İZMIR INSTITUTE OF TECHNOLOGY

CHEMICAL ENGINEERING DEPARTMENT

2008-2009 Spring Semester

CHE 310CHEMICAL ENGINEERING LABORATORY I

Viscosity of Newtonian and Viscosity of Newtonian and Non-Newtonian FluidsNon-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

INTRODUCTIONOf 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 high-polymer 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 PRINCIPLENewtonian 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:

Q = …………………………………...(1)

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

8Q L

( )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)

where C is called the viscometer constant. If C is evaluated by observing te with a liquid of known viscosity, C may be calculated for the apparatus. Then

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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

Cg h RVL

( ) 4

8…………………………(6)

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:

a ......................(7)

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 n1 and shear thickening behaviour to n1. The special case, n1, 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.

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

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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.

……………………(11)

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.

+ ……………………………(12)

The Casson model shows both yield stress and shear-thinning non-Newtonian 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.

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.

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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 size and shape of the spindle is rotating in, and the full-scale torque of the calibrated spring.

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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.

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.

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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 85-weight-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

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

DATA ANALYSISNewtonian Fluids:

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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 NOTEBoth 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: Author thanks Dr. Tıhmınlıoğlu for her helps in preparing this manual.

REFERENCES1. 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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