Influence of textural statistics on drag reduction by scalable, randomly rough superhydrophobic surfaces in turbulent flow

We investigate the influence of statistical measures of surface roughness on the turbulent drag reduction (DR) performance of four scalable, randomly rough superhydrophobic (SH) textures. Each surface was fabricated using readily scalable surface texturing processes to generate a random, self-affine height profile on the base substrate. The frictional drag on all four SH surfaces was measured when fully submerged in shear-driven turbulent flow inside a bespoke Taylor-Couette apparatus at Reynolds numbers in the range 1 × 104 ≲ Re ≲ 1 × 105. An “effective” slip length quantifying the overall drag-reducing ability for each surface was extracted from the resulting Prandtl-von Kármán friction plots. Reductions in the frictional drag of up to 26% were observed, with one of the hierarchically textured surfaces exceeding a wall shear stress of 26 Pa (corresponding to a Reynolds number Re ≈ 7 × 104) before the onset of flow-induced plastron collapse. The surface morphology of each texture was characterized using noncontact optical profilometry, and the influence of various statistical measures of roughness on the effective slip length was explored. The lateral autocorrelation length was identified as the key textural parameter determining the drag-reducing ability for randomly rough SH textures, playing the role analogous to the spatial periodicity of regularly patterned SH surfaces. A large autocorrelation length, a small surface roughness, and the presence of hierarchical roughness features were observed to be the three important design requirements for scalable SH textures for optimal DR in turbulent flows.