A kinetic theory for polymer melts. IV. Rheological properties for shear flows

Abstract

Curtiss and Bird recently developed a kinetic theory for undiluted polymers, modeling the fluid as a collection of interacting Kramers freely jointed bead–rod chains. The theory yielded a constitutive equation in which the stress tensor is given as the sum of two integrals over the strain history. Here, the constitutive equation is used to calculate the steady‐state shear flow rheological properties (shear‐rate dependent viscosity and normal‐stress functions) and also unsteady‐state shear flow responses (shear and normal stress growth at the inception of shear flow, shear and normal stress relaxation after the cessation of shear flow, and the stress response in small‐amplitude oscillatory motion). The rheological functions for an earlier slip‐link network theory by Doi and Edwards are also obtained.