Nonlinear bubble dynamics

Abstract

The standard approach to the analysis of the pulsations of a driven gas bubble is to assume that the pressure within the bubble follows a polytropic relation of the form p=p0(R0/R)3κ, where p is the pressure within the bubble, R is the radius, κ is the polytropic exponent, and the subscript zero indicates equilibrium values. For nonlinear oscillations of the gas bubble, however, this approximation has several limitations and needs to be reconsidered. A new formulation of the dynamics of bubble oscillations is presented in which the internal pressure is obtained numerically and the polytropic approximation is no longer required. Several comparisons are given of the two formulations, which describe in some detail the limitations of the polytropic approximation.