magmatic melts. For Sievert’s law the analytical treatment of the problem of bubble dissolution in a pure solvent is also presented.'
address: |
    Department of Physics, St. Petersburg State University\
    Ulyanovskaya Street 1, Petrodvorets, St. Petersburg, 198504, Russia
author:
- 'Gennady Yu. Gor'
- 'Anatoly E. Kuchma'
- 'Fedor M. Kuni'
title: |
    Gas Bubble Growth Dynamics in a Supersaturated Solution:\
    Henry’s and Sievert’s Solubility Laws
---

Introduction
============

This paper presents a theoretical description of diffusion growth of a gas bubble in liquid solution as a result of a considerable pressure drop (in the order of $ 10^3$ times). These conditions of bubble growth process are observed in magmatic melts during volcanic eruptions \[\[Sparks-1978\], \[Sahagian-1999\]\]. After such a significant pressure drop the solution becomes strongly supersaturated; and homogeneous (fluctuational) nucleation of gas bubbles becomes possible. It is the growth dynamics of such bubbles that is the subject of the present paper. It has to be noted that the growth regularities of a solitary bubble are crucial for the description of the whole kinetics of phase transition in supersaturated solution \[\[Chernov-2004\], \[Slezov-2004\], \[Slezov-2005\]\].

While describing gas bubble growth in supersaturated solution two rough approximations are traditionally made \[\[Chernov-2004\], \[Navon\], \[Lensky\], 