Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#244251] of Thomas P. Witelski


Papers Published

  1. 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. 679-712 [doi]
    (last updated on 2018/11/14)

    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.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320