Exact solution for the extensional flow of a viscoelastic filament

Linda B. Smolka, Andrew Belmonte, Diane M. Henderson, Thomas P. Witelski

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12 Scopus citations


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 languageEnglish (US)
Pages (from-to)679-712
Number of pages34
JournalEuropean Journal of Applied Mathematics
Issue number6
StatePublished - Dec 2004

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


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