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

摘要

This paper deals numerically with nonlinear oscillations of spherical bubbles in a sound field. A Governing equation of a cluster of interacting spherical bubbles is obtained by taking account of the compressibility of a liquid. This equation includes 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 multiple bubbles with the same radii which are arrayed symmetrically in a sound field is similar to that of an isolated bubble driven by sound of higher frequency. When bubbles with different initial radii oscillate in a sound field, the independent oscillation of each bubble is suppressed by bubble interactions and the bubbles take on a collective behavior.