Temporal Averaging of the Liquid Rise Dynamics In Periodically Patterned Capillary

Summary The one-dimensional problem of capillary rise in a transverse-periodically wettability-patterned tube is considered in the framework of the classical Lucas–Washburn model. A recently introduced temporal averaging approach is applied for the assessment of effective wettability surface properties. The temporally averaged contact angle is defined via averaging the capillary driving force which is proportional to the Laplace pressure. The analysis supports the previously made empirical observation in the literature about the inapplicability of Cassie’s law in the form of a simple rule of mixtures for the cosines of the contact angles of the periodic heterogeneous surface.