92168.pdf

250 Rheology

particles are dispersed in a liquid medium, and arrived at the

expression

17 = 170 (1 + k$)

where k is a constant equal to 2.5 - i.e.

ifc = 2.5* or fok = 2.5 (9.5)

The effect of such particles on the viscosity of a dispersion depends,

therefore, only on the total volume which they occupy and is

independent of their size.

The validity of Einstein's equation has been confirmed experiment-

ally for dilute suspensions ((f><c 0.02) of glass spheres, certain spores

and fungi, polystyrene particles, etc., in the presence of sufficient

electrolyte to eliminate charge effects.

For dispersions of non-rigid spheres (e.g. emulsions) the flow lines

may be partially transmitted through the suspended particles, making

k in Einstein's equation less than 2.5.

The non-applicability of the Einstein equation at moderate

concentrations is mainly due to an overlapping of the disturbed

regions of flow around the particles. A number of equations, mostly

of the type 17 = 170 (1 +a<(>+b<j>^2 +.. .), have been proposed to allow

for this.

Salvation and asymmetry

The volume fraction term in viscosity equations must include any
solvent which acts kinetically as a part of the particles. The intrinsic
viscosity is, therefore, proportional to the solvation factor (i.e. the
ratio of solvated and unsolvated volumes of dispersed phase). The,
solvation factor will usually increase with decreasing particle size.
Particle asymmetry has a marked effect on viscosity and a number
of complex expressions relating intrinsic viscosity (usually extrapolated
to zero velocity gradient to eliminate the effect of orientation) to
axial ratio for rods, ellipsoids, flexible chains, etc., have been
proposed. For randomly orientated, rigid, elongated particles, the
intrinsic viscosity is approximately proportional to the square of the
axial ratio.