Radius evolution for bubbles with elastic shells

TL;DR

This paper extends the Rayleigh-Plesset equation to model the radius evolution of elastic-walled microorganisms like bacteria and viruses, incorporating curvature-dependent pressure terms and providing analytical solutions.

Contribution

It introduces a novel extended RP equation with an elastic membrane term and derives analytical solutions using elliptic functions.

Findings

Analytical solutions for elastic bubble radius evolution

Inclusion of curvature-dependent pressure in RP equation

Application to biological microorganisms

Abstract

We present an analysis of an extended Rayleigh-Plesset (RP) equation for a three dimensional cell of microorganisms such as bacteria or viruses in some liquid, where the cell membrane in bacteria or the envelope (capsid) in viruses possess elastic properties. To account for rapid changes in the shape configuration of such microorganisms, the bubble membrane/envelope must be rigid to resist large pressures while being flexible to adapt to growth or decay. Such properties are embedded in the RP equation by including a pressure bending term that is proportional to the square of the curvature of the elastic wall. Analytical solutions to this extended equation are obtained in terms of elliptic functions.