VISCOMETERS

 DETERMINATION OF FLOW PROPERTIES

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Viscosity of both Newtonian and Non newtonian fluids are measured using various types of Viscometers.

SELECTION OF VISCOMETER

The classification and applications of equipment to different types of fluids are given in Figure 7-15. 

In case of Newtonian systems, the rate of shear is directly proportional to the shearing stress. Therefore, single point viscometer, i.e., the equipment that works at a single rate of shear, is sufficient. The following viscometers are used.

1. Capillary Viscometer             

2. Falling Sphere Viscometer

3. Rotational Viscometer

For the evaluation of non-Newtonian fluids, multipoint viscometers are required, because the apparent viscosity is to be determined at a several of rates of shear to get entire consistency curve. Multi-point viscometers can also be used to determine the viscosity of Newtonian fluids, when maintained at constant rate of shear. The following viscometers are used.

1. Cup and Bob Viscometer

2. Cone and Plate Viscometer

CAPILLARY VISCOMETERS

Capillary instruments are very accurate for the measurement of viscosity of Newtonian fluids having low viscosity. During measurement the time for the fluid to flow by gravity from one mark in a capillary column to the second mark is measured. The time of flow of the liquid under test is compared with the time required for a liquid of known viscosity (usually water) to pass between the two marks.

If η1 and η2 are the viscosities of the unknown and standard liquid, ρ 1 and ρ ₂ are the densities of the liquids and t1 and t2 are the respective flow times in seconds, the absolute viscosity of the unknown liquid η1 is determined by substituting the experimental value in the equation:

η1/ η2 = ρ1 t1/ ρ2 t2

The value η1/ η2 = η rel is known as relative viscosity of the liquid under test.

The above equation is based on Poiseuille's Law for a liquid flowing through a capillary tube,

η = πr4t∆P / 8 lv

where

r is the radius of the inside capillary,

t is the time of flow,

∆P is the pressure head in dyne/cm² under which the liquid flows,

l is the length of the capillary 

V is the volume of fluid flowing.

This equation can also be written as :

η = Κt ΔΡ

where K is a constant.

The pressure head ∆P depends on the density ρ of the liquid being measured, the acceleration due to gravity, and the difference in heights of the liquid level in the two arms of the viscometer. The acceleration of gravity is a constant and if the levels in the capillary are kept constant for all liquids, all the terms can be incorporated into a constant. The viscosities of the unknown and standard liquids can then be given as:

η1 = K’t1 ρ1

η2= K’t2 ρ2

Diving both the terms,

η 1/ η 2 = ρ1 t1/ ρ2 t2

Viscometers with capillary of varying diameters are available commercially for the measurement of fluids over a wide range of viscosity such as the Ostwald's viscometer, the Ubbelohde viscometer and the Cannon-Fenske viscometer

THE OSTWALD'S U-TUBE VISCOMETER

Fig. Oswald's U-tube capillary viscometer

The apparatus consists of a 'U' tube of which the left arm has a bulb at its lower part marked as A above the bulb. The right arm of the tube also has a bulb but at the upper part marked as B and C above and below the bulb and just below this bulb is a capillary tube. 

Liquid is introduced into the viscometer through the left arm until the level reaches the mark A. The viscometer is fixed vertically in a thermostated bath and allowed to attain the required temperature. The sample volume is adjusted and the liquid is sucked or blown into the right arm until the meniscus is just above mark B. The suction or pressure is released and the time taken for the bottom of the meniscus to fall from B to C is noted.

In order to determine the relative viscosity of a liquid with respect to water, the experiment is undertaken first with water and then with the liquid whose viscosity is to be determined. The time taken for the liquid t1, and that for water t2, are determined. 

The relative viscosity is calculated as:

Relative viscosity = η1/ η2 = ρ1 t1/ ρ2 t2

The absolute viscosity of the liquid may be calculated by multiplying the value of relative viscosity with the absolute viscosity of water.

FALLING SPHERE VISCOMETER

The principle of this instrument is based on Stoke's law which states that when a body falls through a viscous medium, it experiences a resistance or viscous drag which opposes the motion of the body. At the initial stage, the body experiences an acceleration due to the influence of gravity but soon this acceleration is balanced by the viscous drag and the body falls with a uniform terminal velocity.

Thus, Viscous drag on the body = Force responsible for the downward movement

Or 3πdηv = π/6d³g (ρ s- ρ ₁)

Where,

η is the coefficient of viscosity

d is the diameter of the sphere

g is the acceleration due to gravity

v is the terminal velocity

ρ s is the density of the sphere and

ρ ₁ is the density the liquid

Rearranging the above equation, we get :

η= d^2g(ρs - ρ₁)/ 18v

A falling sphere viscometer consists of a tube having two marking A and B on the outer surface. The tube is filled with the liquid whose viscosity is to be determined. The tube is clamped vertically inside a constant temperature bath and sufficient time is allowed for equilibration of temperature and for removal of air-bubbles from the liquid.

A ball of suitable material such as steel or glass is then allowed to fall through the glass tube inside the falling tube. The time taken for the sphere to fall from the point A to B is noted and the terminal velocity is obtained by dividing the distance between the two marks and the time. By substituting all the values in the above equation, the viscosity of the liquid is determined.

The above equation assumes that the sphere is falling through a medium of infinite dimension. A largest possible diameter should be employed. However, since the liquid in the experiment is contained in a cylindrical tube, a correction factor is introduced to nullify the effect of the tube wall on the fall of the sphere.

Correction factor (F) = 1 – 2.104 d/D + 2.09 d³/D³ - 0.95 d^5/D^5

where d is the diameter of the sphere and D is the diameter of the tube.

The corrected viscosity = η x F

An example of the falling sphere viscometer is the Hoeppler Ball Viscometer. It is a falling ball instrument which uses a short, nearly vertical glass tube of large diameter and a closely fitting ball of either steel or glass. The sample and a ball are loaded into the inner cylinder and brought to the temperature of measurement by means of a constant temperature outer jacket. The apparatus is inverted to place the ball in the initial starting position. The time for the ball to traverse the distance between two marks is measured. A minimum falling time of 30 seconds is used for best results.

 ROTATIONAL VISCOMETER

These instruments work on viscous drag exerted on a body when it is rotated in the fluid, for which the viscosity is to be determined. Here wide range of shear rate can be achieved by varying shear stress. Thus also useful for Non-newtonian type fluids. The two categories of instruments are:

1. Cup and Bob Viscometer

2. Cone and Plate Viscometer

(a) Cup and Bob Viscometer

This type of instrument consists of two coaxial cylinders of different diameters. The outer cylinder forms the cup into which the inner cylinder or bob is fixed centrally. The sample to be analysed is sheared in the space between the outer wall of the bob and the inner wall of the cup. The different types of commercially available instruments differ mainly in whether the torque set up in the bob is due to the rotation of the outer cup or due to the rotation of the bob itself.

The Stormer Viscometer

The stormer viscometer is an instrument in which the bob rotates and the cup is stationary. The instrument can be used to obtain fundamental rheological properties such as yield value, plastic viscosity and the thixotropic index.

In operation, the test system is placed in the space between the cup and the bob and allowed to reach temperature equilibrium. A weight is placed on the hanger and the time for the bob to rotate a specific number of times is recorded. This data is then converted to rpm. The weights are increased gradually and the whole procedure is repeated. In this way, a rheogram is obtained by plotting rpm vs weight added. By the use of appropriate constants, the rpm value can be converted to actual rates of shear in sec¹. Similarly, the weights added can be transposed into the units of shear stress, namely dynes cm ².

The viscosity of the material may be calculated using the following equation:

ŋ = Kv w/v

where,

w is the weight in grams

v is the rpm generated due to w

Kv is an instrument constant which can be determined by analysing an oil of known viscosity using the instrument.

The plastic viscosity may be calculated using the equation :

U = Kv (W-Wf)/V

where U is the plastic viscosity in poise and Wf is the yield value intercept in grams.

(b) Cone and Plate Viscometer

The instrument essentially consists of a flat circular plate with a wide angle cone placed centrally.

During operation, the sample is placed at the centre of the plate, which is then raised into position under the cone. The cone is driven by a variable speed motor and the sample is sheared in the narrow gap between the stationary plate and the rotating cone. The rate of shear in revolution per minute is increased and decreased and the torque produced on the cone is measured. A plot of rpm or rate of shear versus scale reading or shearing stress may thus be constructed in an ordinary manner. The Ferranti-shirley viscometer is an example of a rotational cone and plate viscometer.

The viscosity in poises of a Newtonian liquid measured in the cone-plate viscometer is calculated by the use of the equation :

h= C T/V

where,

C is an instrumental constant,

T is the torque reading,

v is the speed of the cone in revolutions per minute

For a material showing plastic flow, the plastic viscosity is given by the equation:

U = C (T-Tf)/V

And the yield value is given by

f = C x Tf

Where Tf is the torque at the shearing stress and C is an instrumental constant.