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/content/aip/journal/pof2/28/2/10.1063/1.4941769
1.
1.J. P. Rothstein, “Slip on superhydrophobic surfaces,” Annu. Rev. Fluid Mech. 42, 89109 (2010).
http://dx.doi.org/10.1146/annurev-fluid-121108-145558
2.
2.A. B. D. Cassie and S. Baxter, “Wettability of porous surfaces,” Trans. Faraday Soc. 40, 546551 (1944).
http://dx.doi.org/10.1039/tf9444000546
3.
3.J. R. Philip, “Flows satisfying mixed no-slip and no-shear conditions,” Z. Angew. Math. Phys. 23, 353372 (1972).
http://dx.doi.org/10.1007/BF01595477
4.
4.J. Lauga and H. Stone, “Effective slip in pressure-driven Stokes flow,” J. Fluid Mech. 489, 5577 (2003).
http://dx.doi.org/10.1017/S0022112003004695
5.
5.A. V. Belyaev and O. I. Vinogradova, “Effective slip in pressure-driven flow past super-hydrophobic stripes,” J. Fluid Mech. 652, 489499 (2010).
http://dx.doi.org/10.1017/S0022112010000741
6.
6.M. Sbragaglia and A. Prosperetti, “A note on the effective slip properties for microchannel flows with ultrahydrophobic surfaces,” Phys. Fluids 19, 043603 (2007).
http://dx.doi.org/10.1063/1.2716438
7.
7.C. Ybert, C. Barentin, and C. Cottin-Bizonne, “Achieving large slip with superhydrophobic surfaces: Scaling laws for generic geometries,” Phys. Fluids 19, 123601 (2007).
http://dx.doi.org/10.1063/1.2815730
8.
8.A. M. J. Davis and E. Lauga, “Hydrodynamic friction of fakir-like superhydrophobic surfaces,” J. Fluid Mech. 661, 402411 (2010).
http://dx.doi.org/10.1017/S0022112010003460
9.
9.K. Kamrin, M. Z. Bazant, and H. A. Stone, “Effective slip boundary conditions for arbitrary periodic surfaces: The surface mobility tensor,” J. Fluid Mech. 658, 409437 (2010).
http://dx.doi.org/10.1017/S0022112010001801
10.
10.J. Ou, J. B. Perot, and J. P. Rothstein, “Laminar drag reduction in microchannels using ultrahydrophobic surfaces,” Phys. Fluids 16, 46354643 (2004).
http://dx.doi.org/10.1063/1.1812011
11.
11.J. Ou and J. P. Rothstein, “Direct velocity measurements of the flow past drag-reducing ultrahydrophobic surfaces,” Phys. Fluids 17, 13606 (2005).
http://dx.doi.org/10.1063/1.2109867
12.
12.C.-H. Choi and C.-J. Kim, “Large slip of aqueous liquid flow over a nanoengineered superhydrophobic surface,” Phys. Rev. Lett. 96, 066001 (2006).
http://dx.doi.org/10.1103/PhysRevLett.96.066001
13.
13.C.-H. Choi, U. Ulmanella, J. Kim, C.-M. Ho, and C.-J. Kim, “Effective slip and friction reduction in nanograted superhydrophobic microchannels,” Phys. Fluids 18, 087105 (2006).
http://dx.doi.org/10.1063/1.2337669
14.
14.T. Min and J. Kim, “Effects of hydrophobic surface on skin-friction drag,” Phys. Fluids 16, L55L58 (2005).
http://dx.doi.org/10.1063/1.1755723
15.
15.M. B. Martell, J. B. Perot, and J. P. Rothstein, “Direct numerical simulations of turbulent flows over superhydrophobic surfaces,” J. Fluid Mech. 620, 3141 (2009).
http://dx.doi.org/10.1017/S0022112008004916
16.
16.R. Daniello, N. E. Waterhouse, and J. P. Rothstein, “Drag reduction in turbulent flows over superhydrophobic surfaces,” Phys. Fluids 21, 085103 (2009).
http://dx.doi.org/10.1063/1.3207885
17.
17.B. Woolford, J. Prince, D. Maynes, and B. W. Webb, “Particle image velocimetry characterization of turbulent channel flow with rib patterned superhydrophobic walls,” Phys. Fluids 21, 085106 (2009).
http://dx.doi.org/10.1063/1.3213607
18.
18.M. B. Martell, J. P. Rothstein, and J. B. Perot, “An analysis of superhydrophobic turbulent drag reduction mechanisms using direct numerical simulation,” Phys. Fluids 22, 065102 (2010).
http://dx.doi.org/10.1063/1.3432514
19.
19.H. Park, G. Sun, and C.-J. Kim, “Superhydrophobic turbulent drag reduction as a function of surface grating parameters,” J. Fluid Mech. 747, 722734 (2014).
http://dx.doi.org/10.1017/jfm.2014.151
20.
20.S. Türk, G. Daschiel, A. Stroh, Y. Hasegawa, and B. Frohnapfel, “Turbulent flow over superhydrophobic surface with streamwise grooves,” J. Fluid Mech. 747, 186217 (2014).
http://dx.doi.org/10.1017/jfm.2014.137
21.
21.J. Seo, R. García-Mayoral, and A. Mani, “Pressure fluctuations and interfacial robustness in turbulent flows over superhydrophobic surfaces,” J. Fluid Mech. 783, 448473 (2015).
http://dx.doi.org/10.1017/jfm.2015.573
22.
22.H. Tennekes and J. Lumley, A First Course in Turbulence (MIT Press, 1972).
23.
23.D. Coles, “The law of the wake in the turbulent boundary layer,” J. Fluid Mech. 1, 191226 (1956).
http://dx.doi.org/10.1017/S0022112056000135
24.
24.P. Luchini, F. Manzo, and A. Pozzi, “Resistance of a grooved surface to parallel flow and cross-flow,” J. Fluid Mech. Digital Arch. 228, 87109 (1991).
http://dx.doi.org/10.1017/s0022112091002641
25.
25.J. Jiménez, “On the structure and control of near wall turbulence,” Phys. Fluids 6, 944 (1994).
http://dx.doi.org/10.1063/1.868327
26.
26.J. Jiménez, “Turbulent flows over rough walls,” Annu. Rev. Fluid Mech. 36, 173196 (2004).
http://dx.doi.org/10.1146/annurev.fluid.36.050802.122103
27.
27.R. García-Mayoral and J. Jiménez, “Hydrodynamic stability and breakdown of the viscous regime over riblets,” J. Fluid Mech. 678, 317347 (2011).
http://dx.doi.org/10.1017/jfm.2011.114
28.
28.K. Fukagata, N. Kasagi, and P. Koumoutsakos, “A theoretical prediction of friction drag reduction in turbulent flow by superhydrophobic surfaces,” Phys. Fluids 18, 051703 (2006).
http://dx.doi.org/10.1063/1.2205307
29.
29.A. Busse and N. D. Sandham, “Influence of an anisotropic slip-length boundary condition on turbulent channel flow,” Phys. Fluids 24, 055111 (2012).
http://dx.doi.org/10.1063/1.4719780
30.
30.R. A. Bidkar, L. Leblanc, A. J. Kulkarni, V. Bahadur, S. L. Ceccio, and M. Perlin, “Skin-friction drag reduction in the turbulent regime using random-textured hydrophobic surfaces,” Phys. Fluids 26, 085108 (2014).
http://dx.doi.org/10.1063/1.4892902
31.
31.S. Srinivasan, J. A. Kleingartner, J. B. Gilbert, R. E. Cohen, A. J. B. Milne, and G. H. McKinley, “Sustainable drag reduction in turbulent Taylor-Couette flows by depositing sprayable superhydrophobic surfaces,” Phys. Rev. Lett. 114, 014501 (2015).
http://dx.doi.org/10.1103/PhysRevLett.114.014501
32.
32.H. Park, H. Park, and J. Kim, “A numerical study of the effects of superhydrophobic surface on skin-friction drag in turbulent channel flow,” Phys. Fluids 25, 110815 (2013).
http://dx.doi.org/10.1063/1.4819144
33.
33.T. O. Jelly, S. Y. Jung, and T. A. Zaki, “Turbulence and skin friction modification in channel flow with streamwise-aligned superhydrophobic surface texture,” Phys. Fluids 26, 095102 (2014).
http://dx.doi.org/10.1063/1.4894064
34.
34.H. Haibao, D. Peng, Z. Feng, S. Dong, and W. Yang, “Effect of hydrophobicity on turbulent boundary layer under water,” Exp. Therm. Fluid Sci. 60, 148156 (2015).
http://dx.doi.org/10.1016/j.expthermflusci.2014.08.013
35.
35.J. Kim and P. Moin, “Application of a fractional step method to incompressible Navier-Stokes equations,” J. Comput. Phys. 59, 308323 (1985).
http://dx.doi.org/10.1016/0021-9991(85)90148-2
36.
36.C. Schönecker, T. Baier, and S. Hardt, “Influence of the enclosed fluid on the flow over a microstructured surface in the Cassie state,” J. Fluid Mech. 740, 168195 (2014).
http://dx.doi.org/10.1017/jfm.2013.647
37.
37.J. Kim, P. Moin, and R. D. Moser, “Turbulence statistics in fully developed channel flow at low Reynolds number,” J. Fluid Mech. 177, 133166 (1987).
http://dx.doi.org/10.1017/S0022112087000892
38.
38. While in our simulations we maintained desired L+ by adjusting the texture size, we should note in practice Reynolds number is change by changing the flow rate, while keeping the fluid and geometry fixed, which inevitably leads to change of L+.
39.
39.A. Rastegari and R. Akhavan, “On the mechanism of turbulent drag reduction with super-hydrophobic surfaces,” J. Fluid Mech. (Rapid) 773, R4 (2015).
http://dx.doi.org/10.1017/jfm.2015.266
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/content/aip/journal/pof2/28/2/10.1063/1.4941769
2016-02-17
2016-09-25

Abstract

Superhydrophobic surfaces can significantly reduce hydrodynamic skin drag by accommodating large slip velocity near the surface due to entrapment of air bubbles within their micro-scale roughness elements. While there are many Stokes flow solutions for flows near superhydrophobic surfaces that describe the relation between effective slip length and surface geometry, such relations are not fully known in the turbulent flow limit. In this work, we present a phenomenological model for the kinematics of flow near a superhydrophobic surface with periodic post-patterns at high Reynolds numbers. The model predicts an inverse square root scaling with solid fraction, and a cube root scaling of the slip length with pattern size, which is different from the reported scaling in the Stokes flow limit. A mixed model is then proposed that recovers both Stokes flow solution and the presented scaling, respectively, in the small and large texture size limits. This model is validated using direct numerical simulations of turbulent flows over superhydrophobic posts over a wide range of texture sizes from + ≈ 6 to 310 and solid fractions from = 1/9 to 1/64. Our report also embarks on the extension of friction laws of turbulent wall-bounded flows to superhydrophobic surfaces. To this end, we present a review of a simplified model for the mean velocity profile, which we call the shifted-turbulent boundary layer model, and address two previous shortcomings regarding the closure and accuracy of this model. Furthermore, we address the process of homogenization of the texture effect to an effective slip length by investigating correlations between slip velocity and shear over pattern-averaged data for streamwise and spanwise directions. For + of up to (10), shear stress and slip velocity are perfectly correlated and well described by a homogenized slip length consistent with Stokes flow solutions. In contrast, in the limit of large +, the pattern-averaged shear stress and slip velocity become uncorrelated and thus the homogenized boundary condition is unable to capture the bulk behavior of the patterned surface.

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