A parametric study of the hydrophobicity of rough surfaces based on finite element computations

Several biological and artificial hydrophobic surfaces exhibit self-cleaning mechanisms, which ensure smooth sliding/rolling of liquid droplets, allowing them to sweep pollutant particles away from the surface. While enhancing of the self-cleaning property is a major topic in numerous industrial applications, the underlying physics is not yet fully understood. The first step towards analyzing this mechanism is studying the surface hydrophobicity, which is characterized by the contact angle and surface topography. In this article, we investigate the wetting of hydrophobic surfaces at three different length-scales, over a range of surface and droplet parameters. A mathematical model describing multi-scale surface topographies is presented, using exponential functions. The contact between liquid droplets and these surfaces is numerically studied using a finite element (FE) droplet model. The introduced models are verified numerically and experimentally. Numerical examples are shown for axisymmetric droplets of different size on surfaces with various contact angles and various levels of surface roughness, representing different length-scales. The corresponding wetted area is computed in order to evaluate the hydrophobicity of the surface. Significant differences are observed in contact angles and wetted areas captured at different length-scales. This highlights the importance of the multi-scale structure of hydrophobic surfaces on wetting. Furthermore, the presented work provides guidelines for the design of artificial hydrophobic surfaces.