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2.4. Single Droplet Modeling 33
polymer and mannitol solutions in water. Moreover, in case of a polymer, molecular
entanglement leads to solid layer formation. Nesic and Vodnik [151] use a more detailed
description of various stages of droplet evaporation and drying. These stages, as
described by Nesic and Vodnik [151], are that the droplet temperature initially rises
to an equilibrium value and solvent evaporates continuously, which in turn increases
the solute mass fraction within the droplet. When the solute mass fraction at the
droplet surface rises to a critical value, then there starts a thin solid layer formation,
and further drying leads to a dried particle.
Farid [156] shows that the droplet evaporation and drying are controlled by thermaldiffusion
rather than mass-diffusion as assumed by most of the earlier studies [149, 150,
152]. In Farid’s model [156], the time taken for the formation of crust on a colloidal
silica droplet is calculated using the energy balance, which does not account for solvent
and solute composition changes, and the evaporation rate is computed using a
simple relation without accounting for the variation in film and liquid properties. For
droplets with suspended solids inside, the population balance approach is recently developed
[158] to model the nucleation and growth of suspended solids inside an ideal
binary liquid droplet with an assumption that there exist some nuclei of suspended
solids initially. But this method cannot be applied in the present case of droplet
with polymer or sugar, as solute is completely dissolved in water. Golman et al. [160]
presents a model for the evaporation and drying of slurry droplets, which is an improvement
over the receding interface model of Cheong et al [161] for slurry droplets, and
the bi-component liquid mixture is treated as ideal. A detailed review of all existing
theoretical models of evaporation and drying of single droplet containing dissolved and
insoluble solids is given by Mezhericher et al. [162], and a review of evaporation models
in the area of combustion is given by Sazhin [147].
Adhikari et al. [163] and Vehring et al. [164] give a review of the experimental
studies in the area of single droplet evaporation and drying. Tsapis et al. [159] and
Sugiyama et al. [165] have levitated droplets using Leidenfrost phenomenon on a concave
hot plate whereas Yarin et al. [166] levitated droplets using an acoustic levitator.
This technique was successfully used to study shell buckling during particle formation
[165]. A drawback of this approach is that the flow field and temperature field
in the vicinity of the droplet are different from those of a free flowing droplet in a
spray dryer. A chain of mono-disperse free falling droplets has been used by several
experimental groups to study heat and mass transfer, drying, and particle formation
processes. El Golli et al. [154] measured salt droplet evaporation and compared their
results with a theoretical model. A similar technique to study the effect of drying
rates on particle formation was used by Alexander and King [167] and El-Sayed et
al. [168]. Wallack et al. [169] compared measured evaporation rates with a numerical