Analytical solutions for problems of bubble dynamics

TL;DR

This paper provides closed-form analytical solutions to the Rayleigh equation for bubble dynamics in N dimensions, including cases with gas-filled bubbles and surface tension effects.

Contribution

It presents the first general analytical solutions for the Rayleigh equation in N dimensions, incorporating gas effects and surface tension.

Findings

Closed-form solutions for empty bubble dynamics in N dimensions.

Analytical solutions for gas-filled bubble cases.

Inclusion of surface tension effects in the solutions.

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.