Wetting behavior of a drop atop holes

Superhydrophobic surfaces generally involve completely nonwetting or partially wetting roughness. Because the contact angle is closely related to the liquid-gas interfacial tension, the shape of the liquid-gas interfaces within the grooves plays a key role in determining the droplet wetting behavior. We consider a droplet with volume, V, atop holes with radius, r, and obtain the analytical expression of the bottom liquid-air shape based on surface free energy minimization. It is found that the bottom shape in terms of the interfacial angle, theta(1), depends on the hole size through V/r(3) in addition to the intrinsic contact angle, theta(*). For a given droplet volume, the smaller the hole size (r(3)/V --> 0), the more flat the interface (theta(1) --> 0). In addition, the flatness of the interface grows with reducing the intrinsic contact angle. Numerical simulations of Surface Evolver are performed to confirm our theory. Moreover, wetting experiments in which the gravity effect cannot be neglected are conducted, and the results are consistent with those by numerical simulations. Our result points out that such wall-free capillarity may be useful in extracting liquid from microfluidic device spontaneously.