Friction Reduction and Robustness for Laminar Fluid Flow on Spray-Coated Superhydrophobic Mesh Surfaces

~We measure the effective Navier slip length for flow over a liquid-repellent non-wetting surface (fabricated using a spray-deposition technique) which supports a composite solid-liquid-air interface. The morphology of the hydrophobic textured substrate consists of randomly distributed corpuscular microstructures that stabilize a layer of trapped air upon immersion in liquid. The reduction in viscous skin-friction due to this ``plastron layer'' is evaluated using torque measurements in a parallel plate rheometer, and results in measured slip lengths of b$_{slip}\approx $40 $\mu $m, that are comparable to the mean periodicity of the microstructure. The use of dual-textured spray-coated woven meshes increases the magnitude of the effective slip length to between b$_{slip} \approx $ 90 $\mu $m to 200 $\mu $m depending on the mesh dimensions. We compute the wetted-solid fraction $\varphi _{s}$ from surface evolver simulations, and we demonstrate that the experimentally obtained slip-lengths are consistent with the logarithmic prediction of Davis {\&} Lauga. Finally we define a robustness parameter (A$^{\ast })$ to quantify the stability of the plastron. And illustrate the inverse correlation between A$^{*}$~and b$_{slip}$ by means of a design chart.