The polymer diffusive instability in highly concentrated polymeric fluids

The extrusion of polymer melts is known to be susceptible to `melt fracture' instabilities, which can deform the extrudate, or cause it to break entirely. Motivated by this, we consider the impact that the recently discovered polymer diffusive instability (PDI) can have on polymer melts and other concentrated polymeric fluids using the Oldroyd-B model with the effects of polymer stress diffusion included. Analytic progress can be made in the concentrated limit (when the solvent-to-total-viscosity ratio $\beta \rightarrow 0$), illustrating the boundary layer structure of PDI, and allowing the prediction of its eigenvalues for both plane Couette and channel flow. We draw connections between PDI and the polymer melt `sharkskin' instability, both of which are short wavelength instabilities localised to the extrudate surface. Inertia is shown to have a destabilising effect, reducing the smallest Weissenberg number ($W$) where PDI exists in a concentrated fluid from $W\sim 8$ in inertialess flows, to $W \sim 2$ when inertia is significant.