Acoustic waves in monodisperse and polydisperse gas-dust mixtures with intense momentum transfer between phases

Abstract

The paper presents one-dimensional problems of dusty gas dynamics on plane acoustic wave propagation. In the fist problem the dusty gas is considered as polydisperse medium with a zero-volume dust fraction. In the second problem the dusty gas is a monodisperse medium with particles that occupy finite volume. For both problems, dispersion relations are obtained. Then a limiting case when a velocity relaxation time between particles and gas tends to zero is considered. This case corresponds to mixtures with fine dust when intense interaction between phases takes place. For this limiting case expressions for the phase velocity are derived. Moreover, we present formulas for generating particular solutions of corresponding linearized problems. These solutions are intended to be used as a standard in the study of asymptotic, dispersive and dissipative properties of numerical methods. Program codes for generating such solutions are published and available for download.