Statistical Heuristic Wettability Analysis of Randomly Textured Surfaces

The liquid repellency enabled by air bubbles trapped within surface roughness features has drawn the attention of many researchers over the past century. The effects of surface roughness on superhydrophobicity have been extensively studied, mainly using regularly textured, idealized geometries. In comparison, fewer works have investigated the wettability of randomly textured surfaces, although they are much more similar to scalable and bioinspired surfaces. In this work, we investigated whether prior theories developed for understanding the wettability of regularly structured surfaces may be extended to randomly rough surfaces. Sandpapers of varying grit size, when hydrophobized, served as model randomly rough surfaces. Two analyses were conducted. In the first, termed the nonstatistical approach, direct imaging of the surfaces was used to extract an effective texture size and spacing, based on particle analysis and Delaunay triangulation. In the second, termed the statistical approach, two metrology parameters, sample autocorrelation length and mean periodicity, served as the effective texture size and spacing. Overall, the statistical method predicted water contact angles better than the nonstatistical approach, especially for surfaces in the fully wetted Wenzel state or fully nonwetted Cassie state. For surfaces exhibiting a mixed Cassie state of wetting, neither approach was able to predict the apparent contact angles precisely, likely due to the propagation of wetting in three dimensions, as two-dimensional analysis was used to derive the theories of wetting investigated. Estimates on the pressure stability of the nonwetted states were underpredicted when using the statistical parameters. In summation, when randomly rough surfaces exhibit a distribution of texture sizes and spacings, current theories of wettability cannot be directly implemented by a simple mapping using statistical metrology parameters.