In a classical paper Plesset has determined conditions under which a bubble changing in volume maintains a spherical shape. The stability analysis was further developed by Prosperetti to include the effects of liquid viscosity on the evolving shape modes. In the present work the theory is further modified to include the changing density of the bubble contents. The latter is found to be important in violent collapses where the densities of the gas and vapor within a bubble may approach densities of the liquid outside. This exerts a stabilizing influence on the Rayleigh–Taylor mechanism of shape instability of spherical bubbles. A comparison with experimental data shows good agreement with the new theory; the Rayleigh–Taylor instability does provide an extinction threshold for violently collapsing bubbles. It is also explained why earlier works did not produce a slope in the Rayleigh–Taylor stability curve that conforms with that of the present work.
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.