity showed a decreasing particle size. The final
particle density was found to decrease with increasing trehalose content and decreasing humidity.
The final particle density values for the above conditions were 1.03 g/cm 3 (50 mg/ml trehalose) and
0.97 g/cm 3 (400 mg/ml trehalose). Drying under relative velocity conditions showed a decrease in
duration of the first drying stage and a less shallow decline of the evaporation rate after the critical
point with increasing drying air velocity. The values of the evaporation rate in the first drying stage
for a 100 mg/ml trehalose solution increased from 1.1 µg/s/mm 2 at 60°C and 5% humidity in still
air to almost 3.0 µg/s/mm 2 at the same temperature and humidity but with a drying air velocity of
1.5 m/s. The faster evaporation process under relative velocity conditions than in still air resulted in
larger and less dense particles.
Mannitol solutions showed a sharp critical point and a constant particle size and aspect ratio
within the second drying stage due to an abrupt particle formation. Influences of drying
temperature, relative humidity and velocity on the evaporation rate in the constant and falling rate
were as with maltodextrin and trehalose. A determination of the single droplet drying kinetics under
air flow conditions could only be performed up to a drying air velocity of 1.0 m/s. Larger velocities
resulted in strong droplet oscillations starting in the second drying stage. The abrupt particle
formation and unbalanced particle shape in combination with the very low particle density caused
turbulences of the drying air in the area of the pressure node and made the particle susceptible for a
blow-out. Mannitol showed the lowest particle density of all examined substances and formulations.
Under the fasted drying conditions at 60°C and 5% humidity in still air a final particle density of
0.50 g/cm 3 was obtained at a drying air velocity of 1.0 m/s even 0.32 g/cm 3 . The SEM pictures of
particles produced at room temperature showed only partially spherical particles with protuberances
at their surface and a spicular morphology. Experiments with faster solvent evaporation led to
particles with a smoother surface compared to the particles produced at room temperature. The
particles had a hollow interior with blow hole in their surface. The SEM pictures of spray-dried
mannitol in largest magnification showed particles with a smooth surface. A spicular surface

CHAPTER 6 CONCLUSIONS 227
structure could not be determined. Bowl like particles could be found under air flow conditions with
a smooth bottom side into the direction of the air stream and protuberances on the top side.
The drying of bSA solution in the acoustic levitation system showed a behaviour different to
the sugar solutions. Breakage of the new formed particle with hollow interior as well as formation
of large holes in the surface after the critical point led to instable particle behaviour in the second
drying stage with strong oscillations. Analysis of the SEM pictures determined a particle crust with
the thickness of 31.75% of the particle radius for a bSA solution with 100 mg/ml solid content
(60°C; 10% humidity; still air). For a spherical particle with a radius of 500 µm a void volume of
0.166 µl was calculated enlarging the outer surface area of the particle by an interior surface of
1.46 mm 2 to an overall surface area of 4.60 mm 2 . This change in surface area within the second
drying stage resulted in an increase of the evaporation rate to value almost as high as in the constant
rate period. Formulation of bSA with trehalose in a bSA-trehalose (1:1) mixture with 100 mg/ml
solid content did not show increasing evaporation rate values in the falling rate period. Blow holes
or hollow particle interiors could not be found on the SEM, either. A comparison of the pure
protein, the mixture and the pure trehalose showed an increase in duration of the first drying stage
with increasing trehalose content., 65.1% of the solvent was evaporated in the constant rate from the
pure bSA solution droplets, whereas the percentage of solvent evaporated for the mixture and the
pure trehalose was almost equal with 87.8 to 85.6% (60°C; 5% humidity; still air). The evaporation
rate in the first drying stage at 60°C and 10% humidity in still air decreased from 1.21 µg/s/mm 2 for
the pure bSA to 0.91 µg/s/mm 2 for the pure trehalose. The mixture had a value of approximately
1.0 µg/s/mm 2 . With disregard of the pure bSA solution, the decline of the evaporation rate after the
critical point became shallower with increasing trehalose content. A comparison to the spray-dried
bSA and bSA-trehalose product showed very good correlation. Due to the hollow particle interior
the density of 0.62 g/cm 3 of the pure bSA particles produced in the levitation system was
approximately 0.3 units lower than for the mixture with trehalose. A comparison of the bSAtrehalose
(1:1) mixture and the pure trehalose particles resulted in almost the same values for size
and density with slightly larger mixture particles with a minimal lower density. Investigations on
interfacial behaviour of bSA and its mixture with 200 mg/ml trehalose using bubble pressure
tensiometry showed that trehalose increased the dynamic interfacial tension of a 2.0 mmol/l bSA
solution by 3.67 mN/m and of a 4.0 mmol/l bSA solution by even 4.42 mN/m (interfacial lifetime
1.0 s). Calculation of the surface excess concentration using the Gibbs Equation showed a reduction
of bSA at the surface from 87 mg/m 2 to 36 mg/m 2 on the addition of 200 mg/ml trehalose to a

CHAPTER 6 CONCLUSIONS 228
4.0 mmol/l bSA solution at an interfacial lifetime of 1.0 s. The area per molecule in a bSA
monolayer was determined to be 100 nm 2 at the transition from gaseous to liquid-condensed state.
For pure catalase solutions in 50 mM tris buffer at pH 8.0 levitated at 60°C in still air
particles with surface holes of a mean diameter of 45.1 ± 4.3% of the horizontal particle diameter
were found. The solid crust had a thickness of approximately 18.3% of the final particle radius. A
spherical particle with a radius of 500 µm had an overall volume of 0.524 µl with a void volume of
0.286 µl. The surface area of the internal void sphere was calculated to 2.10 mm 2 and enlarged the
outer surface to an overall surface area of 5.24 mm 2 . The increase in surface area resulted in a
meanwhile increase in evaporation rate within the second drying stage. Single droplet drying
investigation on a catalase-trehalose mixture series with an overall solid content of 100 mg/ml
showed that a catalase-trehalose relation of 6:4 was needed to obtain massive particles without
surface holes and to overcome the effects of an additional surface on the evaporation rate in the
second drying stage. With increasing trehalose content, the duration of the first drying stage and
therefore the percentage of solvent evaporated in this phase increased from 61.9% for the pure
catalase at to 85.5% for a catalase-trehalose (2:8) mixture (60°C; 5% humidity; still air). The initial
evaporation rate in the first drying stage decreased from 0.95 µg/s/mm 2 for pure catalase to
0.91 µg/s/mm 2 for the catalase-trehalose (2:8) mixture under the above conditions. The pure
trehalose solution in tris buffer had an initial value of 0.89 µg/s/mm 2 . With increasing trehalose
content the decline in evaporation after the critical point became shallower. The morphological
correlation of levitated and spray-dried product was very good. The density of the levitated particles
increased from 0.43 g/cm 3 for the pure catalase with increasing trehalose content to 0.84 g/cm 3 for
the catalase-trehalose (2:8) mixture (60°C; 5% humidity; still air). Bubble pressure tensiometry
showed that 200 mg/ml trehalose increased the dynamic interfacial tension of a 0.40 mmol/l
catalase solution, equivalent to 100 mg/ml, by 3.9 mN/m at an interfacial lifetime of 1.0 s.
Furthermore, the calculated surface excess concentration was reduced from 575 mg/mm 2 to
400 mg/mm 2 . Investigations on enzyme kinetics in acoustically levitated droplets did not correlate
to the results obtained from the same spray dried catalase-trehalose formulations, due to the long
evaporation time at 60°C and the large droplet size of the samples in the levitation system.
However, a stabilizing influence of trehalose on the residual catalase activity could be shown.
Addition of 20% trehalose in the solid content, equal to a molar ratio catalase-trehalose ratio of
1:183, increased the residual activity from 87.7% to 95.5% at drying conditions of 60°C and 5%
relative humidity in still air. An increase in drying time due to an increase in humidity resulted in a
slightly smaller residual catalase activity.

CHAPTER 6 CONCLUSIONS 229
In summary, the acoustic levitator appears to be a promising tool to investigate the single
droplet drying behaviour of pure solvents, solvent mixtures, suspensions and solutions. Even though
influences of the standing acoustic wave on mass transfer and particle formation could be
demonstrated, it was possible to predict the radius-time course of the evaporation process in the
levitation system with mathematical models and to show a very good morphological correlation of
the levitated particles with the spray-dried powder of the same formulation. These results and the
possibility to set almost every possible drying condition within a given temperature range make the
levitator an interesting tool to perform preliminary test in spray-drying research, especially if there
is only little amount of substance available. Reconstruction of the system with the integration of a
cooled ultrasonic transducer and an automatic droplet injection via a micro-pump system would
offer the possibility to dry at temperature higher than 70°C with a smaller initial droplet size and to
obtain an improved correlation to the spray-drying experiments. The introduction of an IRthermocamera
would enable to determine the surface temperature course of solvents or solutions
with evaporation time what could provide a tool to verify the countless models in literature to
calculate the wet-bulb temperature. Further application areas arise beside the determination of
drying kinetics, particle formation or protein stability. It is quite conceivable to use the ultrasonic
levitation system for basic pharmaceutical investigations of distribution processes inside a liquid
droplet, for in-situ micro-encapsulation or polymerisation or to examine the quality of encapsulation
formulation, for example of volatile substances, not only in pharmaceutical but also in food
technology.

CHAPTER 7 ZUSAMMENFASSUNG 230
7 Zusammenfassung
Die vorliegende Arbeit beschäftigt sich mit dem Aufbau eines akustischen Levitationssystems zur
Untersuchung von pharmazeutischen Peptid- und Proteinformulierungen im Bereich der
Sprühtrocknung. Die Sprühtrocknung ist eine bekannte, schnelle und einfache Methode Peptidoder
Proteinlösungen in trockene Pulver für parenterale oder pulmonale Applikation zu überführen.
Jedoch wird in Veröffentlichungen immer wieder auf Einflüsse bezüglich der Proteinstabilität
hingewiesen, die die Anwendbarkeit der Sprühtrocknung in diesem Bereich limitieren. Um
Auswirkungen der Formulierungszusammensetzung und der Trocknungsbedingungen auf die
Trocknungskinetik und die Partikelbildung zu untersuchen, wurde in den letzten Jahren die
Trocknung einzelner Tropfen mit verschiedenen Methoden zunehmend untersucht. Unter
akustischer Levitation versteht man das berührungslose Arbeiten mit kleinen, festen oder flüssigen
Proben, die im Druckknoten einer stehenden akustischen Welle zwischen einem Ultraschallerreger
und einem Reflektor schweben. Die Eigenschaften dieser stehenden Welle ermöglichen die
Bestimmung der Trocknungskinetik eines einzelnen Tropfens in beiden Trocknungsabschnitten.
Das Ziel dieser Arbeit war zuerst der Aufbau eines akustischen Levitationssystems mit dem es
möglich ist, unter variierenden Bedingungen die Trocknungskinetik einzelner Tropfen zu
untersuchen. Anschließend wurde das Trocknungsverhalten reiner Lösungsmittel und derer
Mischungen untersucht. Dabei sollten Einflüsse des Ultraschallfeldes auf die Trocknung genau
betrachtet werden. Die Ergebnisse mussten anschließend mit einfachen Trocknungsmodellen und
bereits publizierten Daten verglichen werden. Als drittes sollte das Trocknungsverhalten von
Zucker- und Proteinlösungen im Ultraschall-Levitator untersucht und mit Daten aus
Sprühtrocknungsexperimenten und Publikationen verglichen werden.
Im ersten praktischen Teil dieser Arbeit wurde um den einwandigen, akustischen Levitator
mit flacher Geometrie von Ultraschallwandler und Reflektor ein Acrylglascontainer ähnlich einer
Glove-Box konstruiert, um Einflüsse durch die Umgebungsluft zu minimieren. Durchflussmesser
für Gas und Flüssigkeiten wurden mit einem Konditioniersystem kombiniert und eine zusätzliche
Heizung in das System eingebaut. Es war somit möglich definierte Trocknungsbedingungen von
Raumtemperatur bis 70°C mit Luftfeuchten von annähernd trockener Luft bis fast 100%
einzustellen. Verschiedene Zuluftverbindungen zum Levitator ermöglichten die Trocknung sowohl
in ruhiger Luft als auch mit Luftgeschwindigkeiten bis ungefähr 3,0 m/s. Variable Positionen der
CCD-Kamera und der Lichtquelle boten die Möglichkeit sowohl Gegenlicht als auch
Stirnlichtbilder während des Trocknungsprozesses aufzunehmen. Der Vergleich eines levitierten

CHAPTER 7 ZUSAMMENFASSUNG 231
Migliol N812-Tropfens mit einer festen Polypropylenkugel zeigte deutlich die durch
unterschiedliche Werte für die axiale und radiale Leviationskraft verursachte Verformung des
Tropfens. Des Weiteren konnte an der größeren Standardabweichung des Mittelwertes des
horizontalen Tropfendurchmessers von Migliol N812 im Vergleich zur Polypropylenkugel, das
Auftreten interner Tropfenschwingungen in vertikaler Richtung deutlich gemacht werden. Die
Deformation der Flüssigkeitsproben ergab für den geometrischen Körper eines Rotationsellipsoiden
die beste Übereinstimmung bei der Größen- und Volumenberechnung des Tropfens. Mit steigendem
Schalldruck nahm das Achsenverhältnis aus horizontalem und vertikalem Tropfendurchmesser zu.
Gehäusevibrationen, Trocknungsluft oder eine nicht optimal eingestellte stehende akustische Welle
konnten zu einer Auslenkung des Tropfenschwerpunktes aus seiner Ruheposition und zu
Instabilitäten während des Experimentes führen. Um das Leistungsvermögen des akustischen
Levitators hinsichtlich einer stabilen Probenposition zu erhöhen, wurde die ursprünglich flache
Geometrie von Ultraschallwandler und Reflektor gegen eine semikonfokale ausgetauscht. Bei
einem Kurvenradius des Reflektors mit dem doppelten Abstand zwischen Wandler und Reflektor
ergab sich die größte Probenstabilität.
Im zweiten Teil der Arbeit wurde die Verdampfung von reinem Wasser und Ethanol und
derer Gemische untersucht und die experimentellen Ergebnisse mit Trocknungsmodellen
verglichen. Dabei zeigte sich die graphische Darstellung des Tropfenradius
2
t rS
0
2
rS rS
0
2 / gegen die Zeit
/ zur Kompensation unterschiedlich großer Anfangsvolumina am besten geeignet. Unter
Bedingungen des d 2 -Gesetzes ergab die Steigung des Graphen den für die Verdampfung des reinen
Lösungsmittels charakteristischen Trockungskoeffizienten β r . Experimente mit Wasser bei 25°C
zeigten eine schnellere Verdampfung des Tropfens als mit dem „Diffusionskontrollierten
Trocknungsmodell“ vorhergesagt wurde und eine langsamere Verdampfung als mit dem
„Levitationsmodell“ berechnet. Hieraus ließen sich die Einflüsse der stehenden akustischen Welle
auf den Trocknungsprozess deutlich erkennen. Während die innere akustische Strömung durch
Scherbeanspruchung der Tropfenoberfläche den Massenübergang und die Sherwood-Zahl erhöhte,
wurde durch Dampfanreicherung im Wirbelsystem der äußeren akustischen Strahlung der
Trocknungsprozess hingegen verlangsamt. Die Einbettung des Tropfens in einen
Trocknungsluftstrahl mit einer Geschwindigkeit von ungefähr 1.0 m/s zeigte sich als ausreichend,
um das den Tropfen umgebende Wirbelsystem frei zu blasen. Experimente bei 25°C mit einer
Luftgeschwindigkeit von 1.0 m/s stimmten mit dem vorhergesagten Trocknungsverlauf des
„Levitationsmodelles“ überein. Für einen anfänglich 2.0 µl großen Tropfen ergab sich unter diesen
Bedingungen eine anfängliche Sherwood-Zahl von 5.3. Dieselbe Übereinstimmung experimenteller

CHAPTER 7 ZUSAMMENFASSUNG 232
Daten mit dem „Levitationsmodell“ wurde auch bei 40°C und 60°C Trocknungstemperatur mit
einer Luftfeuchte von 0.1% gefunden. Für einen 2.0 µl großen Tropfen bei 40°C erhöhte sich dabei
die anfängliche Sherwood-Zahl auf 8.0. Trocknungsexperimente mit einer Luftgeschwindigkeit
> 1.0 m/s konnten aufgrund eines zusätzlichen konvektiven Einflusses nicht mehr durch das
„Levitationsmodell“ beschrieben werden. Mittels der Ranz-Marshall Gleichung war eine
Vorhersage der vorliegenden Sherwood-Zahl und damit des Trocknungsverlaufes möglich. In
unbewegter Trocknungsluft nahm der Trocknungskoeffizient mit steigender Temperatur und
abnehmender Luftfeuchte zu. Mit zusätzlicher Luftgeschwindigkeit stieg β r von 0,00193 mm 2 /s
(unbewegte Luft / 60°C / 0,1% Feuchte) auf 0,00458 mm 2 /s (Luftgeschwindigkeit 1,98 m/s /
60°C / 0,1% Feuchte) an. Die Werte wurden bei einem Tropfendurchmesser zwischen 1200 µm und
800 µm bestimmt. Gleichzeitig nahm die Trocknungszeit eines Tropfens mit einem Volumen von
1,0 µl von 225 s auf 80 s ab. Experimente mit direkter Luftströmung ergaben eine Zunahme von β r
mit zunehmender Luftgeschwindigkeit und abnehmender Feuchte.
Aufgrund des höheren Dampfdrucks bei gleicher Temperatur zeigten Ethanoltropfen eine
schnellere Verdampfung und größere β r -Werte als Wassertropfen. In unbewegter Luft bei 60°C
und 0,1% Feuchte stieg der Trocknungskoeffizient für Ethanol auf 0.00542 mm 2 /s an. Die Einflüsse
der inneren und äußeren akustischen Strahlung hatten die gleiche Auswirkung auf das
Trocknungsverhalten von Ethanoltropfen. Das „Levitationsmodell“ und die Ranz-Marshall
Gleichung konnten zur Vorhersage des Trocknungsverlaufes bei verschiedenen Temperaturen und
Luftfeuchten ≤ 3.0% verwendet werden. Mit Erhöhung der Luftfeuchte wurde ein zweiphasiges
Verdampfungsverhalten bei Ethanol beobachtet, das von einer Kondensation von Feuchte aus der
Trocknungsluft an der Tropfenoberfläche mit nachfolgender Diffusion ins Tropfeninnere
gekennzeichnet war. In der ersten Phase, geprägt durch die Verdampfung von Ethanol, führte eine
Erhöhung der relativen Feuchte der Trocknungsluft zu einer Erhöhung der Verdampfungsrate des
Ethanols. Die durch die Kondensation freiwerdende Energie erhöhte die anfängliche Verdampfung
des Ethanols pro Zeiteinheit. Die Mischung aus Ethanol und kondensierter Feuchte hatte eine
höhere Kühlgrenztemperatur als der reine Ethanol, was wiederum zu größeren Verdampfungsraten
und damit zu einem größeren β r führte. Die Kühlgrenztemperatur am Ethanoltropfen bei 60°C
Trocknungsluft steigt dabei von 13.3°C bei 0,1% Feuchte auf 32,6°C bei 40% Feuchte an. Nach der
Verdampfung des Ethanols wurde der Trocknungsverlauf durch die Verdampfung der
kondensierten Feuchte dominiert. Vergleichende Betrachtungen der zweiten Verdampfungsphase
von Ethanoltropfen in feuchter Luft mit Wassertropfen zeigten sehr gute Übereinstimmung.
Luftgeschwindigkeiten von 1.7 m/s bei 60°C und 0.1% relativer Feuchte erhöhten den

CHAPTER 7 ZUSAMMENFASSUNG 233
Verdampfungskoeffizienten auf 0.01308 mm 2 /s. Dabei sank die Verdampfungszeit eines 1.0 µl
Tropfens von 83.0 s in unbewegter Luft auf 27.3 s ab.
Ein zweiphasiges Verdampfungsverhalten wurde auch für die binäre Mischung aus Wasser
und Ethanol gefunden. In der ersten Phase zeigte sich mit zunehmendem Ethanolanteil eine
Zunahme von β r . Die Werte lagen dabei zwischen denen der reinen Lösungsmittel. Der zweite Teil
war durch ein konstantes β r unabhängig von der ursprünglichen Zusammensatzung des Tropfens
gekennzeichnet. Ein Vergleich des zweiten Abschnitts mit reinen Wassertropfen ergab eine sehr
gute Übereinstimmung.
Im dritten Teil dieser Arbeit wurde das akustische Levitationssystem für die Untersuchung
der Trocknungskinetik von Lösungstropfen verwendet. Dabei lag das Hauptinteresse auf
Substanzen und Formulierungen, die in pharmazeutischen Bereichen der Sprühtrocknung
Anwendung finden, wie Zucker (Maltodextrin, Trehalose und Mannitol), Proteine (bovines Serum
Albumin und Katalase) und deren Mischungen. Untersuchungen zum Einfluss des Ultraschallfeldes
auf Maltodextrinlösungen zeigten einen Zusammenhang zwischen der Stärke des Ultraschallfeldes,
den Achsenverhältnissen der Tropfen und der daraus entstehenden Partikeln. Zwischen beiden
letzteren konnte ein linearer Zusammenhang gefunden werden (R 2 = 0.98). Zur Minimierung der
Einflüsse auf die Partikelbildung wurde die für eine stabile Levitation nötige, niedrigste Stärke des
Ultraschallfeldes gewählt. Bezüglich ihres Trocknungsverhaltens zeigten Maltodextrinlösungen am
Übergang vom ersten zum zweiten Trocknungsabschnitt einen deutlichen kritischen Punkt. Kleine
Veränderungen des vertikalen Durchmessers in der zweiten Trocknungsphase führten zu einer
Abflachung des resultierenden Partikels. Die Darstellung der Trocknungsgeschwindigkeit in
verdampfter Lösungsmittelmenge pro Zeit und Oberfläche gegen
2
t rS
0
/ bot die Möglichkeit
Experimente mit unterschiedlich großen Anfangstropfen zu vergleichen. Mit Erhöhung der
Maltodextrinkonzentration in der Lösung kam es zu einer Verkürzung des ersten und einem
flacheren Abfallen der Trocknungsgeschwindigkeit im zweiten Trocknungsabschnitt. Für einen
1,8 µl Tropfen, getrocknet bei 40°C und 0,1% Feuchte in unbewegter Luft, verkürzte sich die erste
Trocknungsphase von durchschnittlich 445,3 s bei einem Feststoffgehalt von 50 mg/ml auf 91,5 s
bei 400 mg/ml. Im Gegenzug nahm die Dauer des zweiten Trocknungsabschnittes von 162,4 s auf
708,6 s zu. Die Trocknungsrate sank von 0,75 µg/s/mm 2 auf 0,58 µg/s/mm 2 ab. Eine Erhöhung der
Trocknungstemperatur von 25°C auf 60°C verkürzte die Trocknungszeit beider Phasen. Mit
zunehmendem Feststoffgehalt in der Lösung nahm die Größe der getrockneten Partikel zu, wobei
die Dichte bei 25°C mit 0,85 g/cm 3 in etwa konstant blieb. Bei 40°C und 60°C hingegen wurde mit

CHAPTER 7 ZUSAMMENFASSUNG 234
steigender Maltodextrinkonzentration ein leichter Anstieg der Dichte von 0,7 g/cm 3 auf 0,75 g/cm 3
festgestellt. Die rasterelektronenmikroskopischen Aufnahmen (REM) zeigten eine eingedellte und
mit kleinen Kratern übersähte Oberfläche. Eine Verbindung dieser Krater zu Kapillaren im Inneren
konnte nicht festgestellt werden. Die resultierenden Partikel waren massiv ohne Hohlräume und
zeigten deutliche morphologische Ähnlichkeit zu den größeren Partikeln der sprühgetrockneten
Pulver.
Trehaloselösungen zeigten am Übergang vom ersten zum zweiten Trocknungsabschnitt
keinen deutlichen kritischen Punkt. Lediglich ein beginnender Anstieg des Halbachsenverhältnisses
deutete auf eine Krustenbildung hin. Ein Abflachen der Trehalosepartikel ähnlich wie beim
Maltodextrin konnte nicht beobachtet werden. Ansonsten zeigten Trehaloselösungen ein ähnliches
Trocknungsverhalten. Mit zunehmender Konzentration kam es zu einer Verkürzung des ersten und
einer Verlängerung des zweiten Trocknungsabschnittes. Die Trocknungszeit eines 1,8 µl Tropfen
bei 60°C und 5% relativer Feuchte in unbewegter Luft nahm von durchschnittlich 274,4 s bei
50 mg/ml Trehalose auf 138,9 s bei 400 mg/ml Trehalose ab. Im Gegenzug stieg die Dauer des
zweiten Trocknungsabschnittes von 234,0 s auf 668,6 s an. Mit zunehmender Konzentration zeigte
sich eine langsamere Abnahme der Trocknungsgeschwindigkeit nach dem kritischen Punkt. Bei
400 mg/ml Trehalose getrocknet bei 60°C in unbewegter Luft mit einer Feuchte von 40% konnte
kein kritischer Punkt und damit kein Übergang vom ersten zum zweiten Trocknungsabschnitt mehr
erkannt werden. Bei gleicher Temperatur mit 5% Feuchte in unbewegter Luft nahm die
Partikelgröße von 37,4% der ursprünglichen Tropfengröße bei 50 mg/ml Trehalose auf 75,5% bei
400 mg/ml zu. Zunehmende Luftfeuchte führte zu einer abnehmenden Partikelgröße. Die
Partikeldichte nahm mit zunehmendem Feststoffgehalt und abnehmender Feuchte ab. Unter den
obigen Bedingungen bei 5% Feuchte ergaben sich Dichten von 1,03 g/cm 3 (50 mg/ml Trehalose)
und 0,97 g/cm 3 (400 mg/ml Trehalose). Ein Trocknen mit Luftströmung führte mit zunehmender
Luftgeschwindigkeit zu einer Verkürzung des ersten Trocknungsabschnittes und zu einem steileren
Abfall der Trocknungsgeschwindigkeit nach dem kritischen Punkt. Im Falle einer 100 mg/ml
Trehaloselösung nahm die Trocknungsgeschwindigkeit bei 60°C und 5% Feuchte von 1,1 µg/s/mm 2
in unbewegter Luft auf fast 3,0 µg/s/mm 2 bei einer Strömung von 1,5 m/s zu. Die schnellere
Trocknung führte zu größeren und weniger dichten Trehalosepartikeln.
Mannitollösungen zeigten einen sehr deutlichen kritischen Punkt am Übergang vom ersten
zum zweiten Trocknungsabschnitt, sowie eine konstante Partikelgröße und ein konstantes
Halbachsenverhältnis in der zweiten Phase. Die Einflüsse der Trocknungstemperatur, Luftfeuchte
und Luftströmung auf die Trocknungsgeschwindigkeit waren wie bei Maltodextrin und Trehalose.

CHAPTER 7 ZUSAMMENFASSUNG 235
Allerdings konnten Versuche in bewegter Luft nur bis zu einer Luftgeschwindigkeit von 1,0 m/s
durchgeführt werden. Stärkere Luftströmung führte zu starken Tropfenschwingungen im zweiten
Trocknungsabschnitt. Die schlagartige Partikelbildung und die ungleichmäßige Partikelform in
Kombination mit einer sehr niedrigen Dichte führten zur Ausbildung von Turbulenzen im Bereich
des Druckknotens und zu einem Herausblasen des Partikels aus der stehenden akustischen Welle.
Bei 60°C und 5% Feuchte in unbewegter Luft wurde eine Partikeldichte von 0,50 g/cm 3 erhalten, in
Luftgeschwindigkeit von 1,0 m/s sogar 0,32 g/cm 3 . REM-Bilder von Partikeln entstanden bei
Raumtemperatur zeigten eine nur teilweise runde Partikelgestalt mit vielen Ausstülpungen und
einer nadelförmigen Oberflächenmorphologie. Eine schnellere Trocknung führte zu runderen
Partikeln mit glätterer Oberfläche als bei Raumtemperatur. Die Mannitolpartikel waren hohl mit
Löchern in ihrer Oberfläche. Die Morphologie konnte im sprühgetrocknete Produkt in höchster
Vergrößerung nicht gefunden werden. In bewegter Luft wurden im Levitationssystem Partikel mit
„Schüsselgestalt“ erhalten. Die Partikel hatten eine glatte, der Luftströmung zugewandte und eine
von Ausstülpungen übersähte obere Hälfte.
Die Trocknung von bSA-Lösungen zeigte ein den Zuckerlösungen unterschiedliches
Verhalten. Sowohl der Bruch des neu gebildeten hohlen Partikels als auch das Entstehen großer
Löcher in der Oberfläche nach dem kritischen Punkt führten im zweiten Trocknungsabschnitt zu
instabilem Verhalten mit starken Partikelschwingungen. Die Analyse der REM-Bilder ergab eine
Partikelkruste mit einer Breite von 31,75% des Partikelradius für eine 100 mg/ml konzentrierte bSA
Lösung getrocknet bei 60°C und 10% Feuchte in unbewegter Luft. Unter Annahme einer
sphärischen Geometrie mit einem Radius von 500 µm betrug das Hohlraumvolumen 0,166 µl und
die Oberfläche wird durch Entstehen einer 1,46 mm 2 großen inneren Oberfläche auf insgesamt
4,60 mm 2 vergrößert. Hieraus resultierte eine Zunahme der Trocknungsgeschwindigkeit im zweiten
Trocknungsabschnitt auf Werte annähernd so groß wie am kritischen Punkt. Formulierungen von
bSA mit Trehalose in einer bSA-Trehalose (1:1) Mischung mit einer Konzentration von 100 mg/ml
zeigten diesen Anstieg der Trocknungsgeschwindigkeit in der zweiten Phase nicht. Weder konnten
auf den REM-Bildern Löcher in der Kruste noch eine hohle Partikelstruktur gefunden werden. Im
Vergleich mit den beiden Reinsubstanzen bei gleicher Konzentration kam es mit zunehmendem
Trehalosegehalt zu einer Verlängerung des ersten Trocknungsabschnittes. Bei 60°C und 5%
relativer Feuchte in unbewegter Luft nahm der Anteil an verdampftem Lösungsmittel von 65,1%
bei der reinen bSA-Lösung auf 87,8% für die Mischung und 85,6% für die reine Trehaloselösung
zu. Die Trocknungsgeschwindigkeit in unbewegter Luft sank dabei von 1,21 µg/s/mm 2 für reines
bSA auf 0,91 µg/s/mm 2 für reine Trehalose ab. Die bSA-Trehalose-Mischung hatte unter gleichen

CHAPTER 7 ZUSAMMENFASSUNG 236
Bedingungen eine anfängliche Trocknungsgeschwindigkeit von 1,0 µg/s/mm 2 . Unter
Vernachlässigung der reinen bSA-Lösung sank die Trocknungsgeschwindigkeit nach dem
kritischen Punkt mit zunehmendem Trehalosegehalt langsamer ab. Die morphologische
Übereinstimmung zwischen Levitationspartikeln und sprühgetrocknetem Produkt war sehr gut.
Wegen ihrer hohlen Struktur war die Dichte der levitierten Partikel mit 0,62 g/cm 2 (60°C, 5%
Feuchte, unbewegte Luft) um etwa 0,3 Einheiten kleiner als die der bSA-Trehalose Mischung.
Diese hingegen unterschieden sich nur durch minimal kleinere Werte von der Dichte reiner
Trehalosepartikel. Untersuchungen der Grenzflächenaktivität von bSA-Lösungen und ihrer
Mischungen mit 200 mg/ml Trehalose mittels Blasendrucktensiometrie zeigten, dass der Zusatz von
Trehalose die dynamische Oberflächenspannung einer 2,0 mmol/l bSA Lösung um 3,67 mN/m und
die einer 4,0 mmol/l bSA-Lösung sogar um 4,42 mN/m erhöht (Blasenlebenszeit 1,0 s). Berechnung
der bSA-Konzentration in der Oberfläche unter Verwendung der Gibbs-Gleichung ergab für eine
4,0 mmol/l bSA-Lösung durch Trehalosezusatz (200 mg/ml) eine Reduktion von 87 mg/m 2 auf
36 mg/m 2 . Die Fläche eines bSA-Moleküls in einem Monolayer auf der Tropfenoberfläche wurde
zu 100 nm 2 bestimmt.
Reine Katalaselösungen in 50 mM Tris Puffer bei pH 8,0 getrocknet im Ultraschall-
Levitator führten zu Partikeln mit Löchern von durchschnittlich 45,1% ± 4,3% des horizontalen
Durchmessers (60°C; 5% Feuchte; unbewegte Luft). Die Kruste hatte dabei eine Breite von 18,3%
des Partikelradius. Ausgehend von einer sphärischen Geometrie mit einem Radius von 500 µm
ergab sich ein Hohlraumvolumen von 0,286 µl mit einer Oberflächenvergrößerung von 2,10 mm 2
auf eine Gesamtfläche von 5,24 mm 2 . Die Oberflächenvergrößerung führte, wie auch beim bSA, zu
einem zwischenzeitlichen Anstieg der Trocknungsgeschwindigkeit innerhalb des zweiten
Trocknungsabschnittes. Die systematische Untersuchung einer Mischungsreihe aus Katalase und
Trehalose zeigte, dass ab einem Katalase-Trehalose Verhältnis von 6 zu 4 massive Partikel ohne
Hohlraum und Löcher in der Kruste entstehen und ein Anstieg der Trocknungsgeschwindigkeit im
zweiten Trocknungsabschnitt nicht mehr beobachtet werden kann. Mit zunehmendem
Trehalosegehalt nahm die Dauer des ersten Trocknungsabschnittes zu. Ebenso erhöhte sich auch der
Anteil an verdampftem Lösungsmittel von 61,9% für die reine Katalaselösung auf 85,5% für die
Katalase-Trehalose (2:8) Mischung (60°C; 5% Feuchte; unbewegte Luft). Die
Trocknungsgeschwindigkeit sank unter den obigen Bedingungen von 0,95 µg/s/mm 2 für reine
Katalase-Lösung auf 0,91 µg/s/mm 2 für die Katalase-Trehalose (2:8) Mischung ab. Die reine
Trehaloselösung in Tris Puffer hatte eine Trocknungsgeschwindigkeit von 0,89 µg/s/mm 2 . Mit
zunehmendem Trehalosegehalt nahm bei den Katalase-Lösungen die Trocknungsgeschwindigkeit

CHAPTER 7 ZUSAMMENFASSUNG 237
nach dem kritischen Punkt langsamer ab. Es konnte eine sehr gute morphologische Ähnlichkeit zum
sprühgetrockneten Produkt festgestellt werden. Die Dichte der levitierten Partikel nahm von
0,43 g/cm 3 für reine Katalase mit zunehmendem Trehalosegehalt auf 0,84 g/cm 3 für die Katalase-
Trehalose (2:8) Mischung zu (60°C, 5% Feuchte, unbewegte Luft). Mittels Blasendrucktensiometrie
konnte gezeigt werden, dass es bei einer 0,40 mmol/l Katalaselösung (äquivalent zu 100 mg/ml)
durch Zusatz von 200 mg/ml Trehalose zur Erhöhung der dynamischen Oberflächenspannung um
3,9 mN/m bei einer Blasenlebenszeit von 1,0 s kommt. Die Grenzflächenkonzentration von
Katalase reduzierte sich dabei von 575 mg/mm 2 auf 400 mg/mm 2 . Untersuchungen zur Restaktivität
von Katalase in akustisch levitierten Partikel ergaben wegen der vergleichsweise großen Partikel
und langen Trocknungszeit bei 60°C mit Ergebnissen der Sprühtrocknung keine Übereinstimmung.
Jedoch konnte der stabilisierende Einfluss der Trehalose auf die Aktivität der Katalase während der
Trocknung nachgewiesen werden. Der Zusatz von 20% Trehalose im Feststoffgehalt steigerte die
Restaktivität der bei 60°C und 5% Feuchte in unbewegter Luft getrockneten Partikel von 87,7% auf
95,5%. Das molare Verhältnis dieser Lösung aus Katalase zu Trehalose war 1:183. Eine durch
zunehmende Luftfeuchte verursachte Zunahme der Trocknungszeit führte zu leichtem
Aktivitätsverlust bei allen Formulierungen.
Zusammenfassend stellt der akustische Levitator ein viel versprechendes Werkzeug zur
Untersuchung des Trocknungsverhaltens einzelner Lösungsmittel-, Suspensions- und
Lösungstropfen dar. Obwohl Einflüsse der stehenden akustischen Welle auf Massenübergang und
Partikelbildung demonstriert werden konnten, war es möglich den Verlauf der Tropfengröße mit der
Zeit im Levitationssystem mittels mathematischer Modelle vorherzusagen und eine gute
morphologische Übereinstimmung mit den sprühgetrockneten Produkten gleicher
Zusammensetzung zu zeigen. Diese Ergebnisse und die Möglichkeit fast jede mögliche
Trocknungsbedingung innerhalb eines bauartbedingten Temperaturbereiches einzustellen, machen
den Ultraschall-Levitator zum interessanten Werkzeug für Voruntersuchungen in der
Sprühtrocknungsforschung, vor allem dann, wenn nur eine geringe Menge Substanz, zum Beispiel
aus Preisgründen, verfügbar ist. Der Umbau des Systems um die Möglichkeit zu erhalten, den
Ultraschallwandler zu kühlen, sowie die Injektion und Dosierung der Tropfen mittels eines
Mikropumpsystems würde die Möglichkeit eröffnen Trocknungsversuche auch bei Temperaturen
über 70°C und mit kleinerer Anfangstropfengröße durchzuführen. Somit könnte eine noch bessere
Vergleichbarkeit zur Sprühtrocknung geschaffen werden. Die Verwendung einer Infrarot-
Thermokamera würde zusätzlich eine Bestimmung der Oberflächentemperatur der Lösungsmittelund
Lösungstropfen und damit die Überprüfung mathematischer Modelle zur Berechnung

CHAPTER 7 ZUSAMMENFASSUNG 238
zugänglich machen. Weitere Einsatzgebiete zeigen sich auch auf dem pharmazeutischen Sektor.
Eine Verwendung des Levitationssystem zur Untersuchung von Verteilungs-, Mikroverkapselungsoder
Polymerisationsprozessen direkt im levitierten Tropfen, sowie für die Untersuchung der
Qualität von Verkapselungsformulierungen flüchtiger Substanzen ist durchaus denkbar.

Annex
Saturation pressure of water vapour
ANNEX 239
For water vapour at atmospheric pressure the saturation pressure, p saturation , in mbar
(1mbar = 10 2 N/m 2 ) for given temperature TS in degrees Celcius is calculated by
[Seaver et al. 1989]
Equation A.1 p a + T ⋅ [ a + T ⋅ ( a + T ⋅{
a + T ⋅ [ a + T ⋅ ( a + a ⋅T
) ] } ) ]
saturation = 0 S 1 S 2 S 3 S 4 S 5 6
Table A.1: Parameters used to calculate the saturation pressure of water vapour [Seaver et al. 1989].
a0
a1
a2
a3
a4
a5
a6
Saturation pressure of different liquids
6.107799961
4.436518521 x 10 -1
1.428945805 x 10 -2
2.650648731 x 10 -4
3.031240396 x 10 -6
2.034080948 x 10 -8
6.136820929 x 10 -11
The saturation pressure in bar (1 bar = 10 -5 N/m 2 ) for the liquids listed in Table A.2 is given as a
function of temperature TS in Kelvin by [Reid et al. 1987]
Equation A.2
p = 0 . 001333224 ⋅ e
saturation
⎛ B ⎞
⎜ A−
⎟
⎝ TS
+ C ⎠
Table A.2: Liquid parameters used to calculate the saturation pressure of vapour [Reid et al. 1987].
Liquid A B C
methanol 18.5875 3626.55 -34.29
ethanol 18.9919 3803.98 -41.68
2-Propanol 17.5439 3166.38 -80.15
n-heptane 15.8738 2911.32 -56.51
n-octane 15.9426 3120.29 -63.63
n-decane 16.0114 3456.80 -78.67
S

240 ANNEX A
Latent heat of vaporisation of water
The latent heat of vaporisation of water, hv , in cal/g at given Temperature TS in Kelvin is calculated
by [Seaver et al. 1989]
−3
Equation A.3 h 595.
3 + T ⋅ ( 0.
483 + T ⋅1.
2 ⋅10
)
Thermal conductivity of air
v = S
S
The thermal conductivity of air, ka , in cal/cm/°C/s at given temperature TS in degrees Celcius is
calculated by [Seaver et al. 1989]
−5 −7
Equation A.4 ka = 5 . 8⋅10
+ 1.
6 ⋅10
⋅TS
Binary diffusion coefficient
The binary diffusion coefficient, DAB , in cm 2 /s at given temperature TS in degrees Celcius and
pressure, p , in atm is calculated by
Equation A.5
D
AB
1.
00 ⋅10
=
p ⋅
−3
⋅T
1.
75
( 1/
M + 1/
M )
[ ( ) ( ) ] 2
S
A
1/
3
1/
3
∑ υ + ∑ υ
A i
MA and MB are the molecular weights of the substance, whereas ∑ υ
A i and ∑ υ
B i are the summed
special diffusion parameters over atoms, groups and structural features of the diffusion species
[Fuller et al. 1966].
Table A.3: Molecular weight and summed diffusion parameters for air / water and air / ethanol systems
[Fuller et al. 1966].
System MA [ g/mol ] MB [ g/mol ] ∑ υ
A i ∑ υ
B i
Air / water 28.96 18.03 20.1 12.7
Air / ethanol 28.96 46.07 20.1 50.4
B i
B

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256 CURRICULUM VITAE
PERSONAL DATA
Curriculum vitae
Name: Heiko Alexander Schiffter
Date of birth: 02. April 1976
Place of birth: Heilbronn-Neckargartach, Germany
Nationality: German
Family status: single
Address: Friedrich-Ebert-Street 4, 74177 Bad Friedrichshall, Germany
SCHOOL EDUCATION
1982-1986 Basic primary school, Bad Friedrichshall-Hagenbach, Germany
1986-1995 Grammar school – Moenchsee-Gymnasium, Heilbronn, Germany
06/1995 Diploma from German secondary school qualifying for
university administration and matriculation
CIVILIAN SERVICE
1995-1996 Malteser emergency service, Heilbronn, Germany
• Alternative civilian service in care and transportation
of disabled people
PROFESSIONAL AND ACADEMIC TRAINING
1996-2001 Ruprechts-Karls University, Heidelberg, Germany
• Undergraduate studies in pharmacy
09/1998 1 st part of state examination in pharmacy
08-10/1999 German Cancer Research Centre, Heidelberg, Germany
• Research activity in cell biology with interest in
chemoprevention of cancer
04/2001 2 nd part of state examination in pharmacy
2001-2002 Central-Apotheke, Ravensburg, Germany
• Internship in a community-based pharmacy
05/2002 3 rd part of state examination in pharmacy
05/2002 Licensed pharmacist
2002-2005 Department of pharmaceutics (Prof. Dr. Geoffrey Lee),
Friedrich-Alexander University, Erlangen, Germany
• Ph.D. student in pharmaceutics and assistant teacher for
undergraduate students (solid dosage forms and biopharmaceutics)