Ripening of Porous Media

TL;DR

This paper analyzes the stability of interfaces in porous media driven by surface tension, proving planes are the only stable surfaces and discussing the unlikelihood of constant mean curvature surfaces occurring in real systems.

Contribution

It provides a linear stability analysis of surface tension-driven dynamics in porous media, establishing the stability of planes and the instability of CMC surfaces.

Findings

Planes are the only stable interfaces in the studied dynamics.

Constant mean curvature surfaces are generally unstable and unlikely to be observed.

Differences between open and closed system dynamics are discussed.

Abstract

We address the surface tension-driven dynamics of porous media in nearly saturated pore-space solutions. We linearize this dynamics in the reaction-limited regime near its fixed points -- surfaces of constant mean curvature (CMC surfaces). We prove that the only stable interface for this dynamics is the plane, and estimate the time scale for a CMC surface to become unstable. We also discuss the differences between open and closed system dynamics, pointing out the unlikelihood that CMC surfaces are ever realized in these systems on any time scale.