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=8.0×10(4). We show that the mean skin friction coefficient C(f) in the presence of the superhydrophobic coating can be fitted to a modified Prandtl-von Kármán-type relationship of the form (C(f)/2)(-1/2)=Mln (Re(C(f)/2)(1/2))+N+(b/Δr)Re(C(f)/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(+)∼Re(1/2) in the limit of high Re.