Page 260 - Introduction to Colloid and Surface Chemistry

Viscosities of dilute colloidal solutions and dispersions

Functions of viscosity

When colloidal particles are dispersed in a liquid, the flow of the
liquid is disturbed and the viscosity is higher than that of the pure
liquid. The problem of relating the viscosities of colloidal dispersions
(especially when dilute) with the nature of the dispersed particles has
been the subject of much experimental investigation and theoretical
consideration. In this respect, viscosity increments are of greater
significance than absolute viscosities, and the following functions of
viscosity are defined:

t| 0 = viscosity of pure solvent or dispersion medium
TJ = viscosity of solution or dispersion
17/170 == relative viscosity (or viscosity ratio)
17, = 17/170 - 1 = relative viscosity increment (or viscosity ratio
increment)
T?J/C = reduced viscosity (or viscosity number)

= intrinsic viscosity (or limiting viscosity number)

From the above expressions it can be seen that reduced and
intrinsic viscosities have the unit of reciprocal concentration. When
one considers particle shape and solvation, however, concentration is
generally expressed in terms of the volume fraction <£ of the particles
(i.e. volume of particles/total volume) and the corresponding reduced
and intrinsic viscosities are, therefore, dimensionless.

Spherical particles

Einstein (1906) made a hydrodynamic calculation (under assumptions
similar to those of Stokes; see page 22) relating to the disturbance of
the flow lines when identical, non-interacting, rigid, spherical