Edge wetting: Steady state of rivulets in wedges

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