THE CONFINED FLOW OF POLYETHYLENE MELTS PAST A CYLINDER IN A PLANAR CHANNEL

This paper is concerned with the comparison of the results of numerica l simulation of confined flow past a cylinder to birefringence data fo r two polymer melts. The Phan-Thien and Tanner (PTT) constitutive equa tion and the Rivlin-Sawyers (RS) constitutive equation with the Papana stasiou, Scriven, and Macosko (PSM) damping function were each fit to the shear viscosity and extensional viscosity data of both linear low- density polyethylene (LLDPE) and low-density polyethylene (LDPE) melts to determine the values of the model parameters. Finite element calcu lations were carried out using the 4 x 4SUPG and 4 x 4SU methods for t he PTT model and the method developed by Dupont, Marchal, and Crochet for the RS model. Isochromatic birefringence patterns calculated from the predicted stress field and the stress-optic law were compared to b irefringence data. Good agreement was found between the birefringence data and the numerical predictions, except in the immediate vicinity o f the cylinder surface. Large extensional stresses were observed and p redicted along the centerline downstream of the cylinder for LDPE. Thi s behavior was not observed or predicted for LLDPE. Stress fields obta ined from birefringence measurements for LDPE flowing past three cylin ders in a channel indicate an effect of deformation history on the flo w behavior of LDPE. It is shown that the PTT model does not correctly predict the rheological behavior of LDPE as a function of shear histor y because the time scale of structural recovery is much longer than th e relaxation time associated with viscoelasticity.