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Use and misuse of large‐density asymptotics in the reaction‐infiltration instability
Author(s) -
Ladd Anthony J. C.,
Szymczak Piotr
Publication year - 2017
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2016wr019263
Subject(s) - dissolution , instability , porosity , infiltration (hvac) , limit (mathematics) , front (military) , porous medium , mechanics , mineralogy , thermodynamics , materials science , chemistry , mathematics , geology , geotechnical engineering , mathematical analysis , physics , oceanography
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.