Modelling the corrugation of the three-phase contact line perpendicular to a chemically striped substrate

TL;DR

This study models the corrugation of a three-phase contact line on chemically striped substrates, revealing how macroscopic contact angles depend on surface patterning and plate spacing, using two numerical methods for validation.

Contribution

It introduces a combined numerical approach using Lattice Boltzmann and Surface Evolver methods to analyze contact line corrugation on patterned surfaces, highlighting the role of line tension.

Findings

Macroscopic contact angle follows Cassie equation at large spacing.

Transition to local Young equation behavior at small spacing.

Consistent results between two numerical methods when including line tension.

Abstract

We model an infinitely long liquid bridge confined between two plates chemically patterned by stripes of same width and different contact angle, where the three-phase contact line runs, on average, perpendicular to the stripes. This allows us to study the corrugation of a contact line in the absence of pinning. We find that, if the spacing between the plates is large compared to the length scale of the surface patterning, the cosine of the macroscopic contact angle corresponds to an average of cosines of the intrinsic angles of the stripes, as predicted by the Cassie equation. If, however, the spacing becomes of order the length scale of the pattern there is a sharp crossover to a regime where the macroscopic contact angle varies between the intrinsic contact angle of each stripe, as predicted by the local Young equation. The results are obtained using two numerical methods, Lattice Boltzmann (a diffuse interface approach) and Surface Evolver (a sharp interface approach), thus giving a direct comparison of two popular numerical approaches to calculating drop shapes when applied to a non-trivial contact line problem. We find that the two methods give consistent results if we take into account a line tension in the free energy. In the lattice Boltzmann approach, the line tension arises from discretisation effects at the diffuse three phase contact line.