  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.
