Angle inequality for judging the transition from Cassie-Baxter to Wenzel states when a water drop contacts bottoms of grooves between micropillars.

A specific criterion is often used to judge the transition from Cassie-Baxter wetting state to that of Wenzel. In this work, we examine the applicability of this specific criterion to the case of micropillars with circular or polygonal cross-sections. For this purpose, we derive an angle inequality. When this angle inequality is violated, the specific criterion holds for the corresponding micropillars. Otherwise, the specific criterion may not be applicable to such micropillars. These results are validated by pressing tests on six types of micropillars, which have circular, triangular, square, hexagonal, T-shaped, and star-like cross-sections.