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

Research output: Contribution to journalArticle

Original languageEnglish
Article numberA19
Number of pages31
JournalJournal of Fluid Mechanics
Volume887
Early online date28 Jan 2020
DOIs
DateSubmitted - 2019
DateE-pub ahead of print - 28 Jan 2020
DatePublished (current) - 25 Mar 2020

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 non-linear 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. A conservation law balancing pressure and elastic energy permits to calculate the thread thickness exactly. 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.

    Research areas

  • Drops and Bubbles: Drops, Interfacial Flows (free surface): Capillary flows, Non-Newtonian Flows: Polymers

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  • Full-text PDF (accepted author manuscript)

    Rights statement: This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Cambridge University Press at https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/selfsimilar-breakup-of-polymeric-threads-as-described-by-the-oldroydb-model/DEA6F68AC5971D198AB13FB8B29ACCB6. Please refer to any applicable terms of use of the publisher.

    Accepted author manuscript, 3.15 MB, PDF document

    Embargo ends: 28/01/22

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