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A theory of magnetic-like fields for viscoelastic fluids

Published online by Cambridge University Press:  20 February 2019

Thibault Vieu Open the ORCID record for Thibault Vieu [Opens in a new window]  and
Innocent Mutabazi Open the ORCID record for Innocent Mutabazi [Opens in a new window]
Thibault Vieu
Affiliation:
Normandie Université, UNIHAVRE, Laboratoire Ondes et Milieux Complexes, CNRS UMR 6294, 53 rue de Prony, 76058 Le Havre CEDEX, France International Centre for Fundamental Physics, Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France Magistère de Physique Fondamentale, Université Paris-Saclay, Bât. 470, F-91405 Orsay, France
Innocent Mutabazi*
Affiliation:
Normandie Université, UNIHAVRE, Laboratoire Ondes et Milieux Complexes, CNRS UMR 6294, 53 rue de Prony, 76058 Le Havre CEDEX, France
*
†Email address for correspondence: innocent.mutabazi@univ-lehavre.fr
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Abstract

We formulate the Oldroyd-B model for viscoelastic fluids in terms of magnetic-like fields obeying a set of equations analogous to Maxwell’s equations. In the limit of infinite relaxation time for the polymer, the polymeric stress tensor can be identified with the Maxwell stress tensor of a magnetic field. Away from this asymptotic case, the stress tensor of the polymer cannot be decomposed in terms of a tensor product of a magnetic field any more and several theoretical issues arise. We show that the analogy between the Oldroyd-B model and Maxwell’s equations can still be rigorously extended provided that one defines three magnetic-like fields obeying Maxwell’s equations with magnetic currents and charges. This solves the theoretical caveats and leads to a better understanding of the viscoelastic instability. In particular, we evidence a gauge symmetry which unifies some previous works, and we investigate several gauge choices. As an illustration we apply our method to viscoelastic Taylor–Couette flow but this theory of ‘viscoelastic fields’ is general and may be useful in a large variety of viscoelastic flows. The present study may also be of interest from the electromagnetic point of view, as it provides real systems possessing magnetic-like charges (monopoles) and currents.

JFM classification

Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 865 , 25 April 2019 , pp. 460 - 491
Copyright
© 2019 Cambridge University Press 

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