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Exact solution for the extensional flow of a viscoelastic filament

Publication ,  Journal Article
Smolka, LB; Belmonte, A; Henderson, DM; Witelski, TP
Published in: European Journal of Applied Mathematics
December 1, 2004

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.

Duke Scholars

Published In

European Journal of Applied Mathematics

DOI

ISSN

0956-7925

Publication Date

December 1, 2004

Volume

15

Issue

6

Start / End Page

679 / 712

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

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Smolka, L. B., Belmonte, A., Henderson, D. M., & Witelski, T. P. (2004). Exact solution for the extensional flow of a viscoelastic filament. European Journal of Applied Mathematics, 15(6), 679–712. https://doi.org/10.1017/S0956792504005789
Smolka, L. B., A. Belmonte, D. M. Henderson, and T. P. Witelski. “Exact solution for the extensional flow of a viscoelastic filament.” European Journal of Applied Mathematics 15, no. 6 (December 1, 2004): 679–712. https://doi.org/10.1017/S0956792504005789.
Smolka LB, Belmonte A, Henderson DM, Witelski TP. Exact solution for the extensional flow of a viscoelastic filament. European Journal of Applied Mathematics. 2004 Dec 1;15(6):679–712.
Smolka, L. B., et al. “Exact solution for the extensional flow of a viscoelastic filament.” European Journal of Applied Mathematics, vol. 15, no. 6, Dec. 2004, pp. 679–712. Scopus, doi:10.1017/S0956792504005789.
Smolka LB, Belmonte A, Henderson DM, Witelski TP. Exact solution for the extensional flow of a viscoelastic filament. European Journal of Applied Mathematics. 2004 Dec 1;15(6):679–712.
Journal cover image

Published In

European Journal of Applied Mathematics

DOI

ISSN

0956-7925

Publication Date

December 1, 2004

Volume

15

Issue

6

Start / End Page

679 / 712

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics