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

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. Us...

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Bibliographic Details
Published inJournal of fluid mechanics Vol. 887
Main Authors Eggers, J., Herrada, M. A., Snoeijer, J. H.
Format Journal Article
LanguageEnglish
Published Cambridge Cambridge University Press 25.03.2020
Subjects
Axisymmetric flow
Computational fluid dynamics
Computer simulation
Elasticity
Fluids
Mathematical models
Polymers
Self-similarity
Similarity solutions
Stress distribution
Thickness
Three dimensional flow
Viscoelastic fluids
Viscoelasticity
Viscosity
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2020.18