Cassie-Baxter State Can Explain the Impaled State

Cassie-Baxter state refers to the wetting state where the droplet is on the rough surface underneath which small air pockets lie, and is responsible for the super-hydrophobicity. While the classical Cassie-Baxter model assumes the flat bottom surface of the droplet, recent experiments show that the droplet on the patterned surface may have the curved bottom surface and stay as the impaled state, which remains not well understood. In this study, we suggest a new theory that can explain the impaled state by modelling the droplet with two spherical caps, sharing the basal surface of the upper one. We conduct numerical free energy analysis to show that the curvature of the bottom surface of the droplet is essential to stabilize the droplet in impaled state, especially when the size of the droplet is comparable to the characteristic length scale of the substrate pattern. Our study offer a more precise description of the droplet in Cassie-Baxter state and can be used to analyze the wetting transition between Cassie-Baxter and the Wenzel state.