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 dis-parity 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.