Hydrodynamics, acoustics and transport in sonoluminescence phenomena

The spherically-symmetric problem of the oscillations of a gas bubble in the center of a spherical flask filled with a compressible liquid that is excited by pressure oscillations on the flask wall is considered. A generalization of the Rayleigh-Plesset equation for a compressible liquid is given in the form of two ordinary difference-differential equations that take into account the pressure waves which are reflected from the bubble and those that are incident on the bubble from the flask wall. The initial value problem for the initiation of bubble oscillations due to flask wall excitation and for the evolution of these oscillations is considered. Linear and non-linear periodic bubble oscillations are analyzed analytically. Non-linear resonant and near-resonant solutions for the bubble nonharmonic oscillations, which are excited by harmonic pressure oscillations on the flask wall, are obtained. The influence of heat transfer phenomena on the bubble oscillations is analysed.