Dynamics of gas bubble growth in a supersaturated solution with Sievert's solubility law

TL;DR

This paper develops a theoretical model for the diffusion-driven growth of gas bubbles in supersaturated solutions, emphasizing the effects of Sievert's law and providing analytical solutions for bubble dynamics.

Contribution

It introduces a differential equation for bubble radius growth under Sievert's law and analyzes conditions for steady diffusion flux during nucleation.

Findings

Derived an analytical solution for bubble growth dynamics.

Identified conditions for steady diffusion flux in bubble nucleation.

Applied model to water vapor bubbles in magmatic melts.

Abstract

This paper presents a theoretical description of diffusion growth of a gas bubble after its nucleation in supersaturated liquid solution. We study systems where gas molecules completely dissociate in the solvent into two parts, thus making Sievert's solubility law valid. We show that the difference between Henry's and Sievert's laws for chemical equilibrium conditions causes the difference in bubble growth dynamics. Assuming that diffusion flux is steady we obtain a differential equation on bubble radius. Bubble dynamics equation is solved analytically for the case of homogeneous nucleation of a bubble, which takes place at a significant pressure drop. We also obtain conditions of diffusion flux steadiness. The fulfillment of these conditions is studied for the case of nucleation of water vapor bubbles in magmatic melts.