Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-09T07:37:37.406Z Has data issue: false hasContentIssue false
  • English
  • Français

The Landau–Squire plume

Published online by Cambridge University Press:  02 August 2017

Eleonora Secchi ,
Sophie Marbach ,
Antoine Niguès ,
Alessandro Siria  and
Lydéric Bocquet Open the ORCID record for Lydéric Bocquet [Opens in a new window]
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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

JFM classification

Wakes/Jets: Jets Low-Reynolds-number flows: Low-Reynolds-number flows Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 826 , 10 September 2017 , R3
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bocquet, L. & Tabeling, E. 2014 Physics and technological aspects of nanofluidics. Lab on a Chip 14, 3143–3158.Google Scholar
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, 1146–1153.CrossRefGoogle ScholarPubMed
Culbertson, C. T., Jacobson, S. C. & Ramsey, J. M. 2002 Diffusion coefficient measurements in microfluidic devices. Talanta 56 (2), 365–373.Google Scholar
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, 197–200.Google Scholar
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), 612–615.Google Scholar
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), 752–754.Google Scholar
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), 5141–5146.CrossRefGoogle ScholarPubMed
Park, H. G. & Jung, Y. 2014 Carbon nanofluidics of rapid water transport for energy applications. Chem. Soc. Rev. 43 (2), 565–576.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.Google Scholar
Secchi, E., Marbach, S., Nigues, A., Siria, A. & Bocquet, L. 2016 Massive radius-dependent flow slippage in carbon nanotubes. Nature 537, 210–213.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), 455–458.Google Scholar
Squire, H. B. 1951 The round laminar jet. Q. J. Mech. Appl. Maths 4 (3), 321–329.Google Scholar
Stein, D. 2015 Nanopore sequencing: forcing improved resolution. Biophys. J. 109, 2001–2002.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.Google Scholar