Theory of melt fracture instabilities in the capillary flow of polymer melts

We present a model for the flow of a polymer melt through a capillary with nonlinear slip boundary conditions at the wall of the capillary. The model consists of the linearized Navier-Stokes equations coupled to a Maxwell constitutive relation for the viscoelasticity and a phase-field model for a first-order transition between stick and slip flow at the boundary. Specializing to the case of a two-dimensional capillary, we perform a linear stability analysis about the steady-state solutions and predict in which parameter regimes the steady-state becomes unstable. A numerical study of the model shows regions of steady flow, as well as regimes with periodic oscillations, spatially uniform but temporally chaotic oscillations, and more complicated spatiotemporal behavior. We show that the oscillations can account for the sharkskin texturing and defect structures seen in the extrusion of polymer melts.