Factors Determining the Stability of a Gas Cell in an Elastic Medium

Abstract

In this paper we consider the stability of a gas cell embedded in an infinite elastic medium. The stability criterion obtained extends the classical result by Gibbs, y < 2E, to include the shear modulus of the elastic material. Interestingly, besides the shear modulus another parameter appears which is a measure of supersaturation and relates the pressure and the gas concentration 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 dilatational modulus, the shear modulus, the surface tension, the supersaturation, 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 or bulk modulus. For small values of superstaturation there is a single stable steady state corresponding to a shrinking gas cell while for moderate values of supersaturation there are two steady states, one stable and one unstable; excessive supersaturation leads to unbounded bubble growth.