Viscometry Lab.pdf

VISCOMETERS
We have defined the viscosity of fluid foods in a variety of ways, including:
1. The resistance to flow offered by the fluid.
2. The ratio of shear stress to shear rate: ! = "
# ˙
= F / A
du / dy
3. The rate at which momentum is transferred through layers of the fluid
4. The rate that energy is dissipated per volume of fluid.
FDST 8080 Lab 2011
In food science, we are interested in the viscosity of foods for several reasons. First,
viscosity is an important sensory attribute of liquid foods. Viscosity correlates with the
perceived “mouthfeel” and “thickness” of liquid products. Also, our ability to suck liquids
through a straw or slurp them off of spoons depends on viscosity. For food processors,
fluid viscosity becomes important for determining the size of pump required to move a
fluid, whether a material can be extruded, how easily a bottle can be filled, and how much
impediment to heat transfer will occur at heat exchanger surfaces.
In this lab, we will explore several common devices used to measure food viscosity. This
includes the capillary viscometer, the rotational viscometer, falling ball viscometer and the
human mouth- the first three being objective physical measurements, the latter a sensory
evaluation. We will evaluate several liquid foods by each of these methods and compare
results. At this stage, we will assume the liquids are ideal and follow Newton’s law
(! = "
# ˙
)
I. ROTATIONAL VISCOMETRY
Rotational viscometers are a common tool in the food industry. A metal cylinder probe is
caused to rotate in the sample. The torque required to rotate the cylinder at a given speed is
measured. The more viscous the sample, the more torque required to rotate the cylinder.
Rotational viscometers are relatively simple to use and can measure a wide range of
viscosity values. This latter feature is possible as rotational viscometers usually come with
a variety of interchangeable probes: thin probes with small surface areas for viscous
materials; larger probes with increased surface area for less viscous liquids. Most can also
operate at a variety of rotational speeds, and therefore shear rates. This allows the operator
to investigate the shear dependency of the sample.
For a concentric cylinder viscometer, the viscosity η of a Newtonian fluid is determined
by:

! = M % 1
4"h# &
'
2
Rb 1
$ 2
Rc (
)
*
R b
!
R c
h
FDST 8080 Lab 2011
where Ω is the angular velocity (RPM), M is the torque, R b the diameter of the inner
cylinder (bob), and R c the diameter of the sample container. Thus, the rotational speed,
measured torque, and consideration of the probe size and shape allow us to determine shear
rate and shear stress. The ratio of shear stress and shear rate are give us the apparent
viscosity. In practice, these constant factors and measured variables are used by computer
software to calculate viscosity. Older instruments may require users to determine
multiplication factors for the given spindle.
In this lab we will measure an apparent viscosity at a single shear rate. Details of operation
depend on the particular instrument. We will use the Brookfield viscometer .
Brookfield
Pour some sample in a beaker. Insert one of the spindles in the Brookfield and put the end
of the spindle in the liquid. Change the rpm/spindles to obtain a reading mid-scale. The
particular spindle (with its specific geometry) must be noted.

II. FALLING BALL VISCOMETERS
FDST 8080 Lab 2011
One very simple type of instrument is the falling ball viscometer. Here, a glass or metal
ball is allowed to fall through the sample. The more viscous the sample is, the longer it
takes the ball to reach the bottom. In the simplest case, this may be just a graduated
cylinder with a steel ball. Once the ball drops, it will soon reach a terminal velocity once
the force of gravity is countered by the frictional forces due to the fluid. By Stokes law:
! = 2(" s # " 2
%
l )gR
&
'
9$
where η is the viscosity, ρ s is the density of the solid ball, ρ l is the density of the fluid, R is
the ball radius, g the gravitational constant, and υ the terminal velocity. The time it takes
for the ball to fall a given distance is determined with a stopwatch, and determines the
velocity (υ=∆x/∆t).
F = mg
g
F = K!"
f
(
)
*

FDST 8080 Lab 2011
Research instruments such as the Hoeppler viscometer are also available. These have
precision made tubes surrounded by an outer jacket, through which constant temperature
water can be circulated. The sample tube can be evacuated to remove air bubbles, then
sealed. Here, the tube is tilted at a 10° angle, and the ball is only slightly smaller than the
inner diameter of the tube; thus, “wall” effects are important and incorporated into the
analysis. For the Hoeppler viscometer, the absolute viscosity is given by:
" = T #(SG s $ SG l ) # B
where T is the time interval of the falling ball and B is a ball constant. Here SG is the
specific gravity (ρ/ρ water)
Type Serial
Number
Ball Diam
@ 20°C
(mm)
Wt of Ball
(g)
SGB @
20°C
Ball
Constant
A2 8440 15.9051 4.6958 2.2290 ----------
C33 8665 15.8059 4.6088 2.2291 0.009529
F6 8269 15.6300 4.4516 2.2266 0.077944
H8 8058 15.5512 15.5447 7.8939 0.13630
K10 8114 14.9846 13.9058 7.8933 1.2691
M12 6869 13.4933 10.1712 7.9071 10.804
Where possible, use the falling ball viscometer to measure the viscosity of the same liquids
you measured in the rotational viscometer. If the liquid is too opaque, this may not be
possible. Record the time it takes for the ball to pass from the first marker to the final one.
We will also need to record the specific gravity of the liquid.
III. Zahn Cup-Type Viscometer
The Zahn cup is an easy-to-use device for assessing the viscosity of oils, paints, syrups, batters
and other liquids. The cup is filled to the top and the liquid allowed to flow through an
opening in the bottom. The viscosity of the liquid is measured in Zahn number, that is, the
time in seconds for a known volume of liquid to flow out of the cup. For thin fluids, a cup with
a small orifice is used; for more viscous mixtures, a cup with a larger whole is used. Although
easy to use, the geometry and driving force for flow are difficult to describe. Thus, no exact
formulas exist to convert viscosity measurements in “Zahn numbers” into absolute viscosity.
However, it is common practice to report the “viscosity” in Zahn numbers. Some empirical
formulas have been developed, however, to relate Zahn number to kinematic viscosity. For
the Boekel brand cups:

FDST 8080 Lab 2011
Zahn Cup# Formula T, Zahn Seconds Range
Specifications
1 η/ρ = 1.1(T-29) 45 - 80
2 η/ρ = 3.5(T-14) 25 - 80
3 η/ρ = 14.8(T-5) 20 - 75
4 η/ρ = 11.7(T-7.5) 20 - 80
5 η/ρ = 23(T-0) 20 –75
Zahn Cup # 1 2 3 4 5
Orifice Diameter (in) .078 0.108 0.148 0.168 0.208
Zahn Range (s) 45-80 25-80 20-75 20-80 20-75
Centistoke Range* 18-56 40-230 150-790 220-1100 460-1725+
Application Very thin
oil
Thin oil Medium
oil
Heavy
mixture,
Batter,
syrup
Very heavy
mixture,
Heavy syrup
*Centistoke is a measure of kinematic viscosity = absolute viscosity (cP)/density (gcm -3 )

FDST 8080 Lab 2011
Measure the temperature of the liquid prior to measurement. The Zahn cup is provided
with a bracket to hold a thermometer. Prior to measurement, raise the bracket so the
thermometer stem is out of the cup. Place a finger in the ring, lift the viscometer
completely out of the liquid and start the stop watch when the top edge of the cup breaks
the surface. Stop the watch when the steady flow of the liquid from the orifice breaks.
Repeat until consistent results are obtained. Express viscosity in Zahn seconds.
IV. Capillary Viscometry
Capillary viscometers are relatively simple and inexpensive instruments for measuring
fluid viscosity, and when used properly, give very accurate measurements of viscosity. In
this approach, gravity causes a fluid to drop between two marks in a capillary tube. The
time required for the fluid level to fall a given distance measures the viscosity.
The Hagen-Poiseuille equation shows that the flow rate Q is related to the pressure drop
(∆P=ρgh), the tube radius R, the tube length L, and the viscosity η:
Q = !("P)R4
8#L
It can be shown that the “kinematic” viscosity is just
!
" = #ghR4
t = kt
8LV

FDST 8080 Lab 2011
That is, the ratio of viscosity to density is proportional to the time it takes for the liquid to
drop between the marks. The absolute viscosity η can be determined by separately
measuring the fluid density. In some cases it is interesting to determine the “intrinsic”
viscosity of a sample [η], as this can be related to the molecular weight of a dissolved
solute.
Capillary viscometers are of limited use in food systems, as particulate systems can clog
the capillary tube. Also, dependence of viscosity on shear rate or shear history is more
difficult to study. It can be very useful, however for studying clear juices, beverages, or
solutions of food macromolecules such as proteins or carbohydrates.
The time in seconds for the fluid to fall between the two markers is recorded. When
multiplied by the capillary constant k, this gives the kinematic viscosity η/ρ.
V. Juice Viscometer
A variant of the capillary viscometer is the AOAC capillary viscometer for juices (AOAC
37.1.108). It Is more appropriate for fruit nectars and juice products, which may have bits
of pulp and particulates that would clog a precision capillary viscometer.

FDST 8080 Lab 2011
To use, the viscometer should be maintained at 24°C. The instrument is first calibrated
with water. Water is filled to the top while the flow is stopped by placing your finger at the
lower end. The top is leveled off with a spatula. Remove the finger and begin timing. A
line is scribed on the side to indicate the level reached by water in 13 s.
Clean and dry the instrument. Add the juice sample and let flow until steady flow is
attained. Place finger over the capillary tube to stop the flow. Fill the tube util almost full
and check for air bubbles. Remove an bubbles with a stir rod. Fill the tube to the top, then
level off with a spatula. Remove finger and begin timing. Record the time to nearest 0.1 s
needed for the juice to reach the calibration line. Obtain at least 2 or more readings.
TO DO:
Lab reports are to be done on a spreadsheet, both text and calculations. Show an example
calculation in the text.
A. Make a table showing the sample and the following information:
Brookfield Viscometer: Spindle #, rotational speed, correction factor, viscosity
Falling Ball: Ball#, SGB, SGL, Time(s), viscosity
Zahn Viscometer: Cup#, time (Zahn seconds), density, viscosity
Capillary Viscometer: Viscometer model, viscometer constant, time, density, viscosity
Juice Viscometer: Time for water, juice, relative viscosity, juice viscosity
B. How do the results of the different measurements compare? Are they well correlated?
C. What advantages or disadvantages do the various approaches offer?