  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.
