Apparent Contact Angle Calculated from a Water Repellent Model with Pinning Effect.

A set of new theoretical equations for apparent contact angles is proposed. The equations are derived from an equilibrium of interfacial tensions of a three-phase contact line pinned at the edges of a fine structure. These equations are validated by comparison with contact-angle measurement results for 2 µL water droplets on poly(methyl methacrylate) microstructured samples with square pillars or holes. The equilibrium contact angles predicted by the new equations reasonably agree with the experimental results. In contrast, the values predicted by the Cassie-Baxter equation or the Wenzel equation do not qualitatively agree with the experimental results in pillar pattern cases because the Cassie-Baxter equation and the Wenzel equation do not account for the pinning effect.