Computer studies of the onset of Brownian motion in a hard sphere fluid

Molecular dynamics calculations on a system of identical hard spheres containing a single test particle of larger size yield a velocity autocorrelation function that has an initial exponential decay agreeing with Enskog exponential decay, followed by a much slower decay. The slow decay does not agree with Stokes exponential decay but fits well the hydrodynamical model which takes into account the dependence of the frictional resistance of the particle on its time history as well as the effect of the inertia of the fluid surrounding the test particle. Binary collision rates computed from the molecular dynamics agree very well with Enskog's theory.