Wetting equilibrium in a rectangular channel

TL;DR

This paper investigates how slight deviations in a rectangular channel's cross-section significantly affect the fluid's wetting equilibrium, especially the fluid fraction in partially filled regions, aligning with experimental data.

Contribution

It introduces a calculation of the fluid fraction $s^*$ for nearly rectangular channels with slight geometric deviations, revealing large impacts on wetting behavior.

Findings

Small geometric deviations cause large changes in $s^*$.

Theoretical results agree with experimental observations.

Minor cross-section changes drastically alter wetting equilibrium.

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.