Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Progress Article
  • Published:

Slippery questions about complex fluids flowing past solids

Abstract

Viscous flow is familiar and useful, yet the underlying physics is surprisingly subtle and complex. Recent experiments and simulations show that the textbook assumption of 'no slip at the boundary' can fail greatly when walls are sufficiently smooth. The reasons for this seem to involve materials chemistry interactions that can be controlled — especially wettability and the presence of trace impurities, even of dissolved gases. To discover what boundary condition is appropriate for solving continuum equations requires investigation of microscopic particulars. Here, we draw attention to unresolved topics of investigation and to the potential to capitalize on 'slip at the wall' for purposes of materials engineering.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Blowing a surface clean of dust particles.
Figure 4: Influence of wall roughness on flow past partially wetted surfaces.
Figure 5: Illustration that deviations from the traditional no-slip boundary condition depend systematically on surface roughness.
Figure 6: Illustration that the onset of 'slip' depends on dissolved gas, when simple newtonian fluids flow past atomically smooth surfaces, either wetted or partially wetted.
Figure 7: Illustration of what happens when contact of a water droplet with a solid surface is minimized by making the surface very rough.

Photo courtesy of Aurélie Lafuma and David Quéré, Collège de France, Paris.

Figure 2: Surface roughness promotes stick.
Figure 3: Slip of fluid past a surface can be apparent or real.

Similar content being viewed by others

References

  1. Massey, B.S. Mechanics of Fluids 6th edn Section 5.6 (Chapman and Hall, London 1989).

    Google Scholar 

  2. Goldstein, S. Mechanics of Fluids Vol. II 677–680 (Clarendon, Oxford, 1938).

    Google Scholar 

  3. Vinogradova, O.I. Slippage of water over hydrophobic surfaces. Int. J. Miner. Process 56, 31–60 (1999).

    Article  CAS  Google Scholar 

  4. Schowalter, W.R. The behavior of complex fluids at solid boundaries. J. Non-Newton. Fluid 29, 25–36 (1988).

    Article  CAS  Google Scholar 

  5. Léger, L., Raphael, E. & Hervet, H. Surface-anchored polymer chains: their role in adhesion and friction. Adv. Polym. Sci. 138, 185–225 (1999).

    Article  Google Scholar 

  6. Denn, M.M. Extrusion instabilities and wall slip. Annu. Rev. Fluid Mech. 33, 265–287 (2001).

    Article  Google Scholar 

  7. Debye, P. & Cleland, R.L. Flow of liquid hydrocarbons in porous Vycor. J. Appl. Phys. 30, 843–49 (1958).

    Article  Google Scholar 

  8. Ruckenstein, E. & Rajora, P. On the no-slip boundary condition of hydrodynamics. J. Colloid Interface Sci. 96, 488–493 (1983).

    Article  CAS  Google Scholar 

  9. Churaev, N.V., Sobolev, V.D. & Somov, A.N. Slippage of liquids over lyophobic solid surfaces. J. Colloid Interface Sci. 97, 574–581 (1984).

    Article  CAS  Google Scholar 

  10. Chan, D.Y.C. & Horn, R.G. The drainage of thin liquid films between solid surfaces. J. Chem. Phys. 83, 5311–5324 (1985).

    Article  CAS  Google Scholar 

  11. Israelachvili, J.N. Measurement of the viscosity of liquids in very thin films. J. Colloid Interface Sci. 110, 263–271 (1986).

    Article  CAS  Google Scholar 

  12. Georges, J.M., Millot, S., Loubet, J.L. & Tonck, A. Drainage of thin liquid-films between relatively smooth surfaces. J. Chem. Phys. 98, 7345–7360 (1993).

    Article  CAS  Google Scholar 

  13. Wein, O. & Tovchigrechko, V.V. Rotational viscometry under presence of apparent wall slip. J. Rheol. 36, 821–843 (1992).

    Article  CAS  Google Scholar 

  14. Barnes, H.A. A review of the slip (wall depletion) of polymer solutions, emulsions and particle suspensions in viscometers: its cause, character, and cure. J. Non-Newton. Fluid 56, 221–251 (1995).

    Article  CAS  Google Scholar 

  15. Achilleos, E.C., Georgiou, G. & Hatzikiriakos, S.G. Role of processing aids in the extrusion of molten polymers. J. Vinyl Addit. Technol. 8, 7–24 (2002).

    Article  CAS  Google Scholar 

  16. Noever, D.A. Diffusive slip and surface transport-properties. J. Colloid Interface Sci. 147, 186–191 (1991).

    Article  CAS  Google Scholar 

  17. Granick, S. Soft matter in a tight spot. Phys. Today 52, 26–31 (1999).

    Article  CAS  Google Scholar 

  18. Thompson, P.A. & Robbins, M.O. Shear flow near solids: epitaxial order and flow boundary condition. Phys. Rev. A 41, 6830–6839 (1990).

    Article  CAS  Google Scholar 

  19. Thompson, P.A. & Troian, S. A general boundary condition for liquid flow at solid surfaces. Nature 389, 360–362 (1997).

    Article  CAS  Google Scholar 

  20. Barrat, J.-L. & Bocquet, L. Large slip effect at a nonwetting fluid-solid interface. Phys. Rev. Lett. 82, 4671–4674 (1999).

    Article  CAS  Google Scholar 

  21. Brenner, H. & Ganesan, V. Molecular wall effects: are conditions at a boundary 'boundary conditions'? Phys. Rev. E. 61, 6879–6897 (2000).

    Article  CAS  Google Scholar 

  22. Gao, J., Luedtke, W.D. & Landman, U. Structures, solvation forces and shear of molecular films in a rough nano-confinement. Tribol. Lett. 9, 3–134 (2000).

    Article  CAS  Google Scholar 

  23. Denniston, C. & Robbins, M.O. Molecular and continuum boundary conditions for a miscible binary fluid. Phys. Rev. Lett. 87, 178302 (2001).

    Article  CAS  Google Scholar 

  24. Campbell, S.E., Luengo, G., Srdanov, V.I., Wudl, F. & Israelachvili, J.N. Very low viscosity at the solid-liquid interface induced by adsorbed C-60 monolayers. Nature 382, 520–522 (1996).

    Article  CAS  Google Scholar 

  25. Kiseleva, O.A., Sobolev, V.D. & Churaev, N.V. Slippage of the aqueous solutions of cetyltriimethylammonium bromide during flow in thin quartz capillaries. Colloid J. 61, 263–264 (1999).

    CAS  Google Scholar 

  26. Pit, R., Hervet, H. & Léger, L. Direct experimental evidence of slip in hexadecane-solid interfaces. Phys. Rev. Lett. 85, 980–983 (2000).

    Article  CAS  Google Scholar 

  27. Craig, V.S.J., Neto, C. & Williams, D.R.M. Shear-dependent boundary slip in aqueous Newtonian liquid. Phys. Rev. Lett. 87, 54504 (2001).

    Article  CAS  Google Scholar 

  28. Zhu, Y. & Granick, S. Rate-dependent slip of Newtonian liquid at smooth surfaces. Phys. Rev. Lett. 87, 096105 (2001).

    Article  CAS  Google Scholar 

  29. Zhu, Y. & Granick, S. Limits of the hydrodynamic no-slip boundary condition. Phys. Rev. Lett. 88, 106102 (2002).

    Article  Google Scholar 

  30. Zhu, Y. & Granick, S. Apparent slip of Newtonian fluids past adsorbed polymer layers. Macromolecules 36, 4658–4663 (2002).

    Article  Google Scholar 

  31. Zhu, Y. & Granick, S. The no slip boundary condition switches to partial slip when the fluid contains surfactant. Langmuir 18, 10058–10063 (2002).

    Article  CAS  Google Scholar 

  32. Bonaccurso, E., Kappl, M. & Butt, H.-J. Hydrodynamic force measurements: boundary slip of water on hydrophilic surfaces and electrokinetic effects. Phys. Rev. Lett. 88, 076103 (2002).

    Article  Google Scholar 

  33. Baudry, J., Charlaix, E., Tonck, A. & Mazuyer, D. Experimental evidence of a large slip effect at a nonwetting fluid-solid interface. Langmuir 17, 5232–5236 (2002).

    Article  Google Scholar 

  34. Tretheway, D.C. & Meinhart, C.D. Apparent fluid slip at hydrophobic microchannel walls. Phys. Fluids 14, L9–L12 (2002).

    Article  CAS  Google Scholar 

  35. Britton, M.M. & Callaghan, P.T. Two-phase shear band structures at uniform stress. Phys. Rev. Lett. 78, 4930–4933 (1997).

    Article  CAS  Google Scholar 

  36. Nye, J.F. A calculation on the sliding of ice over a wavy surface using a Newtonian viscous approximation. Proc. Roy. Soc. A 311, 445–467 (1969).

    Article  Google Scholar 

  37. Richardson, S. On the no-slip boundary condition. J. Fluid Mech. 59, 707–719 (1973).

    Article  Google Scholar 

  38. Jansons, K.M. Determination of the macroscopic (partial) slip boundary condition for a viscous flow over a randomly rough surface with a perfect slip microscopic boundary condition Phys. Fluids 31, 15–17 (1988).

    Article  Google Scholar 

  39. Spikes, H.A. The half-wetted bearing. Part 2: potential application to low load contacts. Proc. Inst. Mech. Eng. Part J 217, 15–26 (2003).

    Article  Google Scholar 

  40. de Gennes, P.-G. On fluid/wall slippage. Langmuir 18, 3413–3414 (2002).

    Article  CAS  Google Scholar 

  41. Tyrrell, J.W.G. & Attard, P. Atomic force microscope images of nanobubbles on a hydrophobic surface and corresponding force-separation data. Langmuir 18, 160–167 (2002).

    Article  CAS  Google Scholar 

  42. Ishida, N., Inoue, T., Miyahara, N. & Higashitani, K. Nano bubbles on a hydrophobic surface in water observed by tapping-mode atomic force microscopy. Langmuir 16, 6377–6380 (2000).

    Article  CAS  Google Scholar 

  43. Boehnke, U.C. et al. Partial air wetting on solvophobic surfaces in polar liquids. J. Colloid Interface Sci. 211, 243–251 (1999).

    Article  CAS  Google Scholar 

  44. Lum, K., Chandler, D. & Weeks, J.D. Hydrophobicity at small and large length scales. J. Phys. Chem. B 103, 4570–4577 (1999).

    Article  CAS  Google Scholar 

  45. Zhang, X., Zhu, Y. & Granick, S. Hydrophobicity at a Janus interface. Science 295, 663–666 (2002).

    Article  CAS  Google Scholar 

  46. Onda, T., Shibuichi, S., Satoh, N. & Tsuji, K. Super-water-repellent fractal surfaces. Langmuir 12, 2125–2127 (1996).

    Article  CAS  Google Scholar 

  47. Bico, J., Marzolin, C. & Quéré, D. Pearl drops. Europhys. Lett. 47, 220–226 (1999).

    Article  CAS  Google Scholar 

  48. Herminghaus, S. Roughness-induced non-wetting. Europhys. Lett. 52, 165–170 (2000).

    Article  Google Scholar 

  49. Watanabe, K., Udagawa, Y. & Udagawa, H. Drag reduction of Newtonian fluid in a circular pipe with a highly water-repellent wall. J. Fluid Mech. 381, 225–238 (1999).

    Article  CAS  Google Scholar 

  50. Bechert, D.W., Bruse, M., Hage, W. & Meyer, R. Fluid mechanics of biological surfaces and their technological application. Naturwissenschaften 87, 157–171 (2000).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

For discussions, we are indebted to John Brady, Michel Cloître, Jack Douglas, Steve Meeker, Hugh Spikes, Jan Vermant and Norman Wagner. This work was supported in part by a grant to H.L. by the postdoctoral fellowship program from Korea Science & Engineering Foundation (KOSEF). This work was supported by the U.S. Department of Energy, Division of Materials Science, under Award No. DEFG02-91ER45439 through the Frederick Seitz Materials Research Laboratory at the University of Illinois at Urbana-Champaign.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Steve Granick.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Granick, S., Zhu, Y. & Lee, H. Slippery questions about complex fluids flowing past solids. Nature Mater 2, 221–227 (2003). https://doi.org/10.1038/nmat854

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmat854

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing