Edge wetting: Steady state of rivulets in wedges

Abstract

The geometry of rough, textured, fractured, and porous media is topologically complicated. Such media are commonly modeled as bundles of capillary tubes. However, angle-containing geometries can serve as a more realistic portrayal of their internal structure. A basic element inherent to all of these media is an open wedge-like channel. The classical theory of capillarity ignoring intermolecular interactions implies that liquid entering a wedge must propagate indefinitely along its spine when the liquid–gas interface is concave. This is well known as the Concus–Finn condition. In the present paper, we show that steady-state rivulets can be formed in such channels when surface forces are taken into account. We present a simple model based on the disjoining pressure approach and analyze the shape of rivulets in wedges. We also consider the case when the walls of the wedge are soft and can be deformed by the liquid.