A statistical model for the dynamical properties of hard particle fluids

Abstract

We study simple models for the dynamic properties of fluids composed of hard particles. The simplest model is based on the assumption that each molecule has a constant probability q of reversing direction on each collision, regardless of its previous collision history. The time correlation function for velocity reversal is then a simple exponential. In the more complicated single step intrinsic memory model, the reversal probability is v if the particle suffered a reversal on its last collision and μ otherwise. The velocity reversal correlation function, which is computed analytically, can be oscillatory for certain values of the parameters μ and ν. The distribution of collision times, velocity reversal times and various time correlation functions are computed from a molecular dynamics simulation of the hard sphere fluid at a high density, ρ/ρ0 = 0·65 where ρ0 is the density of closest packing. In this fluid the velocity autocorrelation function and velocity reversal correlation function become negative after about five mean collision times. Although the distribution of collision and velocity reversal times are very well described by the simplest Markovian model, neither of the models considered here can represent the velocity reversal correlation function. This observation provides additional support for the hypothesis that the crossover to negative values displayed by the velocity autocorrelation function is the result of a memory that persists for considerably longer than one collision.