Free energy wells for small gas bubbles in soft deformable materials.

Thermodynamic expressions are derived for the system relative Gibbs free energy, and the relative Gibbs free energy per bubble, for all possible equilibrium bubble states that can form in a soft slightly rigid material, initially supersaturated with a dissolved inert gas (N(2)). While the thermodynamic manipulations are exact, the final expressions are approximate, due to an approximation made in deriving the expression for the elastic free energy of a soft material containing more than a single bubble. The expressions predict that provided the shear modulus of the soft material is not negligibly small, free energy wells which stabilize small gas bubbles for finite periods of time exist in such materials. This is consistent with a previous calculation, based solely on the bubble pressure equation, which resulted in the conjecture that bubbles found in soft materials with some rigidity (or shear resistance) are likely to be small. The possible relevance of this to the field of decompression sickness is outlined.