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Viscoelastic ribbons

Published online by Cambridge University Press:  03 December 2020

I. J. Hewitt Open the ORCID record for I. J. Hewitt [Opens in a new window]  and
N. J. Balmforth Open the ORCID record for N. J. Balmforth [Opens in a new window]
I. J. Hewitt*
Affiliation:
Mathematical Institute, University of Oxford, OX2 6GG, UK
N. J. Balmforth
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BCV6T 1Z2, Canada
*
†Email address for correspondence: hewitt@maths.ox.ac.uk
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Abstract

A reduced model is presented for the dynamics of a slender sheet of a viscoelastic fluid. Starting with the Oldroyd-B constitutive model and exploiting an asymptotic analysis in the small aspect ratio of the sheet, equations are derived for the evolution of a ‘visco-elastica’. These depend on an elastic modulus, a creep viscosity and a solvent viscosity. They resemble standard equations for an elastica or a viscida, to which they reduce under the appropriate limits. The model is used to explore the effects of viscoelasticity on the dynamics of a curling ribbon, a drooping cantilever, buckling sheets, snap-through and a falling catenary. We then incorporate a yield stress, for a fluid that deforms by creep only above a critical stress, revisiting the curling and cantilever problems. This model generalises a number of previous theories for viscoelastic and viscoplastic ribbons.

JFM classification

Mathematical Foundations: General fluid mechanics Non-Newtonian Flows: Viscoelasticity Low-Reynolds-number flows: Lubrication theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , A5
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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