## Abstract

We solve the free boundary problem for the dynamics of a cylindrical, axisymmetric viscoelastic filament stretching in a gravity-driven extensional flow for the Upper Convected Maxwell and Oldroyd-B constitutive models. Assuming the axial stress in the filament has a spatial dependence provides the simplest coupling of viscoelastic effects to the motion of the filament, and yields a closed system of ODEs with an exact solution for the stretch rate and filament thickness satisfied by both constitutive models. This viscoelastic solution, which is a generalization of the exact solution for Newtonian filaments, converges to the Newtonian power-law scaling as t → ∞. Based on the exact solution, we identify two regimes of dynamical behavior called the weakly- and strongly-viscoelastic limits. We compare the viscoelastic solution to measurements of the thinning filament that forms behind a falling drop for several semi-dilute (strongly-viscoelastic) polymer solutions. We find the exact solution correctly predicts the time-dependence of the filament diameter in all of the experiments. As t → ∞, observations of the filament thickness follow the Newtonian scaling 1/√t. The transition from viscoelastic to Newtonian scaling in the filament thickness is coupled to a stretch-to-coil transition of the polymer molecules.

Original language | English (US) |
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Pages (from-to) | 679-712 |

Number of pages | 34 |

Journal | European Journal of Applied Mathematics |

Volume | 15 |

Issue number | 6 |

DOIs | |

State | Published - Dec 2004 |

## All Science Journal Classification (ASJC) codes

- Applied Mathematics