Dynamics of bubble clusters in acoustic field

Abstract

A bubble cluster composed of gas bubbles of various radii oscillating in an unbounded, slightly compressible viscous liquid under the action of an external acoustic field is considered. The mathematical model describing the dynamics of this bubble cluster is presented. The proposed model is used for an analytical study of small (linear) bubble oscillations in monodisperse and polydisperse clusters, for a numerical investigation of large (nonlinear) bubble oscillations, and for a diffusion stability analysis of gas bubbles in the cluster. The following phenomena have been revealed: (1) synchronization of the collapse phases of bubbles with different radii and (2) collapse intensification for bubbles of one size in the presence of bubbles of other size. These effects are explained by the interaction between bubbles of different radii in the cluster. For a monodisperse (one-fraction) cluster, numerical values were obtained for the initial gas concentrations in the liquid at which bubbles tend to one of two equilibrium states due to the rectified diffusion. It is also found that a polydisperse (two fraction) cluster tends to become a one fraction cluster due to the rectified diffusion. [This research is supported by the Grant of the Ministry of Education and Science of the Russian Federation (G34.31.0040).]