Interacting length scales in the reactive-infiltration instability

• Published in: Geophysical research letters Vol. 40; no. 12; pp. 3036 - 3041
• Main Authors: Szymczak, P., C. Ladd, A. J.
• Format: Journal Article
• Language: English
• Published: Washington Blackwell Publishing Ltd 28.06.2013; John Wiley & Sons, Inc
• Subjects: Computational fluid dynamics; Constraining; Dissolution; Exact solutions; Flow rates; Geophysics; Infiltration; Instability; Mathematical analysis; Porosity; Porous media; reactive-infiltration instabilities; Stability; Stability analysis; Wavelengths; wormholing
• ISSN: 0094-8276; 1944-8007
• DOI: 10.1002/grl.50564

The reactive‐infiltration instability, which develops when a porous matrix is dissolved by a flowing fluid, contains two important length scales. Here we outline a linear stability analysis that simultaneously incorporates both scales. We show that the commonly used “thin‐front” model is a limiting case of a more general theory, which also includes convection‐dominated dissolution as another special case. The wavelength of the instability is bounded from below and lies in the range 1 mm to 1 km for physically reasonable flow rates and reaction rates. We obtain a closed form for the growth rate when the change in porosity is small. Key Points There are two competing lengthscales in reactive-infiltration instabilities Previous theories are limiting cases of the model developed here Key parameters characterizing the scale of the developing pattern are identified