Stochastic model for metastable wetting of roughness-induced superhydrophobic surfaces

A stochastic model for metastable wetting of roughness-induced hydrophobic surfaces is proposed. For a rough surface, increased solid-liquid interface area results in increased interface energy, and increases the contact angle (for non-wetting liquids) or decreases it (for wetting liquids). For a very rough surface, a composite solid-liquid-air interface may form with air pockets trapped in the valleys between asperities, as opposed to the homogeneous solid-liquid interface. Both the homogeneous and composite interface configurations correspond to local energy minima of the system and therefore, there are stable states associated with different energy levels. The system may transform from one stable state to the other due to small perturbations, such as capillary waves. Different probabilities are associated with these different stable states, depending on the energy levels. The contact zone consists of a large number of asperities and valleys, which may be in the homogeneous or composite state. The overall contact angle is calculated based on the statistical model. The model may be used for design of roughness-induced superhydrophobic surfaces.