Scaling of bubble growth in a porous medium. Topical report

Processes involving liquid-to-gas phase change in porous media are routinely encountered, for example in the recovery of oil, geothermal processes, nuclear waste disposal or enhanced heat transfer. They involve diffusion (and convection) in the pore space, driven by an imposed supersaturation in pressure or temperature. Phase change proceeds by nucleation and phase growth. Depending on pore surface roughness, a number of nucleation centers exist, thus phase growth occurs from a multitude of clusters. Contrary to growth in the bulk or in a Hele-Shaw cell, however, growth patterns in porous media are disordered and not compact. As in immiscible displacements, they reflect the underlying pore microstructure. The competition between multiple clusters is also different from the bulk. For example, cluster growth may be controlled by a combination of diffusion (e.g. Laplace equation in the quasi-static case) with percolation. Novel growth patterns axe expected from this competition. While multiple cluster growth is important, the simpler problem of single-bubble growth is still not well understood. In this section, we focus on the growth of a single bubble, subject to a fixed far-field supersaturation (e.g. by lowering the pressure in a supersaturated solution or by raising the temperature in a. superheated liquid). Our emphasis is on deriving a scaling theory for growth at conditions of quasi-static diffusion, guided by recent experimental observations. Visualization of bubble growth in model porous media was recently conducted using 2-D etched-glass micromodels