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## Publications [#14134] of Linda B. Smolka

Papers Submitted

1. L. B. Smolka, A. Belmonte, D. M. Henderson, T. P. Witelski, Exact solution for the extensional flow of a viscoelastic filament, European Journal of Applied Mathematics (November, 2003)
(last updated on 2003/12/19)

Abstract:
We solve the free boundary problem for the dynamics of a cylindrical, axisymmetric viscoelastic filament stretching in a purely 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 $t \go \infty$. Based on the exact solution, we identify two regimes of dynamical behavior called the weakly- and strongly-viscoelastic limits. For the weakly-viscoelastic case, corresponding to low Deborah numbers, the dynamics are comparable to Newtonian behavior for all times and yield an effective increase in the filament thickness relative to a Newtonian fluid. In the strongly-viscoelastic case, initial transient dynamics are not comparable to Newtonian behavior and the effective filament thickness decreases with increasing Deborah number. 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 $t \go \infty$, observations of the filament thickness follow the Newtonian scaling $1/\sqrt{t}$. The transition from viscoelastic to Newtonian scaling in the filament thickness is coupled to a stretch-to-coil transition of the polymer molecules.

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