Wetting Transition on Textured Surfaces: A Thermodynamic Approach

Transitions between various states of wetting can have a profound effect on adhesion of a droplet onto a surface. In this study, a three-dimensional free energy (FE) model was developed to investigate the wetting transition for microstructured surfaces with various microgeometries, that is, arrays of pillars (from upright frustum to inverted frustum geometries). The comparison of FE levels for a drop progressively penetrating into troughs of a textured surface allows one to understand the effects of parameters such as contact angle, feature size, and shape on the wetting transition. In particular, transition free energy barrier (FEB) between composite and noncomposite wetting states determines the transition behavior. Preferred wetting states can be determined for a given microstructured surface by comparing FEBcom-non and FEBnoncom. A method to generate wetting maps for designing surface microstructures to keep drops in superhydrophobic (or low adhesion) state is provided. Stable and metastable superhydrophobicity can be seen only if the edge angle for surface features is set at a smaller value than the intrinsic contact angle. Moreover, FE analysis for arrays of two typical re-entrant structures, that is, ones with convex and concave side wall, shows FE curves with minimum and maximum FE states, describing stability for drop penetration process. As such, we provide a framework for designing textured surfaces with superhydrophobic or low adhesion properties.