Abstract
Most theoretical models of drops on super-hydrophobic surfaces assume uniform (either partial or complete) penetration of the liquid into the roughness grooves. While this assumption may be satisfactory for well-defined, single-scale roughness, it may be too coarse for random or multiscale roughness. The purpose of this work was to study the effect of assuming non-uniform penetration into a simple multi-scale roughness structure. The quantitative difference between the two approaches was measured by the difference between the predicted most-stable contact angles. The qualitative difference was presented by identifying the type of penetration regime associated with the most-stable contact angle. The results show that the difference between the contact angles predicted by the two approaches is represented by a complex functional dependence on the Young contact angle and all geometric parameters of the multi-scale roughness. The deviation between the results of the two approaches may reach values of 15%. Moreover, the two approaches may predict different states of the drop (Wenzel, Cassie-Baxter) to be most stable.
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