Finite‐amplitude wave propagation through a two‐phase system using coupled generalized Burgers' equations

Abstract

The propagation of finite‐amplitude acoustic waves through a system of fluid particles in a fluid matrix (aerosols or emulsions) has been examined theoretically by using the continuum volume‐averaged balance equations and linear constitutive equations for a two‐phase system. Utilizing the technique developed by Lighthill for clean perfect gases, and by Davidson [G. A. Davidson, J. Sound Vib. 38, 475–495 (1975)], who employed the equations of Marble to dilute aerosol media, coupled Burgers' equations for each phase were obtained and analyzed by a perturbation method. The behavior of the higher harmonics of an initial sinusoidal plane wave was determined, and compared to previous work. The present results are applicable to moderately concentrated particulate systems. Also, the use of two‐phase equations obtains the effects of viscosity of the media, and also phoresis, such as thermophoresis, on the waveforms.