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Self-similar breakup of polymeric threads as described by the Oldroyd-B model

Published online by Cambridge University Press:  28 January 2020

J. Eggers
Affiliation:
School of Mathematics, University of Bristol, Fry Building, Bristol BS8 1UG, UK
M. A. Herrada
Affiliation:
E.S.I., Universidad de Sevilla, Camino de los Descubrimientos s/n 41092, Spain
J. H. Snoeijer
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, University of Twente, 7500 AE Enschede, The Netherlands
Corresponding
E-mail address:

Abstract

When a drop of fluid containing long, flexible polymers breaks up, it forms threads of almost constant thickness, whose size decreases exponentially in time. Using an Oldroyd-B fluid as a model, we show that the thread profile, rescaled by the thread thickness, converges to a similarity solution. Using the correspondence between viscoelastic fluids and nonlinear elasticity, we derive similarity equations for the full three-dimensional axisymmetric flow field in the limit that the viscosity of the solvent fluid can be neglected. Deriving a conservation law along the thread, we can calculate the stress inside the thread from a measurement of the thread thickness. The explicit form of the velocity and stress fields can be deduced from a solution of the similarity equations. Results are validated by detailed comparison with numerical simulations.

Type
JFM Papers
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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