Sustainable Drag Reduction in Turbulent Taylor-Couette Flows by Depositing Sprayable Superhydrophobic Surfaces

We demonstrate a reduction in the measured inner wall shear stress in moderately turbulent Taylor-Couette flows by depositing sprayable superhydrophobic microstructures on the inner rotor surface. The magnitude of reduction becomes progressively larger as the Reynolds number increases up to a value of 22% at Re=8.0×10⁴. We show that the mean skin friction coefficient Cf in the presence of the superhydrophobic coating can be fitted to a modified Prandtl--von K\'arm\'an--type relationship of the form (Cf/2)^-1/2=Mln (Re(Cf/2)1/2)+N+(b/Δr)Re(Cf/2)1/2 from which we extract an effective slip length of b≈19 μm. The dimensionless effective slip length b⁺=b/δ_ν, where δ_ν is the viscous length scale, is the key parameter that governs the drag reduction and is shown to scale as b⁺~Re1/2 in the limit of high Re.