Diffusion coefficients of interacting Brownian particles

Abstract

Starting from a N-particle diffusion equation, the effective particle (self-) and concentration diffusion coefficients of interacting Brownian particles are studied theoretically. These two diffusion coefficients defined by distinct ways are different for interacting systems. By taking into account both potential and hydrodynamic interactions, the expression for the frequency-dependent particle diffusion coefficient exact to linear order in number density is derived. Detailed calculations of both diffusion coefficients are performed for model systems of hard spheres with a repulsive or an attractive long-range potential. The effects of potential and hydrodynamic interactions on these two diffusion coefficients are clarified. The velocity autocorrelation function is also calculated and non-Markovian behaviors are discussed.