NONLINEAR OSCILLATIONS OF A CLUSTER OF BUBBLES IN A SOUND FIELD - (BIFURCATION STRUCTURE)

This paper deals numerically with nonlinear oscillations of spherical bubbles in a sound field. A Governing equation of a cluster of interac ting spherical bubbles is obtained by taking account of the compressib ility of a liquid. This equation includes previous results for both si ngle 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 ar e arrayed symmetrically in a sound field is similar to that of an isol ated bubble driven by sound of higher frequency. When bubbles with dif ferent initial radii oscillate in a sound field, the independent oscil lation of each bubble is suppressed by bubble interactions and the bub bles take on a collective behavior.