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The holy grail of microfluidics: sub-laminar drag by layout of periodically embedded microgrooves


The sub-laminar drag effect of microgroove surfaces was studied numerically in a steady two-dimensional channel flow at subcritical Reynolds numbers. Considerations are restricted to grooves of a few viscous length scales in depth, which are assumed not to promote the laminar to turbulent transition process. It was found that the drag reduction effect is due to the layout of grooves with respect to the flow direction and contour geometry. Results of computations show that for grooves of curved contour placed normal to the flow direction, drag arising from viscous and pressure forces is modulated due to the functional dependence of forces on the surface area projected in the flow direction. Such a groove layout leads to a large skin-friction reduction, but a comparable increase in pressure drag results in sub-laminar drag if drag over flat surface is considered as a reference. For a curved groove contour, the drag reduction increases with increasing Reynolds number and reaches about 5 % at Reynolds numbers approaching critical.

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  • Alireza M, Floryan JM (2011) Flow in grooved micro-channels. In: Proceedings of the seventh symposium on turbulence and shear flow phenomena (, Ottawa, Canada

  • Choi H, Moin P, Kim J (1991) On the effect of riblets in fully developed laminar channel flow. Phys Fluids 3:1892

    Article  MATH  Google Scholar 

  • Choi H, Moin P, Kim J (1993) Direct numerical simulation of turbulent flow over riblets. J Fluid Mech 255:503–539

    MathSciNet  Article  MATH  Google Scholar 

  • Comet-Version 2.00 User Manual (2001) Institute of Computational Continuum Mechanics, Hamburg

  • Daschiel G (2010) Sub-laminar drag in a two-dimensional channel flow. Diplomarbeit, Institute of Fluid Mechanics, University Erlangen-Nuremberg

  • Djenidi L, Anselmet F, Liandrat J, Fulachier L (1994) Laminar boundary layer over riblets. Phys Fluids 6:2993–3000

    Article  Google Scholar 

  • Dovgal AV, Levchenko V Y, Timofeev V A (1989) Boundary layer control by local heating of the wall. In: Arnal D, Michael R (eds) Laminar-turbulent transition. Springer, Berlin, pp 193–121

  • Ferzinger JH, Perić M (2001) Computational methods for fluid dynamics, 3rd edn. Springer, Berlin

  • Friedmann E (2010) The optimal shape of riblets in the viscous sublayer. J Math Fluid Mech 12:243–265

    MathSciNet  Article  MATH  Google Scholar 

  • Gad-el-Haak M (2000) Flow control: passive, active and reactive flow management. Cambridge University Press, Cambridge

  • Garimella G (2009) Personal communication. Technische Universität Darmstadt

  • Gatski TB, Grosch CE (1985) Embedded cavity drag in steady laminar flow. AIAA J 23:1028–1037

    Article  MATH  Google Scholar 

  • Ghaddar NK, Korczak KZ, Mikić BB, Patera AT (1986) Numerical investigation of incompressible flow in grooved channels. Part 1. Stability and self-sustained oscillations. J Fluid Mech 163:99–127

    MathSciNet  Article  Google Scholar 

  • Hage W (2005) Zur Widerstandsverminderung von dreidimensionalen Riblet-Strukturen und anderen Oberflähen. Mensch and Buch Verlag

  • Jovanović J, Frohnapfel B, Srikantharajah R, Jovanović Dj, Linhart H, Delgado A (2011) Microflow-based control of near-wall fluctuations for large viscous drag reduction. Microfluids Nanofluids 11:733-780

    Google Scholar 

  • Jung YC, Bhushan B (2010) Biomimetic structures for fluid drag reduction in laminar and turbulent flows. J Phys Condens Matter 22:1–9

    Google Scholar 

  • Lang AW, Johnson TJ (2010) Drag reduction over embedded cavities in Couette flow. Mech Res Commun 37:432–435

    Article  MATH  Google Scholar 

  • Lammers P, Jovanović J, Durst F (2006) Numerical experiments on wall turbulence at low Reynolds numbers. J Thermal Sci 10:33–62

    Article  Google Scholar 

  • Lumley JL (1977) Drag reduction in two phase flows. Phys Fluids 20:64–71

    Article  Google Scholar 

  • Metzner AB (1977) Polymer solution and fiber suspension rheology and their relationship to turbulent drag reduction. Phys Fluids 20:145–149

    Article  Google Scholar 

  • Pfenninger W (1961) Transition experiments in the inlet length of tubes at high Reynolds numbers. In: Lachmann Gv (ed) Boundary layer and flow control, vol 2. Oxford University Press, Oxford, pp 970–980

  • Schlichting H (1968) Boundary-layer theory, 6th edn. Mc-Graw Hill, New York

  • Scholle M, Rund H, Aksel N (2005) Drag reduction and improvement of material transport. Arch Appl Mech 75:93–112

    Article  Google Scholar 

  • Sternberg J (1952) A free-flight investigations of the possibility of high Reynolds number supersonic boundary layers. J Aeronaut Sci 19:721–733

    Article  Google Scholar 

  • Toms BA (1949) Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. Proceedings of international congress on rheology, vol 2. North-Holland, Amsterdam, pp 135–141

  • Walsh MJ (1983) Riblets as a drag reduction technique. AIAA 21:485

    Article  Google Scholar 

  • Zakin JL, Lu B, Bewersdorff HW (1998) Surfactant drag reduction. Rev Chem Eng 14:253–320

    Article  Google Scholar 

Download references


This work was initially sponsored by grant Jo 240/5-3. Additional support was obtained from the the Center for Smart Interfaces at the Technische Universität Darmstadt and from the Cluster of Excellence Engineering of Advanced Materials at the University of Erlangen-Nuremberg. In the later stages, the work received support from grant FR 2823/2-1. All fundings were provided by the German Research Foundation (DFG).

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Correspondence to Jovan Jovanović.

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Daschiel, G., Perić, M., Jovanović, J. et al. The holy grail of microfluidics: sub-laminar drag by layout of periodically embedded microgrooves. Microfluid Nanofluid 15, 675–687 (2013).

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  • Viscous drag reduction
  • Drag reduction surfaces
  • Flow control
  • Viscous flow
  • Wall-bounded flows