Viscosity at small scales in polymer melts

Flows around small colloidal particles of diameter b, or in thin films, capillaries, etc., cannot always be described in terms of the macroscopic polymer viscosity. We discuss these features for entangled polymer melts! where two distinct regimes can be found: (a) the thin regime where b is smaller than the coil radius R-0, but larger than the diameter d(t) of the Edwards tube; (b) the ultrathin regime, where b < d(t). We consider (i) non adsorbing particles, where slippage may occur between the melt and the solid surface; (ii) ''hairy" particles, which carry some bound polymer chains. We obtain scaling predictions for mobilities of spheres, of needles, and of clusters of particles. We also discuss translational and rotational diffusion of needles.