Dynamics of bubble clusters

Abstract

A mathematical model which describes the behavior of a gas bubble cluster in an external acoustic field is presented. According to this model the bubbles of different ambient radii are assumed to be submerged into a spherical liquid volume. The boundary of this volume is considered as a cluster’s boundary. This model includes a set of coupled Rayleigh-type equations for bubble radii and cluster radius. The dynamics of a single bubble cluster excited by external periodic pressure is considered. The problem has been solved numerically under the assumption of spherically-symmetric oscillations of bubbles and the cluster’s boundary. A synchronization phenomenon has been found; namely, the numerical results have shown that bubbles of different initial radii in a cluster collapse in phase. Moreover, it has been noted that at some parameter values such a synchronization may lead to the intensification of bubble collapse.