Linear acoustics in bubbly liquids from an effective medium theory

Abstract

Proposed corrections to the lowest-order approximation of an effective wave number obtained from Foldy’s exact multiple scattering theory [Foldy, Phys. Rev. 67, 107 (1945)] has sparked renewed interest in linear wave propagation through bubbly liquids. An alternative approach to wave propagation through a bubbly liquid reduces the governing equations for a two-phase medium to an effective medium. Commander and Prosperetti [J. Acoust. Soc. Am. 85, 732 (1989)], based on this method, derive an expression for the lowest-order approximation to an effective wave number. At this level of approximation the bubbles interact with the mean acoustic field without higher-order rescattering. That is, the field scattered from a bubble may interact with one or more new bubbles in the distribution, but a portion of that scattered field may not be scattered back to any previous bubble. Simple modifications to the results of Commander and Prosperetti lead to a new expression for the effective wave number, which properly accounts for all higher orders of multiple scattering. [Work supported by ONR, Code 321OA.]