Interface Pinning and the Dynamics of Capillary Rise in Porous Media

Abstract

We report a study of the dynamics of capillary rise of water in a column of glass beads. The water column height $h$ is measured over 5 decades in time, $1<t<{10}^{5}\mathrm{s}$. We find that the early time data are well described by the classical Washburn equation for capillary tubes. At late times, however, the dynamics is governed by the randomness of the capillary forces on the air-water interface. Analyzing the data in terms of critical pinning, $\mathrm{dh}/\mathrm{dt}\ensuremath{\propto}({P\ensuremath{-}P}_{T}{)}^{\ensuremath{\beta}}$, results in an anomalously large exponent $\ensuremath{\beta}$. We discuss the significance of this finding in light of recent theories for domain wall pinning in the random-field Ising model.