İZMIR INSTITUTE OF TECHNOLOGY
CHEMICAL ENGINEERING DEPARTMENT
2008-2009 Spring Semester
CHE 310
CHEMICAL ENGINEERING LABORATORY I
Viscosity of Newtonian and
Non-Newtonian Fluids
VISCOSITY OF NEWTONIAN AND NON-NEWTONIAN FLUIDS
OBJECTIVE
 To understand the viscosity behaviour of Newtonian and non-Newtonian
fluids

To investigate the temperature effect on the viscosity behaviour of fluids.
EQUIPMENT

Cannon-Fenske pipette type viscometer

The Brookfield DV-III-RV Rheometer

A glass pycnometer

Flasks and pipette
INTRODUCTION
Of all the fluid properties, viscosity requires the greatest consideration in the
study of fluid flow. Viscosity is that property of a liquid by virtue of which it offers
resistance to shear stress. When a shearing force is applied to a fluid at rest it
causes the fluid to deform. There are two major causes of viscosity in fluids:
molecular attraction and transfer of molecular momentum.
The viscosity of real materials can be significantly affected by such
variables as shear rate, temperature, pressure, molecular structure, molecular
weight and time of shearing. The viscosity of a gas increases with temperature,
but the viscosity of a liquid decreases with temperature. The basic unit of viscosity
is the poise, 1P= 1g /(cm*s) =0.1 Pa.s. It is widely used for materials such as highpolymer solutions and molten polymers. However, it is too large a unit for most
common fluids. Hence, the viscosity of a fluid is expressed in centipoise, where
100 centipoise is equal to 1poise.
Fluids may be classified as Newtonian or non-Newtonian. In Newtonian
fluid, there is a linear relation between the magnitude of applied shear stress and
the resulting rate of deformation. Newtonian fluids have a constant viscosity
(dynamic or absolute viscosity) at a given temperature such as water, benzene
ethyl alcohol or aqueous solutions of salts and sugar. However, a wide range of
industrially important liquids, such as solutions of high molecular weight polymers,
colloids, suspensions, and emulsions exhibit more complex behaviour, which is
termed non-Newtonian. In non-Newtonian fluid, there is a nonlinear relationship
between the magnitude of applied shear stress and the rate of angular
deformation. The viscosity is not independent of the velocity gradient. Namely, the
viscosity will vary with the rate of shear (the difference between velocities of
parallel faces of a fluid element divided by the distances between the faces) of the
fluid. They have a variable viscosity at a constant temperature.
There are many types of non-Newtonian fluids as it is stated above, each
having distinct properties. Measurement of these viscosities is more involved and
requires the additional function of time. Non- Newtonian Fluids are classified into
two categories, which are time independent non-Newtonian Fluids (Pseudoplastic,
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Shear Thickening, Bingham Fluids) and time dependent non-Newtonian Fluids
(Thixotropic, Rheopectic)
THEORY AND PRINCIPLE
Newtonian fluids:
Application of Newton’s law of viscosity and conservation to the steady flow
of a constant density fluid through a straight tube of uniform circular cross section
of length L leads to the Hagen-Poiseuille relationship:
 () R 4
Q=
…………………………………...(1)
8L
Where (-) is the net driving force for the flow, Q is the volumetric flow
rate of fluid and R is the tube radius. The quantity  is defined as (p+ gh) where
p is static, or thermodynamic pressure  is fluid density, g is the acceleration of
gravity and h is the vertical elevation above a datum plane. Thus,  represents
the combined effects of pressure and gravity in causing the fluid motion.
According to the assumptions of the Hagen-Poiseuille law, the flow must be
laminar and free from end effects. If the construction and operation of an
experimental apparatus can conform accurately to the key assumptions, it is
possible to use Equation (1) to measure the viscosity of Newtonian fluids.
Steady flow Q of a fluid in a long, straight tube that is maintained at a
constant temperature and is equipped with a device to measure the pressure
gradient P / L at some distance from the ends of the tube. In most instances, the
control of the operating conditions over the entire length of the tube, the cleaning
difficulties, and the need for a large sample of liquid to fill the length of the tube
prohibit or make very difficult the use of such a device. Other more convenient
and compact types of viscometers to which the Hagen-Poiseuille equation may be
applied have been developed. The Cannon-Fenske viscometer and other
modifications of the Ostwald pipette are examples.
When the total change in the driving force  associated with a flow rate Q
through a tube is due to hydrostatic head alone, Equation (1) may be written as,

 g (  h ) R
8QL
4
……………………….(2)
where (-h) is upstream elevation minus downstream elevation, called the
hydrostatic head difference, and the quantity  is defined as
 =  /  …………………………………(3)
and is called the kinematic viscosity. The kinematic viscosity is often expressed in
units of cm2/sec, which is called stoke. The viscosity,  is frequently referred to as
the absolute viscosity or the dynamic viscosity to avoid confusing it with the
kinematic viscosity,  which is the ratio of viscosity to mass density.
Consider steady fluid flow through a straight capillary tube of fixed length L
for which the hydrostatic head differential h is constant. If one measures the time
for a fixed volume of fluid V to pass through a particular tube, the kinematic
viscosity should be related to the observed efflux time te as follows:
 = C* te…………………………………….(4)
2
where C is called the viscometer constant. If C is evaluated by observing t e with a
liquid of known viscosity, C may be calculated for the apparatus. Then
measurements of te for the same V in the same cell with other fluids allows the
kinematic viscosities of the latter to be calculated from Equation (4). Dynamic
viscosity value is then obtained by multiplication with the density of the liquid.
Equation (4) is derived by substituting the relation.
Q = V / te...................................................(5)
into Equation (2) and combining all constant factors into one term. The viscometer
constant C is thus identified to be
 g (  h) R 4
…………………………(6)
C
8VL
Although the preceding equations are derived for constant h and constant
Q, they may be applied with reasonable success to a pipette-type viscometer in
which a liquid drains under a slowly varying hydrostatic head. In that case, one
may use average values of Q and h in Equations (2) and (6), and the constant C
should still be a property of only the viscometer geometry and not depend on the
properties of the fluid.
Non-Newtonian fluids:
An apparent viscosity, a is often used to describe the flow behaviour of
non-Newtonian fluids, can be defined as follows:
Shearstres s

a    
......................(7)
rateofshear

The flow is analyzed with standard mathematical models. Mathematical
models provide a means to numerically and graphically analyze the behaviour of
fluids flow. Power law, Bingham plastic, Cross and, Casson models are available.
It should be noted that for shear thinning and shear thickening behaviour,
the shear stress-shear rate curve passes through the origin. This type of behaviour
is often approximated by the ‘power law’ and such materials are called ‘power law
fluids’. The power law, also called Ostwald-de Waele equation is usually written as
   * n.................................................(8)
also, power law viscosity becomes as;
a   *  (n-1)...........................................(9)
The power n is known as the power law index or flow behaviour index, and
K as the consistency coefficient. The constants K and n are determined by fitting
the equation to data. Clearly, shear thinning behaviour corresponds to n1 and
shear thickening behaviour to n1. The special case, n1, is that of Newtonian
behaviour and in this case the consistency coefficient K is identical to the viscosity,
. Values of n for shear thinning fluids often extend to 0.5 but less commonly can
be as low as 0.3 or even 0.2, while values of n for shear thickening behaviour
usually extend to 1.2 or 1.3.
The power law model fails at high shear rates, where the viscosity must
ultimately approach a constant value.
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A different kind of time-independent behaviour is that characterized by
materials known as Bingham plastics, which exhibit a yield stress, y. If subject to
shear stress smaller than the yield stress, they retain a rigid structure and do not
flow. It is only at stresses in excess of the yield value that flow occurs. In the case
of a Bingham plastic model, the shear rate is proportional to shear stress in excess
of the yield stress:
 = y + p*…………………………….. (10)
In the Bingham model equation, y and p are both constants; refer to the
yield stress and coefficient of plastic viscosity respectively. The Bingham equation
describes the shear stress/shear rate behaviour of many shear-thinning materials
at low shear rates.
Many materials exhibit Newtonian behaviour at very low shear rates,
however they also have Newtonian behaviour at very high shear rates as shown in
Figure 3. The term pseudoplastic is used to describe this type of behaviour. The
whole flow curve of this type of behaviour can be represented by the Cross model.
o, and  are the values of apparent viscosity for the lower and upper Newtonian
regions respectively. The constant m is the shear rate evaluated at the mean
apparent viscosity (o+ )/2.
 a  
1
……………………(11)

o   1  ( /  m ) n
Figure 3. Variation of apparent viscosity with shear rate for a polymer.
Casson model also can be used in analysis of flow, is similar to Bingham
plastic model. It is based on a structure model of the interactive behavior of solid
and liquid phases of a two-phase suspension.
  o +  ……………………………(12)
The Casson model shows both yield stress and shear-thinning nonNewtonian viscosity.
EXPERIMENTAL:
This experiment consists of two different equipments to measure the
viscosities of Newtonian and non-Newtonian fluids. Equipment I (Cannon-Fenske
capillary-tube) is used to measure the viscosity of Newtonian fluid behaviour and
on the other hand, Equipment II (The Brookfield DV-III-RV Rheometer) will be
used to investigate the viscosity behaviour of non-Newtonian fluids.
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Equipment I











A commercial Number 200 Cannon-Fenske pipette type viscometer, which is
designed for a 20-to-80 centistoke range in kinematic viscosity (Figure 4,a).
A stopwatch.
Constant temperature bath, set at various temperatures.
10 ml graduated pipette.
Acetone.
Distilled water.
A mounting device for holding the viscometer in the water baths.
A stock of 60-weight-percent aqueous sucrose solution.
A stock of approximately 85-weight-percent aqueous glycerol solution.
A glass pycnometer (25 ml).
An analytical balance.
The viscometer may be filled with liquid such that there is an initial elevation
difference, or static head (-h), between the liquid surface in the tube on the right
side and that in the spherical bulb at the bottom of the cell. Both surfaces are at
atmospheric pressure. Liquid is allowed to drain through the capillary tube, and the
efflux time te is measured as the time for the liquid level on the right side to drop
through the lower bulb. The volume V is the fixed volume contained between the
two marks above and below that small reservoir. The elevation difference in
Equation (2) or (6) is taken to be the average difference between the liquid levels
in the larger bulb on the left side, which changes only slightly, and that in the lower
bulb on the right as the liquid level drops from the upper mark to the lower one.
Equipment II






The Brookfield DV-III+ RV Rheometer with a spindle set (Figure 4,b).
50 ml graduated pipette.
500 ml glass beaker
A stock of 50% weight-percent aqueous polymer suspension.
Distilled water.
Constant temperature water bath, set at various temperatures.
The most often seen viscometer types in food and beverage development
are based on rotational viscometry; meaning they measure viscosity by sensing
torque required to rotate a spindle at a constant speed while immersed in the fluid.
The torque is proportional to the viscous drag on the spindle, and thus to the
viscosity of the fluid. Advantages of the rotational viscometers, like Brookfields, are
that they are easy to set up and use, do not require enormous amounts of operator
skill, continuous rotation allows for measurements over time, suitable for
measuring Newtonian and non-Newtonian fluids, can determine shear
dependency if any.
Viscosity values of the prepared solutions will be measured by using
Brookfield DV III Rheometer at a given shear rate as well. The measurement
range of the viscometer is determined by the rotational speed of the spindle, the
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size and shape of the spindle is rotating in, and the full-scale torque of the
calibrated spring.
Working
capillary
a)
b)
Figure 4. a) The Cannon-Fenske Pipette-Type Viscometer for transparent liquids
is depicted. Dimensions are given for size Number 200. b) The Brookfield DVIII
Rheometer.
PROCEDURE I






Ensure that the thermostat baths have attained the predetermined
temperatures at which the viscosity measurements are to be made, at two
different temperatures.
Every time, remember to clean the viscometer thoroughly before using. In the
case where aqueous solutions of organic materials are involved, rinse with
distilled water followed by acetone, and dry with filtered air. (NOTE: In order
for the viscometer to operate properly, it must be absolutely clean.)
Calibrate the viscometer using the 60-weight-percent aqueous sucrose solution
that is provided.
With the viscometer in a vertical position, use the 10-ml graduated pipette to
introduce exactly 6.5 ml of the sucrose solution into the wider leg of the
viscometer. (NOTE: All liquids are to be introduced into the viscometer at room
temperature.)
Place the viscometer in a constant temperature bath in the orientation shown in
Figure 4,a. It should be submerged such that the bath water is at least one
centimeter above the upper of the two small reservoirs. Allow at least ten
minutes for the viscometer and its contents to reach thermal equilibrium with
the bath, particularly at the higher temperatures. The filled viscometer will be
moved from bath to bath to obtain data at various temperatures.
Apply suction to the narrow leg of the viscometer until the liquid level is about
0.5 cm above the etched mark between the two small reservoirs.
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
Place a thumb over open end of narrow leg to maintain the liquid level. At this
point an unbroken column of liquid should extend from the large bulb at the
bottom to a level near the bottom of the upper small reservoir.
 Remove thumb and measure with the stopwatch the time required for the liquid
meniscus to pass from the upper etched mark to the lower etched mark.
 Repeat Steps 7 through 9 to obtain replicate data points. The runs go faster at
the higher temperature so it is more convenient to take replicates in the warmer
baths.
 Repeat Steps 4 through 11, replacing the sucrose solution first with the 85weight-percent aqueous glycerol solution, then with distilled water. For glycerol
use the same temperatures as in the calibration process. With pure water, it is
sufficient to make a measurement only at room temperature; this measurement
will be used to test the applicability of the method to less viscous fluids.
 Collect the following data (water as a standard): Weight of the empty and dry
pycnometer, pycnometer plus distilled water, pycnometer plus sucrose
solution, pycnometer plus glycerol solution and finally temperatures of all
solutions weighed.
These measurements may be done at room temperature. Calculate densities
in order to determine the actual solution concentrations from the density tables.
Note also approximate values of the quantities appearing in Equation (6).
These can be used to estimate the expected value of C.
Always pour the solutions slowly. Otherwise, they will entrain air bubbles that
are very slow to escape and can affect the experimental results.
PROCEDURE II

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
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

Calibrate the viscometer before viscosity measurements of polymer
suspension.
Ensure that the thermostat baths have attained the predetermined
temperatures at which the viscosity measurements are to be made.
Introduce 16 ml 50% w aqueous polymer suspension to the sample cup.
Connect to the inlet and outlet of water bath to the sample cup, shown in
Figure 5.
Viscosities of polymer suspension are measured at different speeds from 10
RPM to 100 RPM at 1 minute intervals.
Wait 15 minutes for reaching the test temperature.
Figure 5. Inlets and outlets of water bath and sample cup
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DATA ANALYSIS
Newtonian Fluids:
1. For the 60-weight-percent aqueous sucrose solution plot: density vs.
temperature, absolute viscosity vs. temperature, kinematic viscosity vs.
temperature.
2. Use the sucrose-solution data with measured efflux times to determine the
viscometer constant C. Consider whether the data indicate any dependence of C
on temperature.
3. Determine the experimental kinematic viscosity of the glycerol solution as a
function of temperature. Plot the results, and for comparison include in the plot a
literature value for the kinematic viscosity of an 85-weight-percent aqueous
glycerol solution at studied temperature.
4. Compare the experimentally determined viscosity of water with published
values.
Non-Newtonian Fluids:
1. Plot for the polymer suspension;
a. Viscosity versus shear rate according to experimental results and different
models for each temperature. Compare the viscosity versus shear rate for
different temperatures.
b. Shear stress versus shear rate at each different temperatures.
2. Calculate the constants for each models. Write your model equations for
viscosity as a function of T, and shear rate(  ).
3. Compare the experimentally and theoretically determined viscosity values of
polymer suspension. What is the most suitable model for polymer suspension?
Discuss your experimental and theoretical data.
SAFETY NOTE
Both Sucrose and Glycerol are generally not hazardous in normal handling,
however good laboratory practices should always be used. Avoid long term
exposure to skin or inhalation.
Acknowledgement:
manual.
Author thanks Dr. Tıhmınlıoğlu for her helps in preparing this
REFERENCES
1. Geankoplis, Christie J., Transport Processes and Unit operations, 2nd. ed., 1983, Allyn
and Bacon Series in engineering, Massachusetts.
2. McCabe, Smith, Harriott, Unit Operations of Chemical Engineering, 4th ed., 1987,
McGraw Hill, New York.
3. Massey, B.S., Mechanics of fluids, 4th ed., 1979, Van Nostrand Reinhold company
Ltd., New York.
4. Barnes H. A., Hutton J.F., Walters K., An Introduction to Rheology, 1989, Elsevier,
Amsterdam.
5. Streeter, Victor L., Fluid Mechanics, 4th ed., 1966, McGraw-Hill Company, New York.
6. University of Wisconsin-Madison, Chemical Engineering Department, Transport
Phenomena Laboratory Guidelines.
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