Wetting on hydrophobic rough surfaces: To be heterogeneous or not to be?

Equilibrium wetting on rough surfaces is discussed in terms of the "competition" between complete liquid penetration into the roughness grooves and entrapment of air bubbles inside the grooves underneath the liquid. The former is the homogeneous wetting regime, usually described by the Wenzel equation. The latter is the heterogeneous wetting regime that is described by the Cassie-Baxter equation. Understanding this "competition" is essential for the design of ultrahydrophobic surfaces. The present discussion puts the Wenzel and Cassie-Baxter equations into proper mathematical-thermodynamic perspective and defines the conditions for determining the transition between the homogeneous and heterogeneous wetting regimes. In particular, a new condition that is necessary for the existence of the heterogeneous wetting regime is added. It is demonstrated that when this condition is violated, the homogeneous wetting regime is in effect, even though the Cassie-Baxter equation may be satisfied.