BUBBLE-GROWTH AND STABILITY IN AN EFFECTIVE POROUS-MEDIUM

This paper examines the in situ growth and stability of a single bubble in an effective porous medium, where the pore microstructure is neglected. The main objective of the study is the effect of mass transfer and flow parameters on bubble stability. Because it is necessary for flow in both phases to be considered, this is actually a generalized phase-change problem involving two fluids in a porous medium. Similarity solutions are developed in both three-dimensional (3-D) and two-dimensional (2-D) geometries, the stability of which is subsequently analyzed. In the absence of capillarity, an instability analogous to Mullins-Sekerka is found, which is independent of the process parameters, including the viscosity ratio, M. Capillary effects are next considered for the 2-D geometry of a Hele-Shaw cell (the analysis is also extended to 3-D geometries). At the large M limit, the stability condition is identical to Patterson's [J. Fluid Mech. 113, 513 (1981)] for the displacement of a liquid by a gas. This theory is found consistent with bubble growth experiments in Hele-Shaw cells. At finite M, the theory predicts that the interface becomes more stable as M increases, which is directly opposite to the effect of M in viscous fingering. This is a novel mechanism of convective stabilization and it is intrinsic to in situ phase growth. Higher solubility and diffusion coefficients also have a stabilizing effect. For conditions typical to bubble growth, however, the sensitivity to these parameters is very weak.