Theory of Sound Propagation in Mixtures of Monatomic Gases

Abstract

Plane wave solutions are sought for the coupled, linearized Boltzmann equations governing sound propagation in a binary mixture. The solvability criteria for the ensuing matrix integral equation determine the dispersion law for sound propagation. In zeroth-order the Laplace sound velocity is obtained, and in first order the Kohler absorption is recovered. In second order an initial sound dispersion is found which could only be calculated from hydrodynamics if the analog of the Burnett equations for mixtures were known. As a preliminary guide to experiments, the absorption and dispersion in helium-argon mixtures are calculated through super-super-Burnett order on the assumption that each of the three interatomic forces is an inverse fifth-power repulsion