Kinetic theory of single-particle motion in a fluid

Abstract

A repeated-ring kinetic theory is derived to describe the thermal motion of a tagged particle of arbitrary size and mass immersed in a fluid. In the spirit of the fully renormalized kinetic theory developed by Mazenko, systematic approximations are made in the exact equations of motion for the tagged-particle phase-space correlation function to cast the dynamics of the system in terms of the two-body Enskog collision operator. In addition to Enskog (uncorrelated collisions) and ring (two correlated collisions) events, we include repeated-ring (3,4,...correlated collisions) events. The theory is applied to the calculation of the velocity autocorrelation function and diffusion coefficient of a large hard sphere immersed in a dense fluid of smaller hard spheres. The accepted long-time behavior of the velocity auto-correlation function $t^{-\frac{3}{2}}$ is obtained and the diffusion coefficient is found to have the same functional form as in the Stokes-Einstein law of hydrodynamics. It is suggested that the theory be applied to study self-diffusion in a dense hard-sphere fluid.