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Epstein and Plesset's seminal work on the rate of gas bubble dissolution andgrowth in a simple liquid is generalized to render it applicable to a gasbubble embedded in a soft elastic medium. Both the underlying diffusionequation and the expression for the gas bubble pressure were modified to allowfor the non-zero shear modulus of the elastic medium. The extension of thediffusion equation results in a trivial shift (by an additive constant) in thevalue of the diffusion coefficient, and does not change the form of the rateequations. But the use of a Generalized Young-Laplace equation for the bubblepressure resulted in significant differences on the dynamics of bubbledissolution and growth, relative to a simple liquid medium. Depending onwhether the salient parameters (solute concentration, initial bubble radius,surface tension, and shear modulus) lead to bubble growth or dissolution, theeffect of allowing for a non-zero shear modulus in the GeneralizedYoung-Laplace equation is to speed up the rate of bubble growth, or to reducethe rate of bubble dissolution, respectively. The relation to previous work onvisco-elastic materials is discussed, as is the connection of this work to theproblem of Decompression Sickness (specifically, "the bends"). Examples oftissues to which our expressions can be applied are provided. Also, a newphenomenon is predicted whereby, for some parameter values, a bubble can bemetastable and persist for long times, or it may grow, when embedded in ahomogeneous under-saturated soft elastic medium.

Gas bubble dynamics in soft materials