Advertisement

Microfluidics and Nanofluidics

, Volume 19, Issue 1, pp 199–207 | Cite as

Assessment of drag reduction at slippery, topographically structured surfaces

  • Clarissa SchöneckerEmail author
  • Steffen Hardt
Research Paper

Abstract

Drag reduction at topographically structured surfaces that contain a second immiscible fluid in their corrugations is evaluated. Based on a model for the effective slip length of a grooved surface, a threshold for the structured surface being superior to a flat surface with respect to drag reduction is derived for fluids of arbitrary viscosity filling the grooves and flowing over the surface. The specific magnitude of drag reduction is given exemplarily for pressure-driven pipe flow. Flow transverse to the grooves as well as flow longitudinal to open and closed grooves is considered. For typical surface geometry parameters, a flow rate enhancement by several tens of percent is predicted.

Keywords

Slip Drag reduction Cassie state Superhydrophobic surfaces Laminar flow Structured surfaces  Surface design 

Notes

Acknowledgments

The authors kindly acknowledge funding from the German Science Foundation (DFG) through the Excellence Cluster “Smart Interfaces” and the Graduate School of Excellence “Computational Engineering”.

References

  1. Barthlott W, Neinhuis C (1997) Purity of the sacred lotus, or escape from contamination in biological surfaces. Planta 202(1):1–8CrossRefGoogle Scholar
  2. Basset A (1888) A treatise on hydrodynamics, vol 2. Cambridge University Press, CambridgezbMATHGoogle Scholar
  3. Brennan JC, Fairhurst DJ, Morris RH, McHale G, Newton MI (2014) Investigation of the drag reducing effect of hydrophobized sand on cylinders. J Phys D Appl Phys 47(20):205–302CrossRefGoogle Scholar
  4. Busse A, Sandham ND, McHale G, Newton MI (2013) Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface. J Fluid Mech 727:488–508zbMATHMathSciNetCrossRefGoogle Scholar
  5. Crowdy D (2010) Slip length for longitudinal shear flow over a dilute periodic mattress of protruding bubbles. Phys Fluids 22(12):121703MathSciNetCrossRefGoogle Scholar
  6. Daschiel G, Perić M, Jovanović J, Delgado A (2013) The holy grail of microfluidics: sub-laminar drag by layout of periodically embedded microgrooves. Microfluid Nanofluid 15(5):675–687CrossRefGoogle Scholar
  7. Davis AMJ, Lauga E (2009) Geometric transition in friction for flow over a bubble mattress. Phys Fluids 21(1):011701CrossRefGoogle Scholar
  8. Davis AMJ, Lauga E (2010) Hydrodynamic friction of fakir-like superhydrophobic surfaces. J Fluid Mech 661:402–411zbMATHCrossRefGoogle Scholar
  9. Eijkel J (2007) Liquid slip in micro- and nanofluidics: recent research and its possible implications. Lab Chip 7(3):299–301CrossRefGoogle Scholar
  10. Gruncell BRK, Sandham ND, McHale G (2013) Simulations of laminar flow past a superhydrophobic sphere with drag reduction and separation delay. Phys Fluids 25(4):043–601CrossRefGoogle Scholar
  11. Hocking LM (1976) A moving fluid interface on a rough surface. J Fluid Mech 76(4):801–817zbMATHCrossRefGoogle Scholar
  12. Lauga E, Stone HA (2003) Effective slip in pressure-driven stokes flow. J Fluid Mech 489:55–77zbMATHMathSciNetCrossRefGoogle Scholar
  13. Lauga E, Brenner MP, Stone HA (2005) Microfluidics: the no-slip boundary condition. In: Foss J, Tropea C, Yarin A (eds) Handbook of experimental fluid dynamics. Springer, BerlinGoogle Scholar
  14. Luchini P, Manzo F, Pozzi A (1991) Resistance of a grooved surface to parallel flow and cross-flow. J Fluid Mech 228:87–109zbMATHGoogle Scholar
  15. Navier M (1823) Mémoire sur les lois du mouvement des fluides. Mémoires de l’Académie royale des Sciences de l’Institut de France 6:389–440Google Scholar
  16. Philip JR (1972) Integral properties of flows satisfying mixed no-slip and no-shear conditions. Z Angew Math Phys (ZAMP) 23(6):960–968zbMATHMathSciNetCrossRefGoogle Scholar
  17. Pironneau O, Arumugam G (1989) On riblets in laminar flows. Control Bound Stab 125:51–65MathSciNetCrossRefGoogle Scholar
  18. Richardson S (1971) A model for the boundary condition of a porous material. Part 2. J Fluid Mech 49:327–336zbMATHCrossRefGoogle Scholar
  19. Richardson S (1973) On the no-slip boundary condition. J Fluid Mech 59:707–719zbMATHCrossRefGoogle Scholar
  20. Rothstein JP (2010) Slip on superhydrophobic surfaces. Ann Rev Fluid Mech 42(1):89–109CrossRefGoogle Scholar
  21. Schönecker C, Hardt S (2013) Longitudinal and transverse flow over a cavity containing a second immiscible fluid. J Fluid Mech 717:376–394zbMATHMathSciNetCrossRefGoogle Scholar
  22. 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 740:168–195MathSciNetCrossRefGoogle Scholar
  23. Solomon B, Khalil K, Varanasi K (2013) H7.00005: Lubricant-impregnated surfaces for drag reduction in viscous laminar flow. In: 66th Annual Meeting of the APS Division of Fluid Dynamics, Session H7: Microfluids: Interfaces and Wetting II, Pittsburgh, Pennsylvania, vol 58Google Scholar
  24. Steinberger A, Cottin-Bizonne C, Kleimann P, Charlaix E (2007) High friction on a bubble mattress. Nat Mater 6:665–668CrossRefGoogle Scholar
  25. Wong TS, Kang SH, Tang SKY, Smythe EJ, Hatton BD, Grinthal A, Aizenberg J (2011) Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity. Nature 477(7365):443–447CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Max Planck Institute for Polymer ResearchMainzGermany
  2. 2.Institute for Nano- and MicrofluidicsTU DarmstadtDarmstadtGermany

Personalised recommendations