LINEAR VISCOELASTICITY OF SEMIDILUTE HARD-SPHERE SUSPENSIONS

We study the linear viscoelasticity of semidilute suspensions of spherical Brownian particles. We consider a simple model in which hydrodynamic interactions and direct interactions apart from hard-sphere repulsion are neglected. We calculate the dynamic viscosity for this model system exactly to second order in the volume fraction. In turns out that the infinite-frequency shear modulus does not exist because the dynamic viscosity falls off with the inverse square root of the frequency. The relaxation-rate spectrum has corresponding inverse-square-root behavior. We find exact expressions for the spectral density and the time-dependent stress-relaxation function. Qualitatively our results resemble those found experimentally for dense hard-sphere suspensions.