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The Landau–Squire plume

Published online by Cambridge University Press:  02 August 2017

Eleonora Secchi
Affiliation:
Laboratoire de Physique Statistique, Ecole Normale Supérieure, PSL Research University, 24 rue Lhomond, 75005 Paris, France
Sophie Marbach
Affiliation:
Laboratoire de Physique Statistique, Ecole Normale Supérieure, PSL Research University, 24 rue Lhomond, 75005 Paris, France
Antoine Niguès
Affiliation:
Laboratoire de Physique Statistique, Ecole Normale Supérieure, PSL Research University, 24 rue Lhomond, 75005 Paris, France
Alessandro Siria
Affiliation:
Laboratoire de Physique Statistique, Ecole Normale Supérieure, PSL Research University, 24 rue Lhomond, 75005 Paris, France
Lydéric Bocquet*
Affiliation:
Laboratoire de Physique Statistique, Ecole Normale Supérieure, PSL Research University, 24 rue Lhomond, 75005 Paris, France
*
Email address for correspondence: lyderic.bocquet@lps.ens.fr

Abstract

In this paper, we analyse the dispersion of a dye by a Landau–Squire plume, generated by a jet flow emerging from a nanocapillary into a reservoir. We demonstrate analytically that the dye concentration profile exhibits a long-range profile decaying as the inverse of the distance to the origin, whereas the plume shape is only a function of a Péclet number defined in terms of the flow characteristics inside the nanocapillary. These predictions are successfully compared with experiments on fluorescent dye dispersion from nanocapillaries under pressure-driven flow. The plume shape allows extraction of the nanojet force characterizing the Landau–Squire velocity profile for a given pressure drop, with results in full agreement with direct velocimetry measurements and finite-element calculations. The peculiarities of the Landau–Squire plume make it a sensitive probe of the flow properties inside the seeding nanocapillary.

Type
Rapids
Copyright
© 2017 Cambridge University Press 

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References

Bocquet, L. & Tabeling, E. 2014 Physics and technological aspects of nanofluidics. Lab on a Chip 14, 31433158.CrossRefGoogle ScholarPubMed
Branton, D., Deamer, D. W., Marziali, A., Bayley, H., Benner, S. A., Butler, T., Di Ventra, M., Garaj, S., Hibbs, A., Huang, X. et al. 2008 The potential and challenges of nanopore sequencing. Nat. Biotechnol. 26, 11461153.CrossRefGoogle ScholarPubMed
Culbertson, C. T., Jacobson, S. C. & Ramsey, J. M. 2002 Diffusion coefficient measurements in microfluidic devices. Talanta 56 (2), 365373.CrossRefGoogle ScholarPubMed
Feng, J., Graf, M., Liu, K., Ovchinnikov, D., Dumcenco, D., Heiranian, M., Nandigana, V., Aluru, N. R., Kis, A. & Radenovic, A. 2016 Single-layer MoS2 nanopores as nanopower generators. Nature 536, 197200.CrossRefGoogle ScholarPubMed
Geng, J., Kim, K., Zhang, J., Escalada, A., Tunuguntla, R., Comolli, L. R., Allen, F. I., Shnyrova, A. V., Cho, K. R., Munoz, D. et al. 2014 Stochastic transport through carbon nanotubes in lipid bilayers and live cell membranes. Nature 514 (7524), 612615.CrossRefGoogle ScholarPubMed
Joshi, R. K., Carbone, P., Wang, F.-C., Kravets, V. G., Su, Y., Grigorieva, I. V., Wu, H. A., Geim, A. K. & Nair, R. R. 2014 Precise and ultrafast molecular sieving through graphene oxide membranes. Science 343 (6172), 752754.CrossRefGoogle ScholarPubMed
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics, chap. 2, pp. 81–83. Course of Theoretical Physics, vol. 6. Pergamon.Google Scholar
Laohakunakorn, N., Gollnick, B., Moreno-Herrero, F., Aarts, D., Dullens, R., Ghosal, S. & Keyser, U. 2013 A Landau–Squire nanojet. Nano Lett. 13 (11), 51415146.CrossRefGoogle ScholarPubMed
Park, H. G. & Jung, Y. 2014 Carbon nanofluidics of rapid water transport for energy applications. Chem. Soc. Rev. 43 (2), 565576.CrossRefGoogle ScholarPubMed
Secchi, E., Nigues, A., Jubin, L., Siria, A. & Bocquet, L. 2016 Scaling behavior for ionic transport and its fluctuations in individual carbon nanotubes. Phys. Rev. Lett. 116, 154501.CrossRefGoogle ScholarPubMed
Secchi, E., Marbach, S., Nigues, A., Siria, A. & Bocquet, L. 2016 Massive radius-dependent flow slippage in carbon nanotubes. Nature 537, 210213.CrossRefGoogle ScholarPubMed
Siria, A., Poncharal, P., Biance, A.-L., Fulcrand, R., Blase, X., Purcell, S. T. & Bocquet, L. 2013 Giant osmotic energy conversion measured in a single transmembrane boron nitride nanotube. Nature 494 (7438), 455458.CrossRefGoogle Scholar
Squire, H. B. 1951 The round laminar jet. Q. J. Mech. Appl. Maths 4 (3), 321329.CrossRefGoogle Scholar
Stein, D. 2015 Nanopore sequencing: forcing improved resolution. Biophys. J. 109, 20012002.CrossRefGoogle ScholarPubMed
Werber, J. R., Osuji, C. O. & Elimelech, M. 2016 Materials for next-generation desalination and water purification membranes. Nat. Rev. Mater. 1, 16018.CrossRefGoogle Scholar
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