92168.pdf

Rheology 247

might block the capillary, must be removed from the liquid prior to

its introduction into the viscometer. A viscometer is selected which

gives a flow time in excess of c. 100 s; otherwise a kinetic energy

correction is necessary.

The capillary method is simple to operate and precise (c. 0.01-0.1

per cent) in its results, but suffers from the disadvantage that the rate

of shear varies from zero at the centre of the capillary to a maximum

(which decreases throughout the determination) at the wall. Thus,

with asymmetric particles a viscosity determination in an Ostwald

viscometer could cover various states of orientation and the measured

viscosity, although reproducible, would have little theoretical sig-

nificance.

Rotational methods

Concentric cylinder and cone and plate instruments are particularly

useful for studying the flow behaviour of non-Newtonian liquids.

In the first of these techniques an approximation to uniform rate of

shear throughout the sample is achieved by shearing a thin film of the

liquid between concentric cylinders. The outer cylinder can be

rotated (or oscillated) at a constant rate and the shear stress

measured in terms of the deflection of the inner cylinder, which is

suspended by a torsion wire (Figure 9.2); or the inner cylinder can be

rotated (or oscillated) with the outer cylinder stationary and the

resistance offered to the motor measured.

If (a is the angular velocity of the outer cylinder and 6 the angular

deflection of the inner cylinder, the coefficient of viscosity of the

liquid is given by

„-*? (9.4)

at

where k is an apparatus constant (usually obtained by calibration with
a liquid of known viscosity). The necessity for an end-correction can
be avoided if the inner cylinder is appropriately cone-shaped at its
end, or if air is entrapped in a hollowed-out inner cylinder base.
Cone and plate instruments (see Figure 9.3) permit the velocity
gradient to be kept constant throughout the sample, and are
particularly useful for studying highly viscous materials. A very
versatile cone and plate rheometer, known as a rheogoniometer, has
been developed by Weissenberg, which enables both tangential