Geometry-driven wetting thermodynamics on angular-faceted superhydrophobic surfaces with threefold symmetry

Surface microstructure geometry plays a critical role in regulating interfacial wetting behavior and the stability of superhydrophobic states. In this work, based on Gibbs free energy theory, we investigate the geometry-driven wetting thermodynamics of faceted microstructured surfaces with threefold symmetry. The proposed surfaces consist of periodically arranged equicoordinated faceted microstructures. By explicitly incorporating geometry-induced variations in interfacial areas and surface tensions, the stability of the Cassie–Baxter and Wenzel wetting states, as well as the energy barriers associated with their transitions, are systematically analyzed. Transition criteria between different wetting states are established based on the laws governing three-phase contact line motion, characterizing the thermodynamic mechanisms underlying wetting state transitions. Furthermore, the effects of intrinsic contact angle, structural size, and height on the apparent contact angle and wetting state stability are discussed with quantitative results. The results demonstrate that the threefold symmetry and faceted geometry introduce pronounced geometric confinement of the three-phase contact line, which effectively increases the energy barrier for wetting transitions and enhances the stability of the superhydrophobic state. This study provides a thermodynamic framework for the rational design of highly stable superhydrophobic surfaces and offers valuable insight for applications in anti-icing, droplet manipulation, and interfacial engineering.