Cassie and Wenzel: Were They Really So Wrong?

Abstract

The properties of superhydrophobic surfaces are often understood by reference to the Cassie-Baxter and Wenzel equations. Recently, in a paper deliberately entitled to be provocative, it has been suggested that these equations are wrong; a suggestion said to be justified using experimental data. In this paper, we review the theoretical basis of the equations. We argue that these models are not so much wrong as have assumptions that define the limitations on their applicability and that with suitable generalization they can be used with surfaces possessing some types of spatially varying defect distributions. We discuss the relationship of the models to the previously published experiments and using minimum energy considerations review the derivations of the equations for surfaces with defect distributions. We argue that this means the roughness parameter and surface area fractions are quantities local to the droplet perimeter and that the published data can be interpreted within the models. We derive versions of the Cassie-Baxter and Wenzel equations involving roughness and Cassie-Baxter solid fraction functions local to the three-phase contact line on the assumption that the droplet retains an average axisymmetry shape. Moreover, we indicate that, for superhydrophobic surfaces, the definition of droplet perimeter does not necessarily coincide with the three-phase contact line. As a consequence, the three-phase contact lines within the contact perimeter beneath the droplet can be important in determining the observed contact angle on superhydrophobic surfaces.