Range of applicability of the Wenzel and Cassie-Baxter equations for superhydrophobic surfaces

The Wenzel and Cassie-Baxter equations depending on the extent of liquid/solid interfacial contact area were generally used to estimate water contact angles on superhydrophobic surfaces. In this study, a simple method is proposed on the criterion to use the Wenzel and Cassie-Baxter equations to evaluate the contact angle results on superhydrophobic surfaces. In this method, the difference between the theoretical (geometric) and experimental contact angle-dependent Wenzel roughness parameter, Delta r(w), and Cassie-Baxter solid/liquid contact area fraction, Delta f(s)(CB) were determined, and the validity of these equations was evaluated. We used the data of eight recent publications where the water drop sits on square and cylindrical pillar structured superhydrophobic model surfaces. We evaluated the contact angle results of 166 patterned samples with our method. We also found that the effect of contact angle error margins was low to vary these parameters. In general, the use of the Wenzel equation was found to be wrong for most of the samples (74% of the samples for cylindrical and 58% for square pillar patterned surfaces), and the deviations from the theory were also high for the remaining (26% for cylindrical and 42% for square) samples, and it is concluded that the Wenzel equation cannot be used for superhydrophobic surfaces other than a few exceptions, especially for cylindrical patterns. For the Cassie-Baxter equation, two situations are possible: for positive Delta f(s)(CB), there is only a partial contact of the drop with the top solid surface, and, for negative Delta f(s)(CB), the penetration of the drop in between the pillars is possible, and thus the liquid drop is in contact with the lateral sides of the pillars. We found that 65% of the samples containing cylindrical pillars (52-77% with error margins) and 44% of the samples containing square pillars (38-50% with error margins) resulted in negative Delta f(s)(CB)(red) values. In addition, large deviations of experimental water contact angle results, theta r(e) from the theoretical theta r(CB) were also determined for most of the samples, indicating that the Cassie-Baxter equation should be applied to superhydrophobic surfaces with caution.