A simple model of the melt fracture instability

In this note we develop and analyse a system of equations describing a molten linear polymer being extruded in a capillary rheometer which is operating under the controlled condition that the mean velocity at the capillary inlet is maintained at a constant value. Slipping of the melt at the pipe wall is permitted and an evolution equation for the boundary slip parameter is postulated. The combined system governing the mean cross-sectional velocity and slip parameter is shown to exhibit relaxation oscillations similar to those observed in actual rheometers.