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Reaction-infiltration instability in a compacting porous medium

Published online by Cambridge University Press:  02 August 2018

David W. Rees Jones Open the ORCID record for David W. Rees Jones [Opens in a new window]  and
Richard F. Katz Open the ORCID record for Richard F. Katz [Opens in a new window]
David W. Rees Jones*
Affiliation:
Department of Earth Sciences, University of Oxford, South Parks Road, Oxford OX1 3AN, UK
Richard F. Katz
Affiliation:
Department of Earth Sciences, University of Oxford, South Parks Road, Oxford OX1 3AN, UK
*
†Email address for correspondence: [email protected]
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Abstract

Certain geological features have been interpreted as evidence of channelized magma flow in the mantle, which is a compacting porous medium. Aharonov et al. (J. Geophys. Res., vol. 100 (B10), 1995, pp. 20433–20450) developed a simple model of reactive porous flow and numerically analysed its instability to channels. The instability relies on magma advection against a chemical solubility gradient and the porosity-dependent permeability of the porous host rock. We extend the previous analysis by systematically mapping out the parameter space. Crucially, we augment numerical solutions with asymptotic analysis to better understand the physical controls on the instability. We derive scalings for the critical conditions of the instability and analyse the associated bifurcation structure. We also determine scalings for the wavelengths and growth rates of the channel structures that emerge. We obtain quantitative theories for and a physical understanding of, first, how advection or diffusion over the reactive time scale sets the horizontal length scale of channels and, second, the role of viscous compaction of the host rock, which also affects the vertical extent of channelized flow. These scalings allow us to derive estimates of the dimensions of emergent channels that are consistent with the geologic record.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Low-Reynolds-number flows: Porous media Multiphase and Particle-laden Flows: Reacting multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 852 , 10 October 2018 , pp. 5 - 36
Copyright
© 2018 Cambridge University Press 

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