Propagation of Density Disturbances in a Dense Hard-Sphere Gas

Abstract

Approximate calculations of S(K, ω)—the double Fourier transform of the density—density correlation function—for the linearized Enskog equation for hard spheres are presented. The interaction terms are the usual Boltzmann collision integral and the collisional transfer terms. The former is replaced by a single relaxation-time kinetic model, while the collisional transfer terms are evaluated, as a first approximation, with a local Maxwellian for the distribution function. The numerical results at small K exhibit the expected peak at ω=cK due to sound propagation, in agreement with the predictions of the linearized hydrodynamic calculations. A peak is found to persist at large wavenumbers corresponding to a modified form of collective excitation. However, this peak disappears when first-order corrections to the local Maxwellian approximation in the collisional transfer terms are made. The feasibility of light- and neutron-scattering experiments to investigate the regions of interest is discussed.