Inertially Driven Inhomogeneities in Violently Collapsing Bubbles: The Validity of the Rayleigh-Plesset Equation
When a bubble collapses mildly the interior pressure field is spatially uniform; this is an assumption often made to close the Rayleigh-Plesset equation of bubble dynamics. The present work is a study of the self-consistency of this assumption, particularly in the case of violent collapses. To begin, an approximation is developed for a spatially non-uniform pressure field, which in a violent collapse is inertially driven. Comparisons of this approximation show good agreement with direct numerical solutions of the compressible Navier-Stokes equations with heat and mass transfer. With knowledge of the departures from pressure uniformity in strongly forced bubbles, one is in a position to develop criteria to assess when pressure uniformity is a physically valid assumption, as well as the significance of wave motion in the gas. An examination of the Rayleigh-Plesset equation reveals that its solutions are quite accurate even in the case of significant inertially driven spatial inhomogeneity in the pressure field, and even when wave-like motions in the gas are present. This extends the range of utility of the Rayleigh-Plesset equation well into the regime where the Mach number is no longer small; at the same time the theory sheds light on the interior of a strongly forced bubble.