Hierarchical roughness optimization for biomimetic superhydrophobic surfaces

Superhydrophobic surfaces should have high contact angles (CA) with water and low contact angle hysteresis (CAH). High CA may be achieved by increasing surface roughness, while in order to have low CAH, superhydrophobic surfaces should be able to form a stable composite interface with air pockets between solid and liquid. Capillary waves, nanodroplets condensation, hydrophilic spots due to chemical surface inhomogeneity, and liquid pressure can destroy the composite interface. These destabilizing factors have different characteristic length scales, so a hierarchical roughness is required to resist them. It is shown that convex rather than concave profile enhances stability, so nanoscale convex bumps should be superimposed over microasperities, in order to pin the liquid-air interface. In addition, the nanoroughness is required to support nanodroplets. The ability of the interface to support high pressure requires high asperity density and size, so it is in conflict with the requirement of low fractional solid-liquid contact area for low CAH and slip length. The new parameter, spacing factor for asperities, is proposed, and requirements for optimum design, which combines conflicting conditions, are formulated and discussed. Remarkably, biological superhydrophobic surfaces satisfy these requirements.