Drag Reduction for Viscous Laminar Flow on Spray-Coated Non- Wetting Surfaces†

We estimate the effective Navier-slip length for flow over a spray-fabricated liquid-repellent surface which supports a composite solid-air-liquid interface or ’Cassie-Baxter’ state. The morphology of the coated substrate consists of randomly distributed corpuscular micro-structures which encapsulate a film of trapped air (or ’plastron’) upon contact with liquid. The reduction in viscous skin friction due to the plastron is evaluated using torque measurements in a parallel plate rheometer resulting in a measured slip length of bslip ≈ 39 μm, comparable to the mean periodicity of the microstructure evaluated from confocal fluorescence microscopy. The introduction of a large primary length-scale using dual-textured spray-coated meshes increases the magnitude of the effective slip length to values in the range 94 μm ≤ bslip ≤ 213 μm depending on the geometric features of the mesh. The wetted solid fractions on each mesh are calculated from simulations on model sinusoidal mesh geometries and the trend in measured values of bslip with the mesh periodicity L and the computed wetted solid-fraction rφs are observed to follow existing analytic predictions.