Model for melt fracture instabilities in the capillary flow of polymer melts

We model the capillary flow of a polymer melt, incorporating a stick-slip boundary condition at the wall. The boundary condition is enforced by a phase-field model for the local state of the polymer, which describes the kinetics of a first-order transition. We numerically solve the linearized Navier-Stokes equations, coupled to this prescribed boundary condition and to a Maxwell model for viscoelasticity. In various regimes, the model exhibits steady flow, periodic oscillations, and more complicated spatiotemporal structures, which can be observed experimentally