Interaction of bubbles in a cluster near a rigid surface

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.