Reactive-infiltration instability in radial geometry: From dissolution fingers to star patterns

Abstract

We consider the process of chemical erosion of a porous medium infiltrated by a reactive fluid in a thin-front limit, in which the width of the reactive front is negligible with respect to the diffusive length. We show that in the radial geometry the advancing front becomes unstable only if the flow rate in the system is sufficiently high. The existence of such a stable region in parameter space is in contrast to the Saffman-Taylor instability in radial geometry, where for a given flow rate the front always eventually becomes unstable, after reaching a certain critical radius. We also examine the similarities between the reactive-infiltration instability and the similar instability in the heat transfer, which is driving the formation of star-like patterns on frozen lakes.

Dissolution Phase Diagram in Radial Geometry

“…In such case, the front between the undissolved and dissolved phase is very sharp. In the low-velocity regime, the dissolution front is stable to perturbations [50]. As a result, the emerging dissolution pattern is compact, see Figure 2A.…”

“…At the initial moment, where the flow is isotropic |q(r)| = Q 2π r and the aperture field -homogeneous h(r, φ) = h 0 , the transport equation (2) can be solved analytically. For large Péclet numbers the undersaturation is of a Gaussian form [50]:…”

“…The theoretical determination of the position of this boundary line will require a linear stability analysis of the dissolution problem in radial geometry. So far, such an analysis was only carried out in the limit of infinitely thin reaction front [50], which corresponds to significantly lower velocities than the ones used in the present study. We hope that present results will inspire further theoretical work in this direction.…”

Analytical Solutions of Carbonate Acidizing in Radial Flow

“…The present study considers radial flow and thus simulates the geometry in applications where reactive fluids are injected through a cylindrical well and the relevant geometry can be assumed to be axisymmetric. Radial flow acidizing has been studied theoretically by Grodzki and Szymczak (2019), and experimentally in Indiana limestone and a dolomite by McDuff et al (2010), and in Mons chalk by Walle and Papamichos (2015).…”

Flow-Driven Branching in a Frangible Porous Medium

“…The formation of arborized patterns in physical and chemical systems is driven by a variety of processes all of which involve a combination of erosion, transport, and deposition. On the laboratory scale, these processes can involve chemical dissolution of brittle matrices by a penetrating reactive fluid [2,3], advective rearrangement of unconsolidated media, dielectric breakdown of conducting media [4,5], formation of fingerlike protrusions in dense granular suspensions [6], formation of beach rills in natural drainage systems [7,8], etc. On planetary scales, melt transport in the mantle arises via branching morphologies that lead to localized channels of widths up to 100 m [9][10][11], and water-driven erosion and branching in glaciers arises on scales of the order of 10 m [12].…”