Connection of Intrinsic Wettability and Surface Topography with the Apparent Wetting Behavior and Adhesion Properties

The need for connecting the intrinsic Material wettability with surface geometry, adhesion to liquids, and the apparent wettability is of primary importance When aiming to design advanced functional materials. Here, by solving the Young-Laplace equation, augmented with a Derjaguin pressure) we tackle the necessity for implementing the Young angle boundary condition at the contact line, and thus we are able to compute multiple and reconfigurable three-phase contact lines in equilibrium. Using the finite element method and special parameter continuation techniques, we highlight the highly nonlinear dependence of the apparent contact angle on the Young angle, which quantifies the material wettability. By computing equilibrium shapes of entire droplets, we find multiple Cassie and Wenzel type states in certain wettability regimes. We, for the first time, find a material wettability regime where Cassie, Wenzel, and partially impregnated states are (meta) stable. The energy barriers for transitions between these states are computed, and their dependence on certain surface geometric features is shown. The rose petal effect as well as the lotus effect are illuminated through free and adhesion energy computations, and certain geometries are suggested that favor one state or the other.