6 - Gas bubbles in soft tissue-like solids

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Abstract

We address the problem of the dynamics, i.e., the rate of growth and dissolution, of a gas bubble lodged in a soft elastic solid meant to approximate soft tissues in the body, such as muscles, connective tissues and joint capsules. The basic rate equation used previously for a gas bubble suspended in a simple liquid:

dR/dt=3RTDR(c/r)R,tR2dPh/dt3PhR+4γ

is rederived, with appropriate modifications made to the underlying Young-Laplace equation for gas bubble pressure, and to the diffusion equation for the contribution of elasticity to dissolved solute diffusion. We find that using the generalized Young-Laplace equation, which reduces the gas bubble pressure relative to a simple liquid medium, has a major effect on the gas bubble dynamics, while the modification of solute diffusivity due to elastic effects in the medium is relatively minor. The overall effect of taking the elasticity of the medium into account is to slow down the rate of gas bubble dissolution, increase the rate of gas bubble expansion, and to increase the lifetimes of gas bubbles, relative to their lifetime in a nonelastic medium such as a simple liquid.

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