Beyond the Wenzel and Cassie–Baxter world: Mathematical insight into contact angles

摘要

The Wenzel and Cassie–Baxter wetting states are treated as basis states producing a continuous spectrum of intermediate states. The model considering them as a linear combination of the basis states is proposed and successfully applied to independent data converted within this framework from the terms of absolute vertical deviations as roughness characteristics into the Wenzel r‐based roughness concept. Roughness dependences of apparent contact angles are reproduced therewith. The degree of symmetry is shown to influence measurements, calculations and possibly definition of the contact angle. The cotangent formula linking the drop size and apparent contact angle is derived from the well‐known non‐linear differential model for a drop shape. This enables one to pre‐estimate changes in contact angles due to drop size changes what is important for a more precise definition of superhydrophobicity and superhydrophilicity. The analysis of an oval‐shaped curve as the most general contact line on inclines is performed. The dependence of apparent contact angle on incline tilt and azimuthal angle is derived for the regime of pinning the drop onto a flat surface having been tilted before, unlike the well‐known case of tilting the flat surface with a sessile drop whose contact line is circle‐shaped. The contact angle is found to be a non‐monotonous function of azimuthal angle because the contact line possesses now a reduced symmetry and, therefore, a varying curvature with extrema. Drop ensembles on incline are discussed, and their modeling with application to macroscopic processes requires treatment of the contact line in its most general case, that is, oval shaped.