Math @ Duke

Publications [#244251] of Thomas P. Witelski
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 Smolka, LB; Belmonte, A; Henderson, DM; Witelski, TP, Exact solution for the extensional flow of a viscoelastic filament,
European Journal of Applied Mathematics, vol. 15 no. 6
(2005),
pp. 679712 [doi]
(last updated on 2017/12/11)
Abstract: We solve the free boundary problem for the dynamics of a cylindrical, axisymmetric viscoelastic filament stretching in a gravitydriven extensional flow for the Upper Convected Maxwell and OldroydB 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 powerlaw scaling as t → ∞. Based on the exact solution, we identify two regimes of dynamical behavior called the weakly and stronglyviscoelastic limits. We compare the viscoelastic solution to measurements of the thinning filament that forms behind a falling drop for several semidilute (stronglyviscoelastic) polymer solutions. We find the exact solution correctly predicts the timedependence 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 stretchtocoil transition of the polymer molecules. © 2004 Cambridge University Press.


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