Wetting of rough three-dimensional superhydrophobic surfaces

Wetting of rough three-dimensional periodic surfaces is studied. The contact angle of liquid with a rough surface (theta) is different from that with a smooth surface (theta(0)) due to the difference in the contact area and effect of the air pockets. For non-wetting liquids (theta(0)>pi/2), the contact angle increases with roughness and may approach the value of pi (superhydrophobic surface). For high theta(0), a homogeneous solid-liquid interface, as well as a composite solid-liquid-air interface with air pockets at the valleys of rough surface are possible. These two interfaces correspond to different states of equilibrium and result in different theta. A probability-based approach is introduced to handle the multiple states of equilibrium and to calculate theta. It is found also that increasing droplet size has the same effect as increasing period of roughness (size of asperities). For larger droplets and for larger asperities, the composite interface is less likely. For applications involving liquid's transport near rough walls of a channel, an analogy between a droplet of non-wetting liquid and a gas bubble in wetting liquid is proposed. In order to increase bubbles mobility, the contact angle and the contact angle hysteresis should be minimized. Practical recommendations for design of superhydrophobic surfaces are formulated.