AN ACCURATE NUMERICAL-SOLUTION FOR MASS DIFFUSION-INDUCED BUBBLE-GROWTH IN VISCOUS-LIQUIDS CONTAINING LIMITED DISSOLVED-GAS

A mathematical formulation based on potential theory is used to develop an accurate numerical technique to calculate the mass diffusion-induced growth of a spherical gas bubble surrounded by a viscous Newtonian liquid with a limited dissolved gas concentration under isothermal conditions. We solve for the complete concentration profile of the dissolved gas in the liquid enveloping the bubble to predict the bubble growth. These results are contrasted against the dynamics of bubble growth predicted by the widely used approach of employing polynomial profiles to describe the gas concentration. The influence of key dimensionless parameters on the differences in the bubble growth due to the choice of concentration profile is examined. The investigation reveals that the commonly used approximate solutions for the concentration profile not only underpredict the growth rate at the early stages of the growth but also overestimate the steady-state bubble radius due to the implicit assumption of an unlimited supply of dissolved gas in the liquid.