Gas bubble dynamics in soft materials

TL;DR

This paper extends classical gas bubble dynamics to soft elastic materials, showing how elasticity influences bubble growth and dissolution rates, with implications for biological tissues and decompression sickness.

Contribution

It introduces a generalized model incorporating shear modulus into bubble dynamics equations, revealing significant effects on bubble behavior in elastic media.

Findings

Elasticity speeds up bubble growth or slows dissolution.

A new metastable bubble state is predicted in soft elastic media.

The model applies to biological tissues and decompression sickness scenarios.

Abstract

Epstein and Plesset's seminal work on the rate of gas bubble dissolution and growth in a simple liquid is generalized to render it applicable to a gas bubble embedded in a soft elastic medium. Both the underlying diffusion equation and the expression for the gas bubble pressure were modified to allow for the non-zero shear modulus of the elastic medium. The extension of the diffusion equation results in a trivial shift (by an additive constant) in the value of the diffusion coefficient, and does not change the form of the rate equations. But the use of a Generalized Young-Laplace equation for the bubble pressure resulted in significant differences on the dynamics of bubble dissolution and growth, relative to a simple liquid medium. Depending on whether the salient parameters (solute concentration, initial bubble radius, surface tension, and shear modulus) lead to bubble growth or dissolution, the effect of allowing for a non-zero shear modulus in the Generalized Young-Laplace equation is to speed up the rate of bubble growth, or to reduce the rate of bubble dissolution, respectively. The relation to previous work on visco-elastic materials is discussed, as is the connection of this work to the problem of Decompression Sickness (specifically, "the bends"). Examples of tissues to which our expressions can be applied are provided. Also, a new phenomenon is predicted whereby, for some parameter values, a bubble can be metastable and persist for long times, or it may grow, when embedded in a homogeneous under-saturated soft elastic medium.