Kinetic theory of rough sphere fluids: Density fluctuations

Abstract

We construct a kinetic equation for the phase space density correlation function (PSDCF) in a rough sphere fluid (at the generalized Enskog level) which is valid for arbitrary wave number and frequency. The kinetic equation yields the first two kinetic sum rules exactly; also the density–density correlation function implied by it has the correct first four sum rules exactly. We use the short time behavior of PSDCF and the generalized hydrodynamics approach to construct approximate interpolation formulas for a variety of space–time dependent correlation functions related to conserved variables in the fluid. The coupling of modes described by these correlation functions to the test particle density fluctuations is responsible for the known asymptotic power law decay in the linear and angular velocity correlation functions. As a by-product of this study, we also obtain expressions for various (bare) transport coefficients in a dense rough sphere fluid.