A mechanism for extrusion instabilities in polymer melts

A mechanism for explaining some of the instabilities observed during the ex trusion of polymer melts is further explored. This is based on the combinat ion of nonmonotonic slip and elasticity, which permits the existence of per iodic solutions in viscometric flows. The time-dependent, incompressible, o ne-dimensional plane Poiseuille flow of an Oldroyd-B fluid with slip along the wall is studied using a nonmonotonic slip equation relating the shear s tress to the velocity at the wall. The stability of the steady-state soluti ons to one-dimensional perturbations at fixed volumetric flow rateis analyz ed by means of a linear stability analysis and finite element calculations. Self-sustained periodic oscillations of the pressure gradient are obtained when an unstable steady-state is perturbed, in direct analogy with experim ental observations.