Design of Superhydrophobic Surfaces for Optimum Roll-Off and Droplet Impact Resistance

Abstract

We study the wetting behavior of water droplets on superhydrophobic arrays of lithographically fabricated square posts. To determine the droplet wetting state, we measure static contact angles and compare the results to predictions for equilibrium Cassie and Wenzel states. Surprisingly, we find that roll-off angles are minimized on surfaces expected to induce Wenzel-like wetting in equilibrium. We argue that droplets on these surfaces are metastable Cassie droplets whose internal Laplace pressure is insufficient to overcome the energy barrier required to completely wet the posts. These metastable Cassie droplets show superior roll-off properties because the effective length of the contact line that is pinned to the surface is reduced. We develop a model that can predict the transition between the metastable Cassie and Wenzel regimes by comparing the Laplace pressure of the drop to the capillary pressure associated with the wetting energy barrier of the textured surface. In the case of impacting droplets the water hammer and Bernoulli pressures must be compared with the capillary pressure. Experiments with impacting droplets show very good agreement with this simple pressure-balance model. Together these models can be used to optimize texture design for droplet-shedding and droplet-impact resistant surfaces.