Resonance theory of acoustic wave propagation through bubble screens

Abstract

Liquid media containing clouds of gas bubbles may be characterized by a set of “effective (and frequency‐dependent) material parameters” which differ from those of the liquid and/or gas. A method first proposed by Ament, is used here to determine the effective density and the effective (complex) propagation constant (i.e., the effective sound speed and attenuation) of liquids containing screens or clouds of spherical gas bubbles, by comparing low‐frequency sound scattered from the bubble cloud with scattering from an effective sphere of bubbly liquid. The novelty of our resonance treatment is that we have retained some high‐order terms in the required low‐frequency expansions in order to include the previously ignored dominating effect of the giant monopole resonance. Many numerical results for air bubbles in water are obtained and displayed in graphs. The effects of surface tension and shear viscosity of the liquid and of thermal conduction in the gas, all modify the radiation damping results. We have incorporated all these corrections [in the manner given by R. Nishi, Acustica 33, 65–74 (1975)] into our resonance formulation in order to assess their relative importance in various situations. Comparisons to available experimental results shows very good agreement. [H.Ü. is also at Catholic University, Washington, D.C., and was additionally supported by Code 421 of ONR.]