Dependence of macroscopic wetting on nanoscopic surface textures

The hydrophobicity of a surface can be enhanced by physical textures. However, no existing theories of surface wetting can provide guidance to pinpoint the texture size requirement to achieve super/ultrahydrophobicity. Here, we show that the three-phase contact line tension, tau, is an important link to understand the dependence of macroscopic wetting on physical texture size in an ideal Cassie regime. Specifically, we show that texture size is the dominant parameter in determining surface hydrophobicity when the size approaches a limiting physical length scale, as defined by tau and the surface tension of the liquid.