Reaction-infiltration instability in a compacting porous medium

TL;DR

This paper extends the analysis of magma channelization in the mantle by mapping parameter space, deriving scalings for instability conditions, and understanding the physical controls on channel formation.

Contribution

It provides a systematic parameter space analysis and asymptotic theory for the reaction-infiltration instability in a compacting porous medium, including scalings for channel dimensions.

Findings

Derived critical conditions for instability onset

Analyzed bifurcation structure of channel formation

Estimated channel dimensions consistent with geological observations

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. (1995) 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 critical conditions of the instability and analyse the associated bifurcation structure. We also determine scalings for the wavelength and growth rate 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 set the horizontal length scale of channels; 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.