Effects of geometrical characteristics of surface roughness on droplet wetting

Surface roughness is known to alter the wettability on a solid substrate. In general, either Wenzel or Cassie-Baxter theory is adopted to describe the apparent contact angle. Following the minimum free energy pathway associated with the imbibition process, we have derived a generalized expression for the apparent contact angle on a textured surface and the liquid-gas contact area within the groove that plays a key role. Depending on the geometrical characteristics of the grooves, the surface wetting falls into three regimes: (i) single stable state which is either Wenzel (completely wetted roughness) or Cassie-Baxter (completely nonwetted roughness) state, (ii) two stable states (Wenzel and Cassie-Baxter) separated by an energy barrier, and (iii) single stable state with partially wetted roughness. The sufficient condition for each regime is derived and several groove geometries are given to show the free energy path. Alteration in the geometric parameters may lead to the wetting crossover. We also show that the Cassie-Baxter can occur at a hydrophilic surface for particular pore shapes.