Analysis of plane extrudate-swell of highly elastic liquids with molecular constitutive equations

Abstract

Plane, two-dimensional, polymer extrusion is analyzed by means of the Curtiss-Bird integral constitutive equation, streamlined finite-elements and Newton iteration. The Reynolds number is zero, the surface tension negligible and the melt does not slip at the wall. Starting from the Newtonian liquid of zero elasticity, the Newton iteration converged, within three to five iterations, up to a maximum Weissenberg number beyond 3500. The predicted values of the die-swell at low elasticity are in agreement with those reported in the literature. At hihger elasticities, the die-swell increases monotonically and levels off. Two other models examined, the Doi-Edwards and the Papanastasiou-Scriven-Macosko models, diverged at low Weissenberg numbers, however, the actual point of divergence was a function of the number of relaxation times. It appears that the second term of the Curtiss-Bird model, which incorporates the link tension coefficient, [var epsilon], enhances significant numerical stability, in addition to the one due to the relaxation spectrum, as its different convergence behavior from the Doi-Edwards model implies.