Nonlinear Oscillations of a Cluster of Bubbles in a Sound Field (Bifurcation Structure)

Abstract

This paper deals numerically with nonlinear oscillations of spherical bubbles in a sound field. Governing equations of a cluster of interacting spherical bubbles are obtained by taking account of the compressibility of a liquid. These equations contain previous results for both single bubble and two bubbles as special cases. Bifurcation diagrams are computed for typical configurations of bubbles. It is shown that the bifurcation structure of bubbles which oscillate with the same phase in a sound field is similar to the structure of an isolated bubble driven by a higher frequency than that of the sound field. When bubbles with different initial radii oscillate, the independent oscillation of each bubble is suppressed by the interaction and the bubbles take on a collective behavior. © 1993, The Japan Society of Mechanical Engineers. All rights reserved.