The Rheology of Entangled Polymers at Very High Shear Rates

One of the (few) unrealistic features of the Doi-Edwards model for entangled polymers is that it predicts a steady-state shear stress which decreases indefinitely as the shear rate is increased. As shown by Marrucci and Grizzuti (Gazz. Chim. Ital., 118 (1988) 179) this feature remains, even when one takes into account chain stretching due to elongation of the tube by the flow. Here we suggest a further mechanism for chain stretching which arises because the tube, even when fully aligned with the flow, has a finite lateral dimension which exposes different parts of the chain to different flow velocities. Using a simplified model, we predict the asymptotic behaviour of the shear stress and first-normal-stress difference, and show that stable flow is recovered at high enough shear rates.