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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: lyderic.bocquet@lps.ens.fr
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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
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Copyright
© 2017 Cambridge University Press 

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