Effects of viscous and capillary forces on the growth rates of gas bubbles in supersaturated liquid–gas​ solutions

An analytical and numerical study of diffusion growth of overcritical gas bubbles at degassing of the supersaturated-by-gas solution with the explicit full-scale influence of viscous and capillary forces on internal pressure in the bubbles has been presented. This study is based on our recent semi-analytical approach to the same problem (Kuchma and Shchekin, 2021). Generally, this approach allows one to find how the growth rate of overcritical bubbles depends on gas supersaturation, its diffusivity and solubility in solution, solution viscosity, surface tension at bubble surface and how it changes from zero for critical bubbles at unstable equilibrium with solution to sufficiently large values for large overcritical bubbles. A special question concerns approaching the widely used in kinetics of bubble nucleation stationary diffusion regime of growth and not so widely used self-similar non-stationary diffusion regime. As a first step, we have found analytical formulas for the bubble growth rate and the correction function (which takes into account the balance in the number of gas molecules that have left the liquid solution and came into the growing bubble) of small overcritical gas bubbles at strong viscosity of the solution and full account of capillary pressure in the bubbles as a function of the bubble radius. As a second step, we derived asymptotic formulas for the case of low viscosity and small radii of bubbles. As a third step, we obtained the formulas for the bubble growth rate and the correction function at large overcritical radii. Finally, we numerically evaluated the joint effects of viscous and capillary forces on the rate of gas bubble growth at any radius of the overcritical bubble within the wide range of viscosities of the supersaturated-by-gas solution and confirmed all the asymptotic analytical results.