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

• Main Authors: Lima, J. A. S, da Silveira, F. E. M
• Format: Journal Article
• Language: English
• Published: 16-02-2007
• Subjects: Physics - Fluid Dynamics
• DOI: 10.48550/arxiv.physics/0702147

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.