OBJECTIVE
At the end of the experiment, you should be able to learn viscosity measurement techniques:
1.
Capillary Flow Method (The Ostwald-Fenske Viscometer)
2.
Falling Ball Method (Hoeppler)
3.
Rotating Shaft Viscometer (BROOKFIELD)
BACKGROUND INFORMATION
An applied shearing force which produces flow in a fluid is resisted by a force proportional to the gradient of the flow velocity. The proportionality constant is known as viscosity.
The flow of a fluid is said to be "laminar", if points in the fluid move smoothly in layers.
When one layer flows past another, an internal viscous force is produced that slows down the faster layer and speeds up the slower one. To overcome this drag and maintain a constant velocity gradient between layers, an external force must be exerted. Newton deduced a relationship between the velocity gradient (dU/dX) and the shearing force (F) which produces it. If (A) is the area of contact between the moving layers of fluid, the
Newton's Law of Viscosity is
F = -

.A.dU/dX
Where the factor of proportionality "

" is called the viscosity of the fluid.
(1)
Viscosity of a fluid depends on temperature, pressure and composition. A fluid is said to be a Newtonian fluid if, in laminar flow,

is an independent of the velocity gradient [1].
There are several experimental methods for the determination of the viscosity of fluids.
The methods used are:
1.
Flow through the capillary tubes
2.
Fall of solid spheres through fluids
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METU Chem. Eng. Dept.
Ch.E. 320 Chem. Eng. Lab I
Experiment 7
Viscosity Measurement Techniques
3.
Torque or viscous drag on a rotating disk or cylinder immersed in the fluid
4.
Flow of fluids through an aperture in a plate
1.
CAPILLARY-FLOW METHOD (THE OSTWALD-FENSKE
VISCOMETER)
The Ostwald-Fenske method makes use of the Hagen-Poiseuille equation for the determination of liquid viscosities by measuring the time of flow of a given volume liquid through a vertical capillary tube under the influence of gravity. For a virtually incompressible fluid this flow is governed by the Poiseuille's Law in the form of [2]: dV / dt = (

r4

P) / (8

L ) (1.1)
Where (dV / dt) is the rate of liquid flow through a cylindrical tube of radius r and length
L, and

P is the pressure difference between two ends of the tube, when (dV / dt) is constant, Equation (1.1) becomes

(

r4

P) (t / 8VL) (1.2)
Where t is the time required for the upper meniscus of the liquid in the left arm of the viscometer to fall from the upper to the lower fiducial mark. In the Ostwald-Fenske
Viscometer

P is (
 gh),

being the density and

P is variable since h varies during the measurement. However, its initial and final values are known. Thus equation (1.2) can be written (with some simplifying assumptions) as

r4
 g ht / 8VL = A

t (1.3)
Where A is a constant for a given viscometer which can be determined through calibration with a liquid of known viscosity and density (e.g. water).
EQUIPMENT AND CHEMICALS
Ostwald-Fenske viscometer, constant temperature bath, triethylene glycol, stopwatch, distilled water, ethanol, acetone.
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METU Chem. Eng. Dept.
Ch.E. 320 Chem. Eng. Lab I
EXPERIMENTAL PROCEDURE
Experiment 7
Viscosity Measurement Techniques
1.
The apparatus should be cleaned with ethanol and acetone, and rinsed with distilled water and then with the sample to be investigated. Before starting measurements, the viscometer should be calibrated.
2.
Place the viscometer filled with 10 ml. of liquid sample in the water bath set at a temperature you want, and wait until the sample reaches thermal equilibrium with the bath.
3.
Before placing the viscometer in to the thermostat, attach a rubber bulb to its capillary arm by holding firmly the end of the capillary arm. Do not hold it by the other end.
Even a small torque may cause the fragile viscometer to break.
4.
In removing the rubber bulb push it off the tube. Never pull rubber bulb off the tube for removal. Pulling the rubber bulb causes it to contract in diameter and hold more tightly. Pushing it, however, causes the bore to expand, and the tube then slips off easily.
5.
Draw the liquid in the reservoir up into the capillary arm until it fills the feed bulb and the meniscus is well above the upper fiducial mark. Be very careful in drawing the liquid into feed bulb so as not to cause the liquid to be drawn into the rubber bulb.
6.
Release the suction and let the liquid flow by its own weight. Record the time required for the upper meniscus of the liquid in the feed bulb to pass two calibration marks.
CALCULATIONS
Determine the constant (A) of the viscometer. Then you can calculate viscosity or kinematic viscosity of the liquid sample directly.
Obtain a set of data and compare with the literature values. The temperature dependence of the viscosity of Newtonian fluids can be represented by the relation
μ
(T) = C exp (E/RT) (1.4)
Where C is a constant and E is the activation energy for viscous flow. Determine the constants C and E by appropriate plots.
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METU Chem. Eng. Dept.
Ch.E. 320 Chem. Eng. Lab I
2.
FALLING BALL METHOD (HOEPPLER)
Experiment 7
Viscosity Measurement Techniques
This type of viscometers makes use of the Stokes formula for the determination of viscosity of liquids by measuring the rate of fall of a spherical body through the liquid.
The frictional force (F) resisting the motion of a spherical body moving under the influence of gravitational force in a viscous medium is given by the Stokes equation of hydrodynamics as
F = 6.

.

.r. U (2.1)
Where

is the coefficient of viscosity of the medium, r is the radius of the sphere, and U is the terminal velocity.
EQUIPMENT AND CHEMICALS
Water bath, stopwatch, distilled water, triethylene glycol, , ethanol, acetone, glass rod.
EXPERIMENTAL PROCEDURE
1.
The water jacket is filled up to the opening for thermometer knob (66). The temperature range of water as a jacket liquid is 1o C to 95o C. An air space about 15 mm high at the top of the jacket is left. Escape of air can be controlled by valve (12)
(see Figure 1).
2.
Cleaning of the glass tube is made using ethanol and acetone. Before the glass tube is filled with the liquid under examination, the balls, plugs and washers, and the tube itself must be perfectly dry and free of grease, thereafter, be moistened with the liquid to be examined.
3.
The tube is filled with 30-40 ml of the sample to about 2 cm below the upper end, then the ball is inserted. The adhering bubbles are removed with a glass rod, then the capillary plug (11) is introduced with the washer (37b). The liquid should be slightly above the end of the capillary (C). Then the closing plate (10) is attached and the cap
(7b) is screwed.
4.
To measure the time of fall, the instrument is fixed in the standard position by engaging the locking pine (17) into the stop hole (H) of the carrier beam (5). The level
(13) is adjusted. The time of fall through the distance m
1
to m
2
is measured. A
4

METU Chem. Eng. Dept.
Ch.E. 320 Chem. Eng. Lab I
Experiment 7
Viscosity Measurement Techniques convenient period to measure is the time required for the lower periphery of the ball to traverse the distance between two marks. For dark or opaque liquids, the time is measured when the equator of the ball passes the upper and lower marks.
NOTE: Before proceeding through the determinations, the falling ball viscometer must be calibrated by checking the validity of the ball constants using liquids whose viscosity is known from absolute measurements.
Figure 1.
Falling Ball Viscometer
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METU Chem. Eng. Dept.
Ch.E. 320 Chem. Eng. Lab I
CALCULATIONS
Experiment 7
Viscosity Measurement Techniques
The viscosity in centipoises at the measuring temperature is given by the following formula:

= t (
 b -
 r ) (B)
(2.2)
Where,

: absolute viscosity in centipoise
 b
: density of the ball (g/cm3 )
 r
: density of the fluid at the measuring temperature (g/cm3 )
B t
: ball constant
: time of fall (s)
The variation of the density of the balls with temperature is usually too slight. It can be accounted for, however, by deducting 0.0003 for glass and 0.0015 for metal for every
10o C rise above 20o C from the values given in Table 1.
Table 1.Properties of balls used in Hoeppler Method
Ball number Diameter (mm) Weight (g) Constant
Density (g/cm3 )
2.392 1
2
15.80
15.66
4.937
4.806
0.00907
0.0506 2.390
8.146 3
4
15.62
15.20
16.258
14.991
0.0755
0.639
5 14.28 11.748
8.157
7.699 4.55
6 11.10 5.517 7.696 33.6
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METU Chem. Eng. Dept.
Ch.E. 320 Chem. Eng. Lab I
Experiment 7
Viscosity Measurement Techniques
3.
ROTATING SHAFT VISCOMETER (BROOKFIELD)
This kind of viscometer is a simple rotational viscometer, specially used for fast comparison tests on liquids. The viscosity is indicated directly on the scale as result of torque that is caused by the immersing the rotor driven by a speed controlled battery operated motor into the liquid.
Brookfield viscometer is designed for measurement of viscosity at a given shear rates. The principle of operation is to drive a spindle, which is immersed in the test fluid, through a calibrated spring. The viscous drag of the fluid against the spindle is measured by the spring deflection, which is detected with a rotary transducer [3].
Figure 2. Rotating shaft viscometer (Brookfield) [4]
The goal is to obtain a Viscometer dial or display (% torque) reading between 10 and 100, remembering that relative error of measurement improves as the reading approaches 100. If the reading is over 100, select a slower speed and/or a smaller spindle. Conversely, if the reading is under 10, select a higher speed and/or a larger spindle [4].
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METU Chem. Eng. Dept.
Ch.E. 320 Chem. Eng. Lab I
Experiment 7
Viscosity Measurement Techniques
EXPERIMENTAL PROCEDURE
1.
Before operating the Viscometer, be sure that it is securely attached to its stand and has been properly leveled. Select a spindle and speed combination and attach the spindle to the Viscometer.
2.
Turn the Viscometer on and allow it to run until a constant reading is obtained. wait until the reading appears relatively constant for a reasonable time
3.
Repeat measurement for different speeds for the same spindle
4.
Change the spindle, measure viscosity of the same liquid for the selected speed values
REFERENCES
[1] Shomaker, D.P. et al., Experiments in Physical Chemistry , 3 rd
Ed., McGraw-Hill Book
Co., NewYork, 1974
[2] Moore, W.J., Physical Chemistry , 3 rd
Ed., Prentice Hall, Inc., Englewood Cliffs, New
Jersey, 1962
[3] Forsbacka, L., Experiences in slag viscosity measurement by rotation cylinder method.
Retrieved at 18/02/2015 from http://www.chemshow.cn/UploadFile/datum/1000/zhengcan_200822610150805484.pdf
[4] Brookfield Engineering Labs, More solutions to sticky problems: A Guide to Getting
More From Your Brookfield Viscometer , 2006.
ATTENTION
The report of this experiment will be prepared at the end of the experiment on laboratory notebooks individually. Each group should bring a computer which will help you analyze your results at the end of the experiment. The figures required for us to see your results will be printed and glued to your notebook by all the group members at the end of the day. After the control of your notebook for short repot, there will be no other report submission for this experiment.
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METU Chem. Eng. Dept.
Ch.E. 320 Chem. Eng. Lab I
PRELIMINARY WORK
Experiment 7
Viscosity Measurement Techniques
1.
Before the lab hour, prepare your laboratory notebook and study related concepts
(theories used in the measurements, classification of fluids based on their shear stress vs. shear rate behavior, constitutive equations for power law fluids) in detail.
2.
Before the lab hour, see and examine the apparatus
3.
Determine which physical properties of the sample you need and find the necessary physical properties from literature.
4.
Think about the parameters that affect the viscosity and then you can choose any parameter that will be helpful.
5.
Starting from the Stokes equation derive equation (2.2) which is the expression for calculating viscosity of liquids by falling ball method.
6.
Bring at least one computer for preparation of the short report.
SUGGESTED READING
Barrow, G.M., Physical Chemistry , 5 th
Ed., McGraw-Hill Book Co., New York, 1970.
Daniels, F., et.al., Experimental Physical Chemistry , 7 th
Ed., McGraw-Hill Book Co.,
New York, 1970.
McCabe, W.L., and Smith, J.C., Unit Operations of Chemical Engineering , 2 nd
Ed.,
McGraw-Hill-Kogakusha Book Co., Tokyo, 1967.
Moore, W.J., Physical Chemistry , 3 rd
Ed., Prentice Hall, Inc., Englewood Cliffs, New
Jersey, 1962
Shomaker, D.P. , et.al., Experiments in Physical Chemistry , 3 rd
Ed., McGraw-Hill Book
Co., NewYork, 1974
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