Hard, and Slightly Deformable, Spheres

The simplest suspensions are composed of so-called hard spheres in which the only inter-actions between particles are rigid repulsions that occur when particles come into contact Even suspensions as simple as these can show rather complex rheological phenomena. 

At very low volume fractions (0 SO.O3), the shear viscosity rj of a suspension of hard spheres can be predicted by the simple formula 

The expansion, Eq. (6-2), was extended to higher order in 0 by a simple, though approximate, effective medium argument of Arrhenius (1917). According to this argument, we suppose that we increase hy d4 the particle concentration in a suspension of viscosity 

A similar argument can be made for arbitrarily shaped particles, yielding 

Here [ 7] is the intrinsic viscosity, which for suspensions is the dilute limit of the viscosity increment per unit particle volume fraction, divided by the solvent viscosity. Thus, it is a dimensionless quantity defined as 

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