Low-frequency approximations for the radiation damping of a bubble

Abstract

The recent work by Ainslie and Leighton [J. Acoust. Soc. Am. 126, 2163 (2009)] pointed out that there exist two different expressions in the literature for the scattering cross-section of a spherical gas bubble in liquid. The difference between the two expressions is contained in the term corresponding to the losses due to acoustic radiation. The more common expression, often attributed to R. Wildt [“Acoustic theory of bubbles,” in Physics of Sound in the Sea], is based on a low-frequency approximation and is thus only accurate when the wavelength of the incident wave is large compared to the circumference of the bubble. The purpose of the present work is to investigate specifically the accuracy of this low-frequency approximation for various physical parameters and frequencies of interest. An alternative low-frequency approximation is also suggested, which is both simpler and more accurate than the present approximation. Finally the case of a nonspherical bubble is considered, and an expression for the scattering cross-section is given that is based on the same low-frequency assumptions made by Wildt. [Work supported by the IR&D program at ARL:UT.]