Some Analytical Aspects of Bubble Dynamics

Abstract

A unified, systematic survey of the recent developments of bubble dynamics is presented with the emphasis on its analytical aspects. A general formulation of the problem is established first; then it is shown how simplifications may result from the spherical symmetry of the system and the assumption of uniform interior of the bubble. Two classes of problems of physical interest are treated subsequently; namely, the growth and collapse of a bubble, and the bubble in oscillation. In the first category, various aspects of the problem are investigated depending on whether the inertial, the thermal, or the diffusive effect is the dominating controlling factor of the motion. In the second category, the nonlinear mechanical oscillations are discussed, as well as the linear oscillations with thermal and diffusive interactions. The paper concludes with a study of the stability of the spherical symmetry of the flow system.