The Doi-Edwards model in slow flows. Predictions on the Weissenberg effect

The model of Doi and Edwards describing the dynamics of flexible polymers in melts and concentrated solutions is here applied to the rheology of slow flows. The predictions which are obtained differ from those of the Doi-Edwards constitutive equation because the latter, though obviously based on the same model, makes use of an approximation called "independent alignment". One purpose of the paper is to show that the model of Doi and Edwards, contrary to their constitutive equation, correctly predicts a positive Weissenberg effect. The analysis, though developed in all details for the limiting case of slow flows only, opens the way to removing the approximation also in the general case.