Effect of flow on topological interactions in polymers

The dynamics of concentrated polymers of high molecular mass is dominated by topological interactions (or entanglements). The nonlinear effects shown by these systems in fast flows are still poorly understood, however. We have recently noted that a mechanism of convective constraint release should play a significant role in the nonlinear range, and preliminary calculations have been made both for a simple dumbbell model and for the tube model of Doi and Edwards. Here we show that further elaboration of the simple dumbbell model can predict quite complex rheological behaviours such as those observed dy Navard and coworkers in semi-dilute solutions of ultrahigh molecular mass polymers