Hierarchical roughness makes superhydrophobic states stable

Roughness enhances hydrophobicity of a solid surface leading to high contact angles with water. To achieve low contact angle hysteresis along with a high contact angle, superhydrophobic surfaces should form composite interface (CI) with air pockets in the valleys between asperities. The CI is often unstable and can be irreversibly transformed into the homogeneous interface. We formulate stability criterion, identify mechanisms, which lead to destabilization of the CI, and show that these mechanisms are scale-dependent. To effectively resist these scale-dependent mechanisms, a multiscale (hierarchical) roughness is required. Such multiscale roughness is found in natural and artificial superhydrophobic surfaces.