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, sโ, is an important quantity related to the capillary pressure. We
calculate the value of sโ 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 sโ. This result is consistent with experimental
observations.Comment: 23 pages, 8 figures, submitted to Soft Matte