Liquid-vapor transition on patterned solid surfaces in a shear flow

Liquids on a solid surface patterned with microstructures can exhibit the Cassie-Baxter (Cassie) state and the wetted Wenzel state. The transitions between the two states and the effects of surface topography, surface chemistry as well as the geometry of the microstructures on the transitions have been extensively studied in earlier work. However, most of these work focused on the study of the free energy landscape and the energy barriers. In the current work, we consider the transitions in the presence of a shear flow. We compute the minimum action path between the Wenzel and Cassie states using the minimum action method [W. E, W. Ren, and E. Vanden-Eijnden, Commun. Pure Appl. Math. 57, 637 (2004)]. Numerical results are obtained for transitions on a surface patterned with straight pillars. It is found that the shear flow facilitates the transition from the Wenzel state to the Cassie state, while it inhibits the transition backwards. The Wenzel state becomes unstable when the shear rate reaches a certain critical value. Two different scenarios for the Wenzel-Cassie transition are observed. At low shear rate, the transition happens via nucleation of the vapor phase at the bottom of the groove followed by its growth. At high shear rate, in contrary, the nucleation of the vapor phase occurs at the top corner of a pillar. The vapor phase grows in the direction of the flow, and the system goes through an intermediate metastable state before reaching the Cassie state.