Reactive-infiltration instabilities in rocks. Part 2. Dissolution of a porous matrix

A reactive fluid dissolving a uniform porous material triggers an instability in the dissolution front, leading to spontaneous formation of pronounced well-spaced channels in the surrounding rock matrix. The concentration field within the dissolving region contains two different length scales, upstream (no reaction) and downstream of the front position. Previous investigations of the reactive-infiltration instability have considered one or other of the scales to be dominant, leading to rather different conclusions. Here we describe a more general linear stability analysis which includes both length scales simultaneously. We show how previous work corresponds to special cases of our more general analysis and obtain closed-form solutions for small permeability gradients.