Kinetic theory of self-diffusion in a hard-sphere fluid

Abstract

A repeated-ring kinetic equation for the velocity-autocorrelation function in a hard-sphere fluid is presented. In this theory contributions from uncorrelated (Enskog) collisions, correlated (single-ring) collisions, and multiple (repeated-ring) collisions are included. A quasihydrodynamic approximation is made to describe the intermediate propagation between correlated collisions. We obtain an expression for the self-diffusion coefficient $D$ which suggests that its density dependence arises from a competition between the shear and density fluctuations of the fluid. Using interpolation formulas to numerically evaluate the coupling of the test-particle motion to the fluid fluctuations we have computed $D$. The variation of $D$ with density is found to be in good qualitative agreement with computer molecular-dynamics simulation. For low to moderate density the coupling of the test-particle motion to the fluid shear (vortex) fluctuations leads to an enhancement of $D$ relative to its Enskog value. At high density the coupling to the fluid-density fluctuations yields a sharp decrease in $D$.