A NON-AFFINE NETWORK MODEL FOR POLYMER MELTS

In this paper, a network model of polymer melts is proposed in which n etwork junction points move non-affinely. In this non-affine motion, j unction points follow particle paths as seen by an observer rotating a t the fluid element's net rigid-rotation rate. The speed at which junc tion points move is reduced as the network segments near their maximum extensions. In order to maintain a frame invariant model, it is neces sary that the vorticity be decomposed into two portions, such that, om ega = omega(R) + omega(D). The deformational vorticity, omega(D), aris es from shear deformation and is frame invariant while the rigid vorti city, omega(R), is frame dependent. A constitutive equation based on t his finitely extensible network strand (FENS) motion is developed. The model illustrates how rotations that cause changes in the relative or ientation of a fluid element with its surroundings can be incorporated into a constitutive equation using the deformational vorticity. The F ENS model predicts a shear-thinning viscosity, and the Trouton viscosi ty predicted by the model is finite for all elongation rates. Finally, stochastic simulation results are presented to justify a mathematical approximation used in deriving the constitutive equation.