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Turbulent flows over superhydrophobic surfaces: flow-induced capillary waves, and robustness of air–water interfaces

Published online by Cambridge University Press:  27 November 2017

Jongmin Seo ,
Ricardo García-Mayoral  and
Ali Mani Open the ORCID record for Ali Mani [Opens in a new window]
Jongmin Seo
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
Ricardo García-Mayoral
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK
Ali Mani*
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: alimani@stanford.edu
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Abstract

Superhydrophobic surfaces can retain gas pockets within their microscale textures when submerged in water. This property reduces direct contact between water and solid surfaces and presents opportunities for improving hydrodynamic performance by decreasing viscous drag. In most realistic applications, however, the flow regime is turbulent and retaining the gas pockets is a challenge. In order to overcome this challenge, it is crucial to develop an understanding of physical mechanisms that can lead to the failure of superhydrophobic surfaces in retaining gas pockets when the overlying liquid flow is turbulent. We present a study of the onset of failure in gas retention by analysing direct numerical simulations (DNS) of turbulent flows over superhydrophobic surfaces coupled with the deformation of air–water interfaces that hold the gas pockets. The superhydrophobic surfaces are modelled as periodic textures with patterned slip and no-slip boundary conditions on the overlying water flow. The liquid–gas interface is modelled via a linearized Young–Laplace equation, which is solved coupled with the overlying turbulent flow. A wide range of texture sizes and interfacial Weber numbers are considered in this study. Our analysis identifies flow-induced upstream-travelling capillary waves that are coherent in the spanwise direction as one mechanism for failure in retention of gas pockets. To confirm physical understanding of these waves, a semianalytical inviscid linear analysis is developed; the wave speeds obtained from the space–time correlations in the DNS data were found to match with the predictions of the semianalytical model. The magnitude of the pressure fluctuations due to these waves was found to increase with decreasing surface tension, and increase with a much stronger dependence on the slip velocity, when all numbers are reported in wall units. Based on a fitted scaling, a threshold criterion for the failure of superhydrophobic surfaces is developed that is based on estimates of the onset condition required for the motion of contact lines. The second contribution of this work is the development of boundary maps that identify stable and unstable zones in a parameter space consisting of working parameter and design parameters including texture size and material contact angle. We provide a brief description of previously identified failure modes of superhydrophobic surfaces, namely the stagnation pressure and shear-driven drainage mechanisms. In an overlay map, the stable and unstable zones due to each mechanism are presented. For various input conditions, we provide scaling laws that identify the most critical mechanism limiting the stability of gas retention by superhydrophobic surfaces.

JFM classification

Waves/Free-surface Flows: Capillary waves Flow Control: Drag reduction Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 835 , 25 January 2018 , pp. 45 - 85
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Copyright
© 2017 Cambridge University Press 

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References

Aljallis, E., Sarshar, M. A., Datla, R., Sikka, V. & Jone, A. 2013 Experimental study of skin friction drag reduction on superhydrophobic flat plates in high Reynolds number boundary layer flow. Phys. Fluids 25, 025103.Google Scholar
Bidkar, R. A., Leblanc, L., Kulkarni, A. J., Bahadur, V., Ceccio, S. L. & Perlin, M. 2014 Skin-friction drag reduction in the turbulent regime using random-textured hydrophobic surfaces. Phys. Fluids 26, 085108.CrossRefGoogle Scholar
Busse, A. & Sandham, N. D. 2012 Influence of an anisotropic slip-length boundary condition on turbulent channel flow. Phys. Fluids 24, 055111.CrossRefGoogle Scholar
Byun, D., Kim, J., Ko, H. S. & Park, H. C. 2008 Direct measurement of slip flows in superhydrophobic microchannels with transverse grooves. Phys. Fluids 20, 113601.CrossRefGoogle Scholar
Cassie, A. B. D. & Baxter, S. 1944 Wettability of porous surfaces. Trans. Faraday Soc. 40, 546–551.Google Scholar
Choi, C.-H. & Kim, C.-J. 2006 Large slip of aqueous liquid flow over a nanoengineered superhydrophobic surface. Phys. Rev. Lett. 96, 066001.Google Scholar
Choi, H. & Moin, P. 1990 On the spacetime characteristics of wallpressure fluctuations. Phys. Fluids 2, 1450–1460.Google Scholar
Choi, H., Moin, P. & Kim, J. 1993 Direct numerical simulation of turbulent flow over riblets. J. Fluid Mech. 255, 503–539.CrossRefGoogle Scholar
Daniello, R., Waterhouse, N. E. & Rothstein, J. P. 2009 Turbulent drag reduction using superhydrophobic surfaces. Phys. Fluids 21, 085103.CrossRefGoogle Scholar
Davis, A. M. J. & Lauga, E. 2009 Geometric transition in friction for flow over a bubble mattress. Phys. Fluids 21, 011701.Google Scholar
Davis, A. M. J. & Lauga, E. 2010 Hydrodynamic friction of fakir-like superhydrophobic surfaces. J. Fluid Mech. 661, 402–411.Google Scholar
Farabee, T. M. & Casarella, M. J. 1991 Spectral features of wall pressure fluctuations beneath turbulent boundary layers. Phys. Fluids A 3, 2410–2420.Google Scholar
Fukagata, K., Kasagi, N. & Koumoutsakos, P. 2006 A theoretical prediction of friction drag reduction in turbulent flow by superhydrophobic surfaces. Phys. Fluids 18, 051703.Google Scholar
García-Mayoral, R. & Jiménez, J. 2011 Hydrodynamic stability and breakdown of the viscous regime over riblets. J. Fluid Mech. 678, 317–347.Google Scholar
Golovin, K. B., Gose, J. W., Perlin, M., Ceccio, S. L. & Tuteja, A. 2016 Bioinspired surfaces for turbulent drag reduction. Phil. Trans. R. Soc. Lond. A 374, 20160189.Google Scholar
Haibao, H., Peng, D., Feng, Z., Dong, S. & Yang, W. 2015 Effect of hydrophobicity on turbulent boundary layer under water. Exp. Therm. Fluid Sci. 60, 148–156.Google Scholar
Hyväluoma, J. & Harting, J. D. R. 2008 Slip flow over structured surfaces with entrapped microbubbles. Phys. Rev. Lett. 100, 246001.Google Scholar
Jelly, T. O., Jung, S. Y. & Zaki, T. A. 2014 Turbulence and skin friction modification in channel flow with streamwise-aligned superhydrophobic surface texture. Phys. Fluids 26, 095102.Google Scholar
Jung, T., Choi, H. & Kim, J. 2016 Effects of the air layer of an idealized superhydrophobic surface on the slip length and skin-friction drag. J. Fluid Mech. 790, R1.CrossRefGoogle Scholar
Karatay, E., Haase, A. S., Visser, C. W., Sun, C., Lohse, D., Tsaia, P. A. & Lammertink, R. G. H. 2013 Control of slippage with tunable bubble mattresses. Proc. Natl Acad. Sci. 110 (21), 8422–8426.CrossRefGoogle ScholarPubMed
Kim, E. & Choi, H. 2014 Space–time characteristics of a compliant wall in a turbulent channel flow. J. Fluid Mech. 756, 30–53.CrossRefGoogle Scholar
Kim, J. 1988 On the structure of pressure fluctuations in simulated turbulent channel flow. J. Fluid Mech. 205, 421–451.Google Scholar
Kim, J. & Hussain, F. 1993 Propagation velocity of perturbations in turbulent channel. Phys. Fluids 5, 695–706.Google Scholar
Kim, J. & Moin, P. 1985 Application of a fractional step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323.CrossRefGoogle Scholar
Lee, C., Choi, C.-H. & Kim, C.-J. 2008 Structured surfaces for a giant liquid slip. Phys. Rev. Lett. 101, 064501.Google Scholar
Lee, C. & Kim, C.-J. 2009 Maximizing the giant liquid slip on superhydrophobic microstructures by nanostructuring their sidewalls. Langmuir 25, 12812–12818.Google Scholar
Lee, C. & Kim, C.-J. 2011 Influence of surface hierarchy of superhydrophobic surfaces on liquid slip. Langmuir 27, 4243–4248.Google Scholar
Lee, J., Jelly, T. O. & Zaki, T. A. 2015 Effect of Reynolds number on turbulent drag reduction by superhydrophobic surface textures. Flow Turbul. Combust. 95, 277–300.Google Scholar
Lee, M. & Moser, R. D. 2015 Direct numerical simulation of turbulent channel flow up to Re 𝜏 = 5200. J. Fluid Mech. 774, 395–415.CrossRefGoogle Scholar
Li, Y., Alame, K. & Mahesh, K. 2017 Feature-resolved computational and analytical study of laminar drag reduction by superhydrophobic surfaces. Phys. Rev. Fluids 2, 054002.CrossRefGoogle Scholar
Ling, H., Srinivasan, S., Golovin, K., McKinley, G. H., Tuteja, A. & Katz, J. 2016 High-resolution velocity measurement in the inner part of turbulent boundary layers over super-hydrophobic surfaces. J. Fluid Mech. 801, 670–703.Google Scholar
Liu, Y., Wexler, J. S., Schönecker, C. & Stone, H. A. 2016 Effect of viscosity ratio on the shear-driven failure of liquid-infused surfaces. Phys. Rev. Fluids 1, 074003.Google Scholar
Luhar, M., Sharma, A. S. & McKeon, B. J. 2015 A framework for studying the effect of compliant surfaces on wall turbulence. J. Fluid Mech. 768, 415–441.CrossRefGoogle Scholar
Luhar, M., Sharma, A. S. & McKeon, B. J. 2016 On the design of optimal compliant walls for turbulence control. J. Turbul. 17, 787–806.Google Scholar
Martell, M. B., Perot, J. B. & Rothstein, J. P. 2009 Direct numerical simulations of turbulent flows over superhydrophobic surfaces. J. Fluid Mech. 620, 31–41.Google Scholar
Martell, M. B., Rothstein, J. P. & Perot, J. B. 2010 An analysis of superhydrophobic turbulent drag reduction mechanisms using direct numerical simulation. Phys. Fluids 22, 065102.Google Scholar
McKeon, B. J. & Sharma, A. S. 2010 A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336–382.Google Scholar
McKeon, B. J., Sharma, A. S. & Jacobi, I. 2013 Experimental manipulation of wall turbulence: a systems approach. Phys. Fluids 25, 031301.Google Scholar
Min, T. & Kim, J. 2004 Effects of hydrophobic surface on skin-friction drag. Phys. Fluids 16, L55–L58.Google Scholar
Morinishi, Y., Lund, T. S., Vasilyev, O. V. & Moin, P. 1998 Fully conservative higher order finite difference schemes for incompressible flow. J. Comput. Phys. 143, 90–124.Google Scholar
Moser, R., Kim, J. & Mansour, N. 1998 Direct numerical simulation of turbulent channel flow up to Re 𝜏 ≈ 590. Phys. Fluids 11, 943–945.Google Scholar
Ou, J., Perot, J. B. & Rothstein, J. P. 2004 Laminar drag reduction in microchannels using ultrahydrophobic surfaces. Phys. Fluids 16, 4635–4643.Google Scholar
Ou, J. & Rothstein, J. P. 2005 Direct velocity measurements of the flow past drag-reducing ultrahydrophobic surfaces. Phys. Fluids 17, 13606.Google Scholar
Park, H., Park, H. & Kim, J. 2013 A numerical study of the effects of superhydrophobic surface on skin-friction drag in turbulent channel flow. Phys. Fluids 25, 110815.Google Scholar
Park, H., Sun, G. & Kim, C.-J. 2014 Superhydrophobic turbulent drag reduction as a function of surface grating parameters. J. Fluid Mech. 747, 722–734.Google Scholar
Patankar, N. A. 2010 Consolidation of hydrophobic transition criteria by using an approximate energy minimization approach. Langmuir 26, 8941–8945.Google Scholar
Piao, L. & Park, H. 2015 Two-dimensional analysis of air–water interface on superhydrophobic grooves under fluctuating water pressure. Langmuir 31, 8022–8032.Google Scholar
Rastegari, A. & Akhavan, R. 2015 On the mechanism of turbulent drag reduction with super-hydrophobic surfaces. J. Fluid Mech. 773, R4.CrossRefGoogle Scholar
Reynolds, W. C. & Hussain, A. K. M. F. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54, 263–288.Google Scholar
Rosenberg, B. J., Buren, T. V., Fu, M. K. & Smits, A. J. 2016 Turbulent drag reduction over air- and liquid-impregnated surfaces. Phys. Fluids 28, 015103.Google Scholar
Rothstein, J. P. 2010 Slip on superhydrophobic surfaces. Annu. Rev. Fluid Mech. 42, 89–109.Google Scholar
Schönecker, C., Baier, T. & Hardt, S. 2014 Influence of the enclosed fluid on the flow over a microstructured surface in the Cassie state. J. Fluid Mech. 740, 168–195.Google Scholar
Seo, J., García-Mayoral, R. & Mani, A. 2015 Pressure fluctuations and interfacial robustness in turbulent flows over superhydrophobic surfaces. J. Fluid Mech. 783, 448–473.CrossRefGoogle Scholar
Seo, J. & Mani, A. 2016 On the scaling of the slip velocity in turbulent flows over superhydrophobic surfaces. Phys. Fluids 28, 025110.Google Scholar
Seo, J. & Mani, A.2017 Effect of texture randomization on the slip and interfacial robustness in turbulent flows over superhydrophobic surfaces. Preprint, arXiv:1709.05605.Google Scholar
Squire, H. B. 1953 Investigation of the instability of a moving liquid film. Brit. J. Appl. Phys. 4, 167–169.Google Scholar
Srinivasan, S., Kleingartner, J. A., Gilbert, J. B., Cohen, R. E., Milne, A. J. B. & McKinley, G. H. 2015 Sustainable drag reduction in turbulent Taylor–Couette flows by depositing sprayable superhydrophobic surfaces. Phys. Rev. Lett. 114, 014501.CrossRefGoogle ScholarPubMed
Steinberger, A., Cottin-Bizonne, C., Kleimann, P. & Charlaix, E. 2007 High friction on a bubble mattress. Nat. Mater. 6, 665–668.Google Scholar
Taylor, G. I. 1959 The dynamics of thin sheets of fluid. ii. Waves on fluid sheets. Proc. R. Soc. Lond. A 253, 296–312.Google Scholar
Teo, C. J. & Khoo, B. C. 2010 Flow past superhydrophobic surfaces containing longitudinal grooves: effects of interface curvature. Microfluid. Nanofluid. 9, 499–511.Google Scholar
Teo, C. J. & Khoo, B. C. 2014 Effects of interface curvature on Poiseuille flow through microchannels and microtubes containing superhydrophobic surfaces with transverse grooves and ribs. Microfluid. Nanofluid. 16, 225–236.Google Scholar
Tsai, P., Peters, A. M., Pirat, C., Wessling, M., Lammertink, R. G. H. & Lohse, D. 2009 Quantifying effective slip length over micropatterned hydrophobic surfaces. Phys. Fluids 21, 112002.Google Scholar
Türk, S., Daschiel, G., Stroh, A., Hasegawa, Y. & Frohnapfel, B. 2014 Turbulent flow over superhydrophobic surfaces with streamwise grooves. J. Fluid Mech. 747, 186–217.CrossRefGoogle Scholar
Wenzel, R. N. 1936 Resistance of solid surfaces to wetting by water. Ind. Engng Chem. 28, 988–994.CrossRefGoogle Scholar
Wexler, J. S., Grosskopf, A., Chow, M., Fan, Y., Jacobi, I. & Stone, H. A. 2015a Robust liquid-infused surfaces through patterned wettability. Soft Matt. 11, 5023–5029.Google Scholar
Wexler, J. S., Jacobi, I. & Stone, H. A. 2015b Shear-driven failure of liquid-infused surfaces. Phys. Rev. Lett. 114, 168301.Google Scholar
Woolford, B., Prince, J., Maynes, D. & Webb, B. W. 2009 Partical image velocimetry chracterization of turbulent channel flow with rib patterned superhydrophobic walls. Phys. Fluids 21, 085106.Google Scholar
Xue, Y., Lv, P., Liu, Y., Shi, Y., Lin, H. & Duan, H. 2015 Morphology of gas cavities on patterned hydrophobic surfaces under reduced pressure. Phys. Fluids 27, 092003.Google Scholar
Ybert, C., Barentin, C. & Cottin-Bizonne, C. 2007 Achieving large slip with superhydrophobic surfaces: scaling laws for generic geometries. Phys. Fluids 19, 123601.CrossRefGoogle Scholar
Zhang, J., Tian, H., Yao, Z., Hao, P. & Jiang, N. 2015 Mechanisms of drag reduction of superhydrophobic surfaces in a turbulent boundary layer flow. Exp. Fluids 56, 179.Google Scholar

Seo et al. supplementary movie 1

Instantaneous pressure field at y=0, for Re_Tau=197.5, L+=155, and We_L=0.002.

Download Seo et al. supplementary movie 1(Video)
Video 4.2 MB

Seo et al. supplementary movie 2

Instantaneous pressure field at y=0, for Re_Tau=197.5, L+=38, and We_L=0.004.

Download Seo et al. supplementary movie 2(Video)
Video 3.3 MB