A Thermodynamic Analysis of the Validity of Wenzel and Cassie's Equations

Wettable properties of a considered solid on its contact angle (CA) can be analyzed theoretically using the classical Wenzel and Cassie's equations. However, recent strong interest in superhydrophobic surfaces has demanded a re-examination of the applicability of the two equations. We report a thermodynamic analysis to determine the universality, in particular, the limitations of the two equations. Using some special surfaces, we demonstrate that the two equations are valid for micro-scale heterogeneous structures, however they are invalid for macro-scale heterogeneous surfaces. Furthermore, the present calculations suggest that fundamental thermodynamic analysis is the most powerful and reliable approach to determine the comprehensive wettability for various structurally patterned surfaces.