Inversely designed micro-textures for robust Cassie-Baxter mode of super-hydrophobicity

The robust Cassie-Baxter mode of the wetting behaviour on a micro-textured solid surface, is a key topography element yielding stable super-hydrophobicity. To meet this purpose, we propose an inverse computational design procedure for the discovery of suitable periodic micro-textures, based on three different tilings of the plane. The symmetric tiles of the lattice are regular triangles, quadrangles, and hexagons. The goal of the inverse design procedure is to achieve the robust Cassie-Baxter state, in which the liquid/vapour interface is mathematically described using the Young-Laplace equation on the lattice, and a topology optimisation approach is utilised to construct a variational problem for the inverse design procedure. Based on numerical calculations of the constructed variational problem, underlying effects are revealed for several factors, including the Bond number, duty ratio, feature size, and lattice constant. The effects of feature size and lattice constant provide approaches for compromisingly considering the robustness of the Cassie-Baxter mode and manufacturability of the inversely designed micro-textures; the effect of the lattice constant permits the scaling properties of the derived patterns, and this in turn provides an approach to avoid the elasto-capillary instability driven collapse of the micro/nanostructures in the derived micro-textures. Further, a monolithic inverse design procedure for the periodic micro-textures is proposed in the conclusions, with synthetically considering the manufacturability as well as contact angle and surface-volume ratio of the liquid bulge held by the supported liquid/vapour interface.