Use and misuse of large-density asymptotics in the reaction-infiltration instability

Analyzing the dissolution of rocks and other porous materials is simplified by the large disparity between mineral and reactant concentrations. In essence, the porosity remains frozen on the time scale of the reactant transport, which can then be treated as a quasi-stationary process. This conceptual idea can be derived mathematically using asymptotic methods, which show that the length scales in the system are, to a first approximation, independent of the ratio of reactant and mineral concentrations. Nevertheless, in a growing number of papers on dissolutional instabilities, the reactant-mineral concentration ratio has been incorrectly linked to the thickness of the dissolution front. In this paper we critically review the application of asymptotic methods to the reaction-infiltration instability. In particular, we discuss the limited validity of the thin-front or Stefan limit, where the interface between dissolved and undissolved mineral is sharp.