Dynamics of foam growth: Bubble growth in a limited amount of liquid

Abstract

A mathematical model for the growth of a spherical gas bubble in a limited amount of a viscous liquid is presented. The growth of the bubble is assumed to be controlled by both momentum and mass transfer. The simplified approach suggested, by assuming a parabolic concentration profile for the volatile component in the liquid, results in approximated analytical expressions for the final parameters of the process. The numerical results of the model can be used to predict the increase in the bubble size as well as the decrease of the solute concentration in the liquid and the decrease of the cell density with time. The model is able to deal with real processes, such as polymer melt devolatilization and the production of polymeric foams, where many bubbles grow simultaneously. © 2004 Society of Plastics Engineers.