Wetting resistance of heterogeneous superhydrophobic coatings with orthogonally layered fibers

Superhydrophobic coatings comprised of electrospun nanofibers are a low-cost alternative to micro-fabricated surfaces, and can be applied to substrates of any arbitrary geometry. Such coatings with orthogonally oriented layers have properties that allow their wetting resistance to be predictable for a range of solid volume fractions, fiber diameters, and contact angles. In this paper, we have presented a modeling strategy that solves for the air-water interface shape over several layers of such coatings to predict the resistance of superhydrophobic fiber coatings to hydrostatic pressures and to quantify the relationship between microstructure, meniscus penetration depth, and wetted surface area of the fibers. Slip length predictions are also provided to shed some light on the performance of such coatings in drag reduction applications. It was found that while failure pressure for a coating rises with reducing fiber spacing, there is a tradeoff with wetted fiber surface area relative to a bare substrate. This tradeoff can be offset, however, by using smaller fibers for an intended coating. This results in a higher failure pressure for the same wetted area fraction. The results generated in this work are discussed in relation to those reported in the literature whenever possible.