Brownian Dynamics Simulations of Colloidal Liquids: Hydrodynamics and Stress Relaxation

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Abstract
We describe the statistical mechanics background and additional algorithmic features of a recently proposed simple mean-field Brownian Dynamics algorithm formulated to include many-body hydrodynamics, using a local density approximation for the friction coefficient. We show that the equations of motion satisfy the incompressibility of phase space. We make further developments to the model, computing the hydrodynamic effects on the shear stress relaxation function. We show that stress relaxation takes place over two well-defined regimes, in both cases with and without mean field hydrodynamics, MFH. At short times ta 2/D 0 < 10−3, where a is the radius of the colloidal particle and D 0 is the self-diffusion coefficient at infinite dilution, decay of the stress autocorrelation function, Cs(t) is essentially independent of volume fraction and does not fit to a simple analytic form. At longer times than ta 2/D 0 < 10−2 the decay has the fractional exponential form ∼exp(-t β) with β ≫ 1. The transition between these two regimes coincides with a rapid fall in the time-dependent diffusion coefficient from the so-called short-time to long-time values. We do not find any evidence for power law decay in the Cs(t) as predicted by recent mode-coupling based analytical expansions.

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