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

Jens Eggers, Miguel Herrada, Jacco Snoeijer

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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.
Original languageEnglish
Article numberA19
Number of pages31
JournalJournal of Fluid Mechanics
Volume887
Early online date28 Jan 2020
DOIs
Publication statusPublished - 25 Mar 2020

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Keywords

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

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