Massive radius-dependent flow slippage in carbon nanotubes


Measurements and simulations have found that water moves through carbon nanotubes at exceptionally high rates owing to nearly frictionless interfaces1,2,3,4. These observations have stimulated interest in nanotube-based membranes for applications including desalination, nano-filtration and energy harvesting5,6,7,8,9,10, yet the exact mechanisms of water transport inside the nanotubes and at the water–carbon interface continue to be debated11,12 because existing theories do not provide a satisfactory explanation for the limited number of experimental results available so far13. This lack of experimental results arises because, even though controlled and systematic studies have explored transport through individual nanotubes7,8,9,14,15,16,17, none has met the considerable technical challenge of unambiguously measuring the permeability of a single nanotube11. Here we show that the pressure-driven flow rate through individual nanotubes can be determined with unprecedented sensitivity and without dyes from the hydrodynamics of water jets as they emerge from single nanotubes into a surrounding fluid. Our measurements reveal unexpectedly large and radius-dependent surface slippage in carbon nanotubes, and no slippage in boron nitride nanotubes that are crystallographically similar to carbon nanotubes, but electronically different. This pronounced contrast between the two systems must originate from subtle differences in the atomic-scale details of their solid–liquid interfaces, illustrating that nanofluidics is the frontier at which the continuum picture of fluid mechanics meets the atomic nature of matter.

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Figure 1: Nanojet experimental set-up.
Figure 2: Measurement of Landau–Squire flows driven from nanotubes.
Figure 3: Permeability and slip length of individual CNTs and BNNTs.


  1. 1

    Hummer, G., Rasaiah, J. C. & Noworyta, J. P. Water conduction through the hydrophobic channel of a carbon nanotube. Nature 414, 188–190 (2001)

    ADS  CAS  Article  Google Scholar 

  2. 2

    Majumder, M., Chopra, N., Andrews, R. & Hinds, B. J. Nanoscale hydrodynamics: enhanced flow in carbon nanotubes. Nature 438, 44 (2005); erratum 438, 930 (2005)

    ADS  CAS  Article  Google Scholar 

  3. 3

    Holt, J. K. et al. Fast mass transport through sub-2-nanometer carbon nanotubes. Science 312, 1034–1037 (2006)

    ADS  CAS  Article  Google Scholar 

  4. 4

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

    ADS  CAS  Article  Google Scholar 

  5. 5

    Nair, R. R., Wu, H. A., Jayaram, P. N., Grigorieva, I. V. & Geim, A. K. Unimpeded permeation of water through helium-leak-tight graphene-based membranes. Science 335, 442–444 (2012)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Joshi, R. K. et al. Precise and ultrafast molecular sieving through graphene oxide membranes. Science 343, 752–754 (2014)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Park, H. G. & Jung, Y. Carbon nanofluidics of rapid water transport for energy applications. Chem. Soc. Rev. 43, 565–576 (2014)

    CAS  Article  Google Scholar 

  8. 8

    Liu, H. et al. Translocation of single stranded DNA through single-walled carbon nanotubes. Science 327, 64–67 (2010)

    ADS  CAS  Article  Google Scholar 

  9. 9

    Siria, A. et al. Giant osmotic energy conversion measured in a single transmembrane boron nitride nanotube. Nature 494, 455–458 (2013)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Geng, J. et al. Stochastic transport through carbon nanotubes in lipid bilayers and live cell membranes. Nature 514, 612–615 (2014)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Guo, S., Meshot, E. R., Kuykendall, T., Cabrini, S. & Fornasiero, F. Nanofluidic transport through isolated carbon nanotube channels: advances, controversies, and challenges. Adv. Mater. 27, 5726–5737 (2015)

    CAS  Article  Google Scholar 

  12. 12

    Whitby, M. & Quirke, N. Fluid flow in carbon nanotubes and nanopipes. Nat. Nanotechnol. 2, 87–94 (2007)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Bocquet, L. & Charlaix, E. Nanofluidics, from bulk to interfaces. Chem. Soc. Rev. 39, 1073–1095 (2010)

    CAS  Article  Google Scholar 

  14. 14

    Lee, C. Y., Choi, W., Han, J.-H. & Strano, M. S. Coherence resonance in a single-walled carbon nanotube ion channel. Science 329, 1320–1324 (2010)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Secchi, E., Niguès, A., Jubin, L., Siria, A. & Bocquet, L. Scaling behavior for ionic transport and its fluctuations in individual carbon nanotubes. Phys. Rev. Lett. 116, 154501 (2016)

    ADS  Article  Google Scholar 

  16. 16

    Qin, X., Yuan, Q., Zhao, Y., Xie, S. & Liu, Z. Measurement of the rate of water translocation through carbon nanotubes. Nano Lett. 11, 2173–2177 (2011)

    ADS  CAS  Google Scholar 

  17. 17

    Lorenz, U. & Zewail, A. Observing liquid flow in nanotubes by 4D electron microscopy. Science 344, 1496–1500 (2014)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Laohakunakorn, N. et al. A Landau–Squire nanojet. Nano Lett. 13, 5141–5146 (2013)

    ADS  CAS  Article  Google Scholar 

  19. 19

    Eggers, J. & Villermaux, E. Physics of liquid jets. Rep. Prog. Phys. 71, 036601 (2008)

    ADS  Article  Google Scholar 

  20. 20

    Landau, L. D. & Lifshitz, E. M. Fluid Mechanics Vol. 6 of Course of Theoretical Physics 81–83 (Pergamon, 1959)

  21. 21

    Squire, H. B. The round laminar jet. Q. J. Mech. Appl. Math. 4, 321–329 (1951)

    MathSciNet  Article  Google Scholar 

  22. 22

    Thomas, J. A. & McGaughey, A. J. H. Reassessing fast water transport through carbon nanotubes. Nano Lett. 8, 2788–2793 (2008)

    ADS  Article  Google Scholar 

  23. 23

    Falk, K., Sedlmeier, F., Joly, L., Netz, R. R. & Bocquet, L. Molecular origin of fast water transport in carbon nanotube membranes: superlubricity versus curvature dependent friction. Nano Lett. 10, 4067–4073 (2010)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Sampson, R. A. On Stokes’s current function. Phil. Trans. R. Soc. A 182, 449–518 (1891)

    ADS  Article  Google Scholar 

  25. 25

    Mattia, D., Leese, H. & Lee, K. P. Carbon nanotube membranes: from flow enhancement to permeability. J. Membr. Sci. 475, 266–272 (2015)

    CAS  Article  Google Scholar 

  26. 26

    Maali, A., Cohen-Bouhacina, T. & Kellay, H. Measurement of the slip length of water flow on graphite surface. Appl. Phys. Lett. 92, 053101 (2008)

    ADS  Article  Google Scholar 

  27. 27

    Suk, M. E., Raghunathan, A. V. & Aluru, N. R. Fast reverse osmosis using boron nitride and carbon nanotubes. Appl. Phys. Lett. 92, 133120 (2008)

    ADS  Article  Google Scholar 

  28. 28

    Hilder, T. A., Gordon, D. & Chung, S.-H. Salt rejection and water transport through boron nitride nanotubes. Small 5, 2183–2190 (2009)

    CAS  Article  Google Scholar 

  29. 29

    Tocci, G., Joly, L. & Michaelides, A. Friction of water on graphene and hexagonal boron nitride from ab initio methods: very different slippage despite very similar interface structures. Nano Lett. 14, 6872–6877 (2014)

    ADS  Article  Google Scholar 

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L.B. and A.S. thank U. Keyser for discussions. E.S., A.N., S.M. and A.S. acknowledge funding from the European Union’s H2020 Framework Programme/ERC Starting Grant agreement number 637748 — NanoSOFT. L.B. and D.S. acknowledge support from the European Union’s FP7 Framework Programme/ERC Advanced Grant Micromegas. S.M. acknowledges funding from a J.-P. Aguilar grant. L.B. acknowledges funding from a PSL chair of excellence. We acknowledge funding from ANR project BlueEnergy.

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L.B. and A.S. conceived and directed the research. A.N. and A.S. designed and fabricated the nanotube devices. E.S and D.S. designed the fluidic cell. E.S. performed the measurements. The data were analysed by E.S., S.M. and L.B.; S.M. conducted the numerical analysis with input from the other authors. All authors contributed to the scientific discussions and the preparation of the manuscript.

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Correspondence to Alessandro Siria or Lydéric Bocquet.

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The authors declare no competing financial interests.

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Reviewer Information

Nature thanks J. Eijkel and A. Michaelides for their contribution to the peer review of this work.

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Supplementary Information

This file contains Supplementary Methods, Supplementary Figures 1-29, Supplementary Tables 1-3 and additional references (see Contents for more details). (PDF 8018 kb)


This video shows the insertion and sealing procedure of a BNNT inside a nanocapillary. (MP4 24252 kb)

Insertion and sealing procedure of a BNNT

This video shows the insertion and sealing procedure of a BNNT inside a nanocapillary. (MP4 24252 kb)

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Secchi, E., Marbach, S., Niguès, A. et al. Massive radius-dependent flow slippage in carbon nanotubes. Nature 537, 210–213 (2016).

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