Exact solution for the extensional flow of a viscoelastic filament


Journal Article

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. © 2004 Cambridge University Press.

Full Text

Duke Authors

Cited Authors

  • Smolka, LB; Belmonte, A; Henderson, DM; Witelski, TP

Published Date

  • December 1, 2004

Published In

Volume / Issue

  • 15 / 6

Start / End Page

  • 679 - 712

International Standard Serial Number (ISSN)

  • 0956-7925

Digital Object Identifier (DOI)

  • 10.1017/S0956792504005789

Citation Source

  • Scopus