Theory of the nonsteady diffusion growth of a gas bubble in a supersaturated solution of gas in liquid

TL;DR

This paper develops a self-similar, nonsteady theoretical model for the diffusion-driven growth of a gas bubble in a supersaturated solution, accounting for gas and solvent dynamics without assuming low solubility.

Contribution

It introduces a general nonsteady theory for bubble growth that considers the balance of gas molecules and solvent expulsion, expanding beyond previous steady-state models.

Findings

Identifies a rapid increase in bubble growth rate during expansion.

Derives the bubble growth rate dependence on solubility and supersaturation.

Shows the growth process is limited by a maximum product of solubility and supersaturation.

Abstract

Using a self-similar approach a general nonsteady theory is elaborated for the case of the diffusion growth of a gas bubble in a supersaturated solution of gas in liquid. Due to the fact that the solution and the bubble in it are physically isolated, the self-similar approach accounts for the balance of the number of gas molecules in the solution and in the bubble that expells incompressible liquid solvent while growing. The rate of growth of the bubble radius in its dependence from gas solubility and solution supersaturation is obtained. There is a nonsteady effect of rapid increase of the rate of bubble growth simultaneous with the growth of the product of gas solubility and solution supersaturation. This product is supplied with a limitation from above, which also stipulates isothermal conditions of bubble growth. The smallness of gas solubility is not presupposed.