Derivation of the Rayleigh-Plesset equation in terms of volume

Abstract

The most common nonlinear equations of motion for the pulsation of a spherical gas bubble in an infinite body of liquid arise in the various forms of the Rayleigh-Plesset equation, expressed in terms of the dependency of the bubble radius on the conditions pertaining in the gas and liquid. However over the past few decades several important analyses have begun with a heuristically-derived form of the Rayleigh-Plesset equation which considers the bubble volume, instead of the radius, as the parameter of interest, and for which the dissipation term is not derived from first principles. The predictions of these two sets of equations can differ in important ways, largely through differences between the methods chosen to incorporate damping. As a result this report derives the Rayleigh-Plesset equation in terms of the bubble volume from first principles in such a way that it has the same physics for dissipation (viscous shear) as is used in the radius fram