Dynamics and stability of air bubbles in a porous medium

A numerical method is developed for reliably computing the evolution of the boundary of a multiply connected water-saturated domain with air bubbles in the case when the pressure inside them depends on the bubble volume. It is assumed that the distance between the gas bubbles is comparable with their size. Gas bubbles can be near an extended phase transition boundary separating a porous medium flow and a domain saturated with a mixture of air and water vapor. The numerical method is verified by comparing the numerical solution of a test problem with its analytical solution. Caused by finite-amplitude perturbations of the phase interface, the deformation of an air bubble in an extended horizontal water-saturated porous layer with a constant pressure gradient is studied. It is shown that the instability of the bubble boundary with respect to finite perturbations leads to the splitting of the bubble. An analysis of the numerical solution shows that, although all circular bubbles move at the same velocity irrespective of their size, nevertheless, due to instability, a portion of the bubble boundary where the air displaces the fluid moves faster than an opposite portion where the fluid displaces the air. As a result, nearby bubbles are capable of merging before splitting.