The role of multiscale roughness in the Lotus effect: is it essential for super-hydrophobicity?

The role of multiscale (hierarchical) roughness in optimizing the structure of nonwettable (superhydrophobic) solid surfaces was theoretically studied for 2D systems of a drop on three different types of surface topographies with up to four roughness scales. The surface models considered here were sinusoidal, flat-top pillars, and triadic Koch curves. Three criteria were used to compare between the various topographies and roughness scales. The first is the transition contact angle (CA) between the Wenzel (W) and Cassie-Baxter (CB) wetting states, above which the CB state is the thermodynamically stable one. The second is the solid-liquid (wetted) interfacial area, as an indicator for the ease of roll-off of a drop from the superhydrophobic surfaces. The third is the protrusion height that reflects the mechanical stability of the surface against breakage. The results indicate that multiscale roughness per se is not essential for superhydrophobicity; however, it mainly decreases the necessary protrusion height. Thus, multiscale roughness is beneficial for the Lotus effect mostly with regard to mechanical stability. The sinusoidal topography with three levels of roughness scales is best for nonwettability out of the topographies studied here. This observation may partially explain why Nature chose rounded-top protrusions, such as those on the Lotus leaf. The least useful topography is the flat-top pillars with three roughness scales. In the case of the triadic Koch topography, four roughness scales are required to have nonwettable surface.