| Abstract: | A new model is presented for describing the time-dependent flow of entangled polymer liquids at high shear rates. The results were obtained by extending the Doi and Edwards theory to include the effect of chain stretching. This nonlinear phenomenon is predicted to occur when the product of the shear rate and longitudinal relaxation time of the polymer exceeds one. If a constant-shear-rate flow is started under these conditions, it is shown that the shear stress and the normal stress are considerably larger than that predicted by the original reptation model. We also find that both of these stresses can pass through maxima before reaching a steady state and that the times required to reach these maxima are constants independent of the shear rate. In general the new model requires the numerical solution of coupled partial differential equations. However, at the highest shear rates where reptative relaxation is no longer important, an analytical solution for the stresses is found. The results obtained here are shown to agree well with experimental data and to be an improvement over a simpler model recently proposed. |
