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We model an infinitely long liquid bridge confined between two plateschemically patterned by stripes of same width and different contact angle,where the three-phase contact line runs, on average, perpendicular to thestripes. This allows us to study the corrugation of a contact line in theabsence of pinning. We find that, if the spacing between the plates is largecompared to the length scale of the surface patterning, the cosine of themacroscopic contact angle corresponds to an average of cosines of the intrinsicangles of the stripes, as predicted by the Cassie equation. If, however, thespacing becomes of order the length scale of the pattern there is a sharpcrossover to a regime where the macroscopic contact angle varies between theintrinsic contact angle of each stripe, as predicted by the local Youngequation. The results are obtained using two numerical methods, LatticeBoltzmann (a diffuse interface approach) and Surface Evolver (a sharp interfaceapproach), thus giving a direct comparison of two popular numerical approachesto 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 aline tension in the free energy. In the lattice Boltzmann approach, the linetension arises from discretisation effects at the diffuse three phase contactline.

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