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Why are slip lengths so large in carbon nanotubes?

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Abstract

A possible explanation for the enhanced flow in carbon nanotubes is given using a mathematical model that includes a depletion layer with reduced viscosity near the wall. In the limit of large tubes the model predicts no noticeable enhancement. For smaller tubes the model predicts enhancement that increases as the radius decreases. An analogy between the reduced viscosity and slip-length models shows that the term slip-length is misleading and that on surfaces which are smooth at the nanoscale it may be thought of as a length-scale associated with the size of the depletion region and viscosity ratio. The model therefore provides a physical interpretation of the classical Navier slip condition and explains why ‘slip-lengths’ may be greater than the tube radius.

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References

  • Alexeyev AA, Vinogradova OI (1996) Flow of a liquid in a nonuniformly hydrophobized capillary. Colloids Surf A: Physicochem 108:173–179

    Article  Google Scholar 

  • Barrat J-L, Bocquet L (1999) Influence of wetting properties on hydrodynamic boundary conditions at a fluid/solid interface. Faraday Discuss 112:119–27

    Article  Google Scholar 

  • Bhushan B (ed) (2008) Springer handbook of nanotechnology. Springer, Berlin

    Google Scholar 

  • Choi C-H, Westin JA, Breuer KS (2003) Apparent slip flows in hydrophilic and hydrophobic microchannels. Phys Fluids 15(10):2897–2902

    Article  Google Scholar 

  • Cottin-Bizonne C, Cross B, Steinberger A, Charlaix E (2005) Boundary slip on smooth hydrophobic surfaces: intrinsic effects and possible artifacts. Phys Rev Lett 94:056102

    Article  Google Scholar 

  • de Gennes PG (2002) On fluid/wall slippage. Langmuir 18:3413–3414

    Article  Google Scholar 

  • Denn MM (2001) Extrusion instabilities and wall slip. Annu Rev Fluid Mech 33:265–87

    Article  Google Scholar 

  • Eijkel JCT, van den Berg A (2005) Nanofluidics: what is it and what can we expect from it? Microfluid Nanofluid 1:249–267. doi:10.1007/s10404-004-0012-9

    Article  Google Scholar 

  • Holt JK, Park HG, Wang Y, Stadermann M, Artyukhin AB, Grigoropoulos CP, Noy A, Bakajin O (2006) Fast mass transport through sub-2-nanometer carbon nanotubes. Science 312:1034. doi:10.1126/science.1126298

    Article  Google Scholar 

  • Hummer G, Rasaiah JC, Noworyta JP (2001) Water conduction through the hydrophobic channel of a carbon nanotube. Nature 414(8):188–190

    Google Scholar 

  • Joseph S, Aluru NR (2008) Why are carbon nanotubes fast transporters of water. Nano Lett 8(2):452–458

    Article  Google Scholar 

  • Majumder M, Chopra N, Andrews R, Hinds BJ (2005) Enhanced flow in carbon nanotubes. Nat Biotechnol 438:44

    Google Scholar 

  • Matthews MT, Hill JM (2008) Nanofluidics and the Navier boundary condition. Int J Nanotechnol 5(2/3):218–242

    Google Scholar 

  • Mattia D, Gogotsi Y (2008) Review: static and dynamic behavior of liquids inside carbon nanotubes. Microfluid Nanofluid 5:289–305. doi:10.1007/s10404-008-0293-5

    Article  Google Scholar 

  • Myers TG (1998) Thin films with high surface tension. SIAM Rev 40(3):441–462

    Article  MATH  MathSciNet  Google Scholar 

  • Myers TG (2002) Modeling laminar sheet flow over rough surfaces. Water Resour Res 38:1230. doi:10.1029/2000WR000154

    Article  Google Scholar 

  • Myers TG (2005) Application of non-Newtonian models to thin film flow. Phys Rev E 72:066302

    Article  MathSciNet  Google Scholar 

  • Neto C, Evans DR, Bonaccurso E, Butt H-J, Craig VSJ (2005) Boundary slip in Newtonian liquids: a review of experimental studies. Rep Prog Phys 68:2859–2897

    Article  Google Scholar 

  • Noya A et al (2007) Nanofluidics in carbon nanotubes. Nano Today 2(6):22–29

    Article  Google Scholar 

  • O’Donovan EJ, Tanner RI (1984) Numerical study of the Bingham squeeze film problem. J Non-Newton Fluid Mech 15:75–83

    Article  MATH  Google Scholar 

  • Orikasa H, Inokuma N, Okubo S, Kitakami O, Kyotani T (2006) Template synthesis of water-dispersible carbon nano ‘test tubes’ without any post-treatment. Chem Mater 18:1036–1040

    Article  Google Scholar 

  • Poynor A, Hong L, Robinson IK, Granick S (2006) How water meets a hydrophobic surface. Phys Rev Lett 97:266101-1–266101-4

    Article  Google Scholar 

  • Pozhar LA (2000) Structure and dynamics of nanofluids: theory and simulations to calculate viscosity. Phys Rev E 61(2):1432–1446

    Article  Google Scholar 

  • Qian T, Wang X-P, Sheng P (2004) Power-law slip profile of the moving contact line in two-phase immiscible flows. Phys Rev Lett 93(9):094501. doi:10.1103/PhysRevLett.93.094501

    Article  Google Scholar 

  • Ruckenstein E, Rajora P (1983) On the no-slip boundary condition of hydrodynamics. J Colloid Interface Sci 96(2):488–491

    Article  Google Scholar 

  • Thomas JA, McGaughey AJH (2008a) Reassessing fast water transport through carbon nanotubes. Nano Lett 8(9):2788–2793

    Article  Google Scholar 

  • Thomas JA, McGaughey AJH (2008b) Density, distribution, and orientation of water molecules inside and outside carbon nanotubes. J Chem Phys 128:084715. doi:10.1063/1.2837297

    Article  Google Scholar 

  • Travis KP, Todd BD, Evans DJ (1997) Departure from Navier-Stokes hydrodynamics in confined liquids. Phys Rev E 55(4):4288–4295

    Article  Google Scholar 

  • Tretheway DC, Meinhart CD (2002) Apparent fluid slip at hydrophobic microchannel walls. Phys Fluids 14(3):L9–12

    Article  Google Scholar 

  • Verdaguer A, Sacha GM, Bluhm H, Salmeron M (2006) Molecular structure of water at interfaces: wetting at the nanometer scale. Chem Rev 106:1478–1510

    Article  Google Scholar 

  • Verweij H, Schillo MC, Li J (2007) Fast mass transport through carbon nanotube membranes. Small 3(12):1996–2004. doi:10.1002/smll.200700368

    Article  Google Scholar 

  • Vinogradova OI (1995) Coagulation of hydrophobic and hydrophilic solids under dynamic conditions. J Colloid Interface Sci 169:306–12

    Article  Google Scholar 

  • Vinogradova OI (1999) Slippage of water over hydrophobic surfaces. Int J Miner Process 56:31–60

    Article  Google Scholar 

  • Whitby M, Cagnon L, Thanou M, Quirke N (2008) Enhanced fluid flow through nanoscale carbon pipes. Nano Lett 8(9):2632–2637

    Article  Google Scholar 

  • White FM (1991) Viscous fluid flow. McGraw-Hill, New York

    Google Scholar 

  • Werder T et al (2001) Molecular dynamics simulation of contact angles of water droplets in carbon nanotubes. Nano Lett 1:697–702

    Article  Google Scholar 

  • Zhu Y, Granick S (2001) Rate-dependent slip of Newtonian liquids at smooth surfaces. Phys Rev Lett 87:96105

    Article  Google Scholar 

Download references

Acknowledgments

TM gratefully acknowledges the support of this research through the Marie Curie International Reintegration Grant Industrial applications of moving boundary problems, grant no. FP7—256417 and partial support by the project 2009-SGR-345 from AGAUR-Generalitat de Catalunya.

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  1. Centre de Recerca Matemática, Campus de Bellaterra, Edifici C, 08193, Bellaterra, Barcelona, Spain

    Tim G. Myers

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  1. Tim G. Myers
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Correspondence to Tim G. Myers.

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Myers, T.G. Why are slip lengths so large in carbon nanotubes?. Microfluid Nanofluid 10, 1141–1145 (2011). https://doi.org/10.1007/s10404-010-0752-7

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  • DOI: https://doi.org/10.1007/s10404-010-0752-7

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