Reaction-infiltration instability in a compacting porous medium

• Published in: Journal of fluid mechanics Vol. 852; pp. 5 - 36
• Main Authors: Rees Jones, David W., Katz, Richard F.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 10.10.2018
• Subjects: Advection; Bifurcations; Channels; Compacting; Control stability; Dimensions; Equilibrium; Flow stability; Fluid mechanics; Growth rate; Infiltration; Instability; JFM Papers; Lava; Magma; Mapping; Mathematical models; Numerical analysis; Organic chemistry; Permeability; Porosity; Porous media; Rocks; Stability analysis; Wavelengths; geophysical and geological flows; reacting multiphase flow; porous media
• DOI: 10.1017/jfm.2018.524
• ISSN: 0022-1120

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.