A model for the interaction of two bubbles in a sound field [E. A. Zabolotskaya, Sov. Phys. Acoust. 30, 365–368 (1984)] is extended to account for an arbitrary number of bubbles interacting in a cluster. Compressibility of the liquid is taken into account through radiation damping and time delays due to the finite sound speed. Bubble coalescence is also included. A numerical method for implementing the model is described, and simulations of the growth and collapse of a bubble cluster near a rigid surface are presented. The relative effects of compressibility and coalescence are discussed.
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Hamilton et al. (2005) studied this question.
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