Rayleigh's collapsing time of a spherical cavity: the $\Delta$-factor

Abstract

New corrections to the equation of motion and total collapsing time of an empty spherical cavity immersed in an infinite incompressible medium are proposed on the assumption of a non-uniform density. The dimensionless number quantifying the corrections with respect to the standard Rayleigh results (coined the $\Delta$-factor) is fully independent of other possible contributions like surface tension and viscous terms. The $\Delta$-factor effect advocated here can be seen as a direct consequence of a mass-shell non-trivial solution to the continuity equation. The consistency of the corrections with respect to the Bernoulli theorem and some physical consequences in the framework of the Rayleigh-Plesset equation are also discussed.