### 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 language | English |
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Article number | A19 |

Journal | Journal of fluid mechanics |

Volume | 887 |

Early online date | 28 Jan 2020 |

DOIs | |

Publication status | Published - 25 Mar 2020 |

### Keywords

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

## Cite this

Eggers, J., Herrada, M. A., & Snoeijer, J. H. (2020). Self-similar breakup of polymeric threads as described by the Oldroyd-B model.

*Journal of fluid mechanics*,*887*, [A19]. https://doi.org/10.1017/jfm.2020.18