A kinetic theory of dense fluids. Test-particle kinetic equation

Abstract

Mori’s form of the generalized Langevin equation is applied to a system of particles whose pair interactions are sums of short-ranged, rigid-core repulsions and longer-ranged continuous interactions. It is assumed that the memory function decays exponentially from its initial value at a rate characterized by a single, wave number dependent relaxation time. The test–particle kinetic equation resulting from this one key assumption is strongly reminiscent of that associated with the well-known Rice–Allnatt theory. However, in addition to Fokker–Planck and Enskig operators similar to those of the Rice–Allnatt theory, it also includes coupling between rigid-core scattering events and the diffusive, Brownian motions of the particles as well as contributions associated with three-particle rigid-core collisions. A systematic method of solution is developed and applied to a simplified form of this kinetic equation. Solutions generated by this procedure involve matrix elements of the linearized Enskog operator computed in the basis of generalized Hermite polynomials which are eigenfunctions of the Fokker–Planck operator associated with the long-ranged, continuous portion of the pair potential. The approximate solutions obtained are used to compute the density and velocity autocorrelation functions and the coefficient of self-diffusion as well.