On the theory of concentrated hard-sphere suspensions

A systematic theory for the dynamics of hard-sphere suspensions of interacting Brownian particles with both hydrodynamic and direct interactions is presented. A generalized diffusion equation is derived for concentrated suspensions. The volume fraction (φ) dependence of the short- and long-time self-diffusion coefficients are thus explored from a unifying point of view. The long-range hydrodynamic interactions due to the Oseen tensor are shown to play a crucial role in both coefficients, while the short-range hydrodynamic interactions just lead to corrections. The importance of the correlation effects between particles due to the long-range hydrodynamic interactions is also stressed. The nonlocal correlation effect is an important factor, leading to the behavior of the long-time self-diffusion coefficient (DSL) as DSL (1 − φ/φ0)2 near the volume fraction of φ0 = 0.5718. The direct interactions are also found to be drastically reduced by the short-range hydrodynamic interactions.