The polymer diffusive instability in high concentration polymer solutions

Numerous mechanisms have previously been proposed to explain `melt fracture' instabilities that are seen during plastic extrusion, many of which were made on the basis that no linear instability exists. The polymer diffusive instability (PDI) is a recently discovered linear instability that is seen in Oldroyd-B and FENE-P fluids in rectilinear geometries when the effects of polymer stress diffusion are included in the model. We consider PDI in an Oldroyd-B fluid in the concentrated polymer solution limit. We present analytic results, where we identify the boundary layer structure of PDI, and we predict its eigenvalues. We show that PDI could influence the plastic extrusion process due to its large growth rate, and it bears many similarities with the `sharkskin' instability. Inertia is shown to have a destabilising effect, with it lowering the critical Weissenberg number required for the system to become unstable.