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

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Self-similar breakup of polymeric threads as described by the Oldroyd-B model. / Eggers, Jens; Herrada, Miguel; Snoeijer, Jacco.

In: Journal of Fluid Mechanics, Vol. 887, A19, 25.03.2020.

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Eggers, Jens ; Herrada, Miguel ; Snoeijer, Jacco. / Self-similar breakup of polymeric threads as described by the Oldroyd-B model. In: Journal of Fluid Mechanics. 2020 ; Vol. 887.

Bibtex

@article{7a56b67dc72640f19c49ba4db1b107e8,
title = "Self-similar breakup of polymeric threads as described by the Oldroyd-B model",
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.",
keywords = "Drops and Bubbles: Drops, Interfacial Flows (free surface): Capillary flows, Non-Newtonian Flows: Polymers",
author = "Jens Eggers and Miguel Herrada and Jacco Snoeijer",
year = "2020",
month = "3",
day = "25",
doi = "10.1017/jfm.2020.18",
language = "English",
volume = "887",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",

}

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TY - JOUR

T1 - Self-similar breakup of polymeric threads as described by the Oldroyd-B model

AU - Eggers, Jens

AU - Herrada, Miguel

AU - Snoeijer, Jacco

PY - 2020/3/25

Y1 - 2020/3/25

N2 - 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.

AB - 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.

KW - Drops and Bubbles: Drops

KW - Interfacial Flows (free surface): Capillary flows

KW - Non-Newtonian Flows: Polymers

U2 - 10.1017/jfm.2020.18

DO - 10.1017/jfm.2020.18

M3 - Article

VL - 887

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

M1 - A19

ER -