Thermodynamic analysis of the wetting behavior of dual scale patterned hydrophobic surfaces

Nature-made superhydrophobic surfaces, such as lotus leaves, have a dual scale roughness (in micro and nanoscales) which is the main reason for their unique wettability. While there are a lot of experimental studies on wettability of hierarchical roughness, there is a lack of a thorough analysis of the contribution of micro and nanoscale roughness on wettability behavior despite interesting features these surfaces have. In this paper, a thermodynamic approach has been used to predict the wetting behavior of water droplet on a dual scale roughness. The predictions made by the model are compared with experimental results reported in the literature. The thermodynamic analysis has also been used to provide an insight into the origin of the special hydrophobicity of surfaces with dual scale roughness. It was found that there is an interaction between micro and nanoscale roughness on wettability of each other which results in a synergy among the components of roughness in enhancing hydrophobicity. All possible wetting states of a surface with dual scale roughness were presented in a wetting map. The contact angle for each state was also calculated to determine the maximum water repellency condition.