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

Details Rayleigh's collapsing time of a spherical cavity: the $Δ$-factor Rayleigh's collapsing time of a spherical cavity: the $Δ$-factor

2007-02-17

arxiv.org/abs/physics/0702147v1

Physics

Fluid Dynamics

12 pages, no figures

Scientific paper

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.

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