The viscoelastic response of Brownian suspensions

In a simple model for the long-time dynamical behavior of Brownian suspensi ons, particles diffuse independently while simultaneously undergoing direct interactions with each other. Despite its simplicity, this model forms the basis of both the Brownian dynamics computer simulation technique and appa rently successful theories. Here we use the approach to study numerically t he viscoelastic response of a suspension of hard spheres. At low volume fra ctions (10%) we find that the frequency dependence of the viscosity is in a greement with theoretical calculations based on solving the two-particle Sm oluchowski equation. At a higher volume fraction (45%) we find that the mod el is not well described by various extensions of low density theory that h ave been proposed. Including hydrodynamics in a minimal way (by allowing th e particles to diffuse with the short-time diffusion coefficient! and compa ring with experiment, the model successfully reproduces the viscoelastic re sponse over an intermediate range of frequencies. However, at low frequenci es a significant disagreement emerges. A "slowing down'' of the dynamics of the particles at longer times, more apparent in the simulations than in th e experimental results, appears to be the cause of this discrepancy. Ultima tely, this leads to a significant overestimate of the zero frequency (Newto nian) viscosity. The reason theories based on the approach yield such excel lent agreement with experiment, we can only conclude, is because they fail to describe the model adequately. (C) 1999 American Institute of Physics. [ S0021-9606(99)52341-6].