Generalized transport coefficients for hard spheres

Abstract

The wavelength- and frequency-dependent linear transport coefficients and the wavelength-dependent thermodynamic properties have been determined for hard spheres at three different densities and over a region of wavelengths and frequencies that range from the hydrodynamic to the free-streaming regime. The molecular-dynamics calculation involves the evaluation of correlation functions from which the generalized properties can be simply derived consistent with their hydrodynamic definitions. The results are compared with generalized kinetic theory and, except for the viscosity at high density and small wavelength, the predictions of that theory are accurate within a few percent. For the viscosity, mode-coupling theory improves upon the predictions of kinetic theory. A single application is given in which the dependence of the Stokes friction coefficient on the size of the massive Brownian particle is determined using the generalized viscosity. This illustration leads one to believe that generalized hydrodynamics quantitatively applies on the molecular scale.