Axisymmetric bubble collapse in a quiescent liquid pool. I. Theory and numerical simulations

Abstract

In this paper we analyze the final instants of axisymmetric bubble pinch-off in a low viscosity liquid. We find that both the time evolution of the bubble dimensionless minimum radius, R0(t), and of the dimensionless local axial curvature at the minimum radius, 2r1(t), are governed by a pair of two-dimensional Rayleigh-like equations in which surface tension, viscosity, and gas pressure terms need to be retained for consistency. The integration of the above-mentioned system of equations is shown to be in remarkable agreement with numerical simulations and experiments. An analytical criterion, which determines the necessary conditions for the formation of the previously reported tiny satellite bubbles, is also derived. Additionally, an estimation of the maximum velocity reached by the high speed Worthington jets ejected after bubble pinch-off, in the case axisymmetry is preserved down to the formation of the satellite bubble, is also provided.