Finite-amplitude wave propagation through a two-phase system of particles in a viscothermal fluid

Abstract

The propagation of finite-amplitude, planar acoustic waves through a system of nonvolatile fluid particles dispersed in a fluid matrix has been examined theoretically by using the continuum volume-averaged balance equations and linear constitutive equations for a two-phase fluid system having a single variable temperature. These equations contain more information than those introduced by Marble [Ann. Rev. Fluid Mech. 2, 379–447 (1970)], and used by other workers to determine the attenuation and dispersion of sound propagating through a dilute dusty perfect gas. Specifically, terms that account for phoresis of the particles due to thermal and concentration gradients; Dufour heat transport; and the particles’ contribution to the viscous effects are included. We have manipulated the acoustic equations using the methods developed by previous investigators, and obtained coupled Burgers’ equations; one for each phase. In the limit of very small concentration of particles, these equations reduce to those obtained by G. A. Davidson [J. Sound Vibration 38, 475–495 (1975)]. Solutions to the equations were determined by expanding the velocity field in a regular perturbation series in terms of the acoustic Mach number. The attenuation and dispersion of the first- and second-order harmonic terms are presented. These results are not restricted to a perfect gas and should be applicable to semi-concentrated emulsions, suspensions, and aerosols.