Equilibrium, stability and evolution of bubbles in a finite melt volume

Abstract

We consider a simple model of the simultaneous expansion and/or contraction of multiple bubbles, initially having the same size, immersed in a finite melt volume. The bubble growth is due to the presence of a dissolved gas within the melt. The model has multiple equilibria, and we examine the stability of each equilibrium state, via linear stability analysis and numerical experiment. We show that in every case it is the largest bubble size that is stable. Finally, we consider a generalisation of the model which allows a demonstration of the process of Ostwald ripening, where smaller bubbles contract while larger bubbles expand. The model has application to a diverse range of phenomena, including the head on a glass of beer, magma systems and the conversion of coal into coke.