A mechanism for explaining some of the instabilities observed during the extrusion of polymer melts is further explored. This is based on the combination of non-monotonic slip and elasticity, which permits the existence of periodic solutions in viscometric flows. The time-dependent, incompressible, one-dimensional plane Poiseuille flow of an Oldroyd-B fluid with slip along the wall is studied using a non-monotonic slip equation relating the shear stress to the velocity at the wall. The stability of the steady-state solutions to one-dimensional perturbations at fixed volumetric flow rateis analyzed 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 experimental observations.
Fyrillas, M., Georgiou, G., Vlassopoulos, D., & Hatzikriakos, S. (1999). A mechanism for extrusion instabilities in polymer melts. Polymer engineering and science, 39(12), 2498-2504. https://doi.org/10.1002/pen.11637