Liquid compressibility effects in the dynamics of acoustically coupled bubbles

Abstract

Accurate models for clusters of interacting bubbles are sought for both biomedical and underwater applications. Multiple bubble models have been developed by treating the bubbles as a system of interacting oscillators. The models are obtained initially for bubbles in an incompressible, irrotational, and inviscid liquid; additional effects are included in an ad hoc fashion. The existing oscillator models for the dynamics of interacting bubbles are improved by including the effect of liquid compressibility. In particular, while existing models have been improved by including propagation delays in the bubble interactions, the effect of bubble interaction on radiation damping has not been considered. The current work develops corrections for the radiation damping of coupled bubbles in both linear and nonlinear models of bubble dynamics. These corrections eliminate certain instabilities that have been observed in delay differential equation models of coupled-bubble dynamics. Additionally, an increase in the coupling strength between bubbles undergoing high-amplitude radial motion is predicted when coupled radiation damping is included; this increase in coupling strength strongly affects the predicted motion of the system and the resultant pressure in the surrounding medium. [Work supported by the ARL:UT McKinney Fellowship in Acoustics and NIH DK070618.]