Analytical solutions for problems of bubble dynamics

Abstract

Recently, an asymptotic solution of the Rayleigh equation for an empty bubble in $N$ dimensions has been obtained. Here we give the closed--from general analytical solution of this equation. We also find the general solution of the Rayleigh equation in $N$ dimensions for the case of a gas--filled hyperspherical bubble. In addition, we include a surface tension into consideration.

References in corpus (2)

• Analytical Approximations for the Collapse of an Empty Spherical Bubble
• Analytical solutions of the Rayleigh equation for empty and gas--filled bubble

Cited by in corpus (3)

• On the criteria for integrability of the Liénard equation
• On connections of the Liénard equation with some equations of Painlevé--Gambier type
• Solution to the one-dimensional Rayleigh-Plesset equation by the Differential Transform method