Comment on: "Analytical approximations for the collapse of an empty spherical bubble"

TL;DR

This paper analyzes the Rayleigh equation for empty bubble collapse, explaining recent approximations, deriving singularity forms, and proving the asymptotic behavior of series coefficients to improve understanding of bubble dynamics.

Contribution

It provides a rigorous analysis of the Rayleigh equation, including singularity characterization and convergence proof for analytical approximations.

Findings

Derived the form of the singularity at the second boundary point

Proved the convergence of the analytical approximants

Established the asymptotic behavior of power series coefficients

Abstract

We analyze the Rayleigh equation for the collapse of an empty bubble and provide an explanation for some recent analytical approximations to the model. We derive the form of the singularity at the second boundary point and discuss the convergence of the approximants. We also give a rigorous proof of the asymptotic behavior of the coefficients of the power series that are the basis for the approximate expressions.