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Dynamics of a macroscopic elastic fibre in a polymeric cellular flow

Published online by Cambridge University Press:  20 March 2017

Qiang Yang Open the ORCID record for Qiang Yang [Opens in a new window]  and
Lisa Fauci
Qiang Yang
Affiliation:
Department of Mathematics, Tulane University, New Orleans, LA 70118, USA
Lisa Fauci*
Affiliation:
Department of Mathematics, Tulane University, New Orleans, LA 70118, USA
*
†Email address for correspondence: fauci@tulane.edu
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Abstract

We study the dynamics and transport of an elastic fibre in a polymeric cellular flow. The macroscopic fibre is much larger than the infinitesimal immersed polymer coils distributed in the surrounding viscoelastic fluid. Here we consider low-Reynolds-number flow using the Navier–Stokes/Fene-P equations in a two-dimensional, doubly periodic domain. The macroscopic fibre supports both tensile and bending forces, and is fully coupled to the viscoelastic fluid using an immersed boundary framework. We examine the effects of fibre flexibility and polymeric relaxation times on fibre buckling and transport as well as the evolution of polymer stress. Non-dimensional control parameters include the Reynolds number, the Weissenberg number, and the elasto-viscous number of the macroscopic fibre. We find that large polymer stresses occur in the fluid near the ends of the fibre when it is compressed. In addition, we find that viscoelasticity hinders a fibre’s ability to traverse multiple cells in the domain.

JFM classification

Non-Newtonian Flows: Non-Newtonian Flows Non-Newtonian Flows: Viscoelasticity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 817 , 25 April 2017 , pp. 388 - 405
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Copyright
© 2017 Cambridge University Press 

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