Wetting equilibrium in a rectangular channel

Abstract

When a capillary channel with corners is wetted by a fluid, there are regions where the fluid fills the whole cross-section and regions where only the corners are filled by the fluid. The fluid fraction of the partially-filled region, s*, is an important quantity related to the capillary pressure. We calculate the value of s* for channels with a cross-section slightly deviated from a rectangle: the height is larger in the center than those on the two short sides. We find that a small change in the cross-section geometry leads to a huge change of s*. This result is consistent with experimental observations.