2004, Vol.7, No.4, pp.368-376

In acoustic resonator set-ups cavitation bubbles form complex dendritic structures resembling electrical discharge patterns, jellyfishes, etc. The most accurate way of simulating the evolution of such structures is to trace the motion of every bubble in the structure, taking proper account of its interactions with all other bubbles. Modern computing facilities make this way quite realizable. However existing simulations are based on strongly simplified equations of bubble motion, which may lead to loss of important effects. The purpose of this paper is to propose more accurate equations of motion that describe the coupled radial and translational dynamics of an arbitrary bubble in a three-dimensional acoustically driven cluster, allowing for radiation interactions between all bubbles in the cluster up to terms of third order in the inverse separation distances. The equations are derived by using the Lagrangian formalism and the theory of Clebsch-Gordan coefficients. The potentialities of the proposed model in simulating the spatio-temporal bubble dynamics in strong acoustic fields are illustrated by numerical examples.
Key words: bubble dynamics, acoustic cavitation, cavitation bubble structures, acoustic streamer

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