Droplet Wetting Modes On Textured Surfaces

Liquid droplets can have multiple wetting modes on textured surfaces, each corresponding to a stable or metastable state.  In this work, we propose a theoretical model for predicting the free energies of various wetting states for equilibrium shapes of droplets on grooved surfaces.  Using free-energy minimization, we create wetting phase diagrams for both hydrophilic and hydrophobic surfaces with different topographies.  We find a variety of different wetting modes (e.g., Cassie, Wenzel, Inverse Cassie, Upper Wenzel) that depend on droplet size and the parameters that characterize the surface topography.  Gravity affects the droplet shape and wetting modes in conjunction with surface topology. For small droplets, characterized by Bond number much less than unity, the effect of gravity is negligible. However, gravity becomes important with increasing Bond number / drop size.  Our predictions are in good agreement with experimentally measured contact angles for different drop sizes on grooved surfaces. Thus, the resulting wetting phase diagrams may serve as a guideline in creating surfaces with desired wettability.