Neither Lippmann nor Young: enabling electrowetting modeling on structured dielectric surfaces.

Aiming to illuminate mechanisms of wetting transitions on geometrically patterned surfaces induced by the electrowetting phenomenon, we present a novel modeling approach that goes beyond the limitations of the Lippmann equation and is even relieved from the implementation of the Young contact angle boundary condition. We employ the equations of the capillary electrohydrostatics augmented by a disjoining pressure term derived from an effective interface potential accounting for solid/liquid interactions. Proper parametrization of the liquid surface profile enables efficient simulation of multiple and reconfigurable three-phase contact lines (TPL) appearing when entire droplets undergo wetting transitions on patterned surfaces. The liquid/ambient and the liquid/solid interfaces are treated in a unified context tackling the assumption that the liquid profile is wedge-shaped at any three-phase contact line. In this way, electric field singularities are bypassed, allowing for accurate electric field and liquid surface profile computation, especially in the vicinity of TPLs. We found that the invariance of the microscopic contact angle in electrowetting systems is valid only for thick dielectrics, supporting published experiments. By applying our methodology to patterned dielectrics, we computed all admissible droplet equilibrium profiles, including Cassie-Baxter, Wenzel, and mixed wetting states. Mixed wetting states are computed for the first time in electrowetting systems, and their relative stability is presented in a clear and instructive way.