Existence and stability of an intermediate wetting state on circular micropillars

Abstract

It has been recently reported that, after a liquid drop contacts the bottom of a roughness groove, liquid may not completely fill this roughness groove if the groove is covered with nanostructures. Otherwise, liquid may fill the entire groove. In this work, we explore the reasons behind these phenomena for the case of circular micropillars and derive an angle inequality. We show that if the local contact angles satisfy the angle inequality, a locally stable intermediate wetting state may exist. In this intermediate state, liquid does not completely fill the roughness groove, and air pockets still exist in its bottom corners. When roughness grooves have smooth surfaces, the local contact angles are usually less than 135°, violating the angle inequality. However, the incorporation of nanostructures on the grooves may make local contact angles become above 135°, resulting in the satisfaction of the angle inequality. Therefore, the filling phenomena may be different when the grooves are covered with nanostructures or not. In addition to existing experimental results, the derived angle inequality is also validated by in situ observation of water drops in the pressing tests on circular micropillars with and without the coverage of ZnO wires.