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

J. Eggers*, M. A. Herrada, J. H. Snoeijer

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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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 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
Original languageEnglish
Article numberA19
JournalJournal of fluid mechanics
Volume887
Early online date28 Jan 2020
DOIs
Publication statusPublished - 25 Mar 2020

Keywords

  • UT-Hybrid-D
  • capillary flows
  • polymers
  • drops

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