Interacting length scales in the reactive-infiltration instability

TL;DR

This paper presents a comprehensive linear stability analysis of the reactive-infiltration instability, incorporating two key length scales, and reveals bounds on the instability wavelength relevant for geological and engineering processes.

Contribution

It introduces a generalized theory that unifies the thin-front model and convection-dominated dissolution, providing new insights into the instability's wavelength and growth rate.

Findings

Wavelength of instability ranges from 1mm to 1km.

The thin-front model is a special case of the general theory.

Closed-form growth rate derived for small porosity changes.

Abstract

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 1mm to 1km for physically reasonable flow rates and reaction rates. We obtain a closed form for the growth rate when the change in porosity is small.