Factors determining the stability of a gas cell in an elastic medium

In this paper we consider the stability of a gas cell embedded in an infini te elastic medium. The stability criterion obtained extends the classical r esult by Gibbs, gamma < 2E, to include the shear modulus of the elastic mat erial. Interestingly, besides the shear modulus another parameter appears w hich is a measure of supersaturation and relates the pressure and the gas c oncentration at the far field. If it is less than a critical value then any bubble size corresponding to a steady state is stable; above this critical value a condition must be satisfied which is a function of the surface dil atational modulus, the shear modulus, the surface tension, the supersaturat ion, and the bubble radius, and simplifies to the classical result when the shear modulus is zero. Calculations based on an initial cell size of 10(-5 ) m showed that shrinkage of a cell is inhibited by a higher dilatational o r bulk modulus. For small values of superstaturation there is a single stab le steady state corresponding to a shrinking gas cell while for moderate va lues of supersaturation there are two steady states, one stable and one uns table; excessive supersaturation leads to unbounded bubble growth.