  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.
