Modelling of spherical gas bubble oscillations and sonoluminescence

Abstract
The discovery of single–bubble sonoluminescence has led to a renewed interest in the forced radial oscillations of gas bubbles. Many of the more recent studies devoted to this topic have used several simplifications in the modelling, and in particular in accounting for liquid compressibility and thermal processes in the bubble. In this paper the significance of these simplifications is explored by contrasting the results of Lohse and co–workers with those of a more detailed model. It is found that, even though there may be little apparent difference between the radius–versus–time behaviour of the bubble as predicted by the two models, quantities such as the spherical stability boundary and the threshold for rectified diffusion are affected in a quantitatively significant way. These effects are a manifestation of the subtle dependence upon dissipative processes of the phase of radial motion with respect to the driving sound field. The parameter space region, where according to the theory of Lohse and co–workers, sonoluminescence should be observable, is recalculated with the new model and is found to be enlarged with respect to the earlier estimate. The dependence of this parameter region on sound frequency is also illustrated.

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