Interacting length scales in the reactive-infiltration instability

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...

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Bibliographic Details
Published in:Geophysical research letters 2013-06, Vol.40 (12), p.3036-3041
Main Authors: Szymczak, P., C. Ladd, A. J.
Format: Article
Language:English
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
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Summary: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
ISSN:0094-8276
1944-8007
DOI:10.1002/grl.50564