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Boundary layer of elastic turbulence

Published online by Cambridge University Press:  21 September 2018

S. Belan Open the ORCID record for S. Belan [Opens in a new window] ,
A. Chernykh  and
V. Lebedev
S. Belan*
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
A. Chernykh
Affiliation:
Institute of Automation and Electrometry SB RAS, 630090, Academician Koptyug ave. 1, Novosibirsk, Russia Novosibirsk State University, 630073, Prospekt K. Marksa 20, Novosibirsk, Russia
V. Lebedev
Affiliation:
Landau Institute for Theoretical Physics RAS, 142432, Ak. Semenova 1-A, Chernogolovka, Moscow region, Russia Higher School of Economics, 101000, Myasnitskaya 20, Moscow, Russia
*
†Email address for correspondence: sergb27@yandex.ru
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Abstract

We investigate theoretically the near-wall region in elastic turbulence of a dilute polymer solution in the limit of large Weissenberg number. As has been established experimentally, elastic turbulence possesses a boundary layer where the fluid velocity field can be approximated by a steady shear flow with relatively small fluctuations on the top of it. Assuming that at the bottom of the boundary layer the dissolved polymers can be considered as passive objects, we examine analytically and numerically the statistics of the polymer conformation, which is highly non-uniform in the wall-normal direction. Next, imposing the condition that the passive regime terminates at the border of the boundary layer, we obtain an estimate for the ratio of the mean flow to the magnitude of the flow fluctuations. This ratio is determined by the polymer concentration, the radius of gyration of polymers and their length in the fully extended state. The results of our asymptotic analysis reproduce the qualitative features of elastic turbulence at finite Weissenberg numbers.

JFM classification

Complex Fluids: Complex Fluids Low-Reynolds-number flows: Low-Reynolds-number flows Non-Newtonian Flows: Polymers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 855 , 25 November 2018 , pp. 910 - 921
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Copyright
© 2018 Cambridge University Press 

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