Analytical solutions of the Rayleigh equation for empty and gas--filled bubble

TL;DR

This paper derives exact analytical solutions for the Rayleigh equation governing bubble dynamics, applicable to both empty and gas-filled bubbles, providing a new tool for testing numerical methods.

Contribution

It introduces a novel approach to obtain closed-form solutions of the Rayleigh equation, which were previously unavailable.

Findings

Derived closed-form solutions for empty and gas-filled bubbles

Provided solutions useful for testing numerical algorithms

Enhanced understanding of bubble dynamics equations

Abstract

The Rayleigh equation for bubble dynamics is widely used. However, analytical solutions of this equation have not been obtained previously. Here we find closed--form general solutions of the Rayleigh equation both for an empty and gas--filled spherical bubble. We present an approach allowing us to construct exact solutions of the Rayleigh equation. We show that our solutions are useful for testing numerical algorithms.