Edge-induced shear banding in entangled polymeric fluids

Abstract: Despite decades of research, the question of whether solutions and melts of highly entangled polymers exhibit shear banding as their steady state response to a steadily imposed shear flow remains controversial. From a theoretical viewpoint, an important unanswered question is whether the underlying constitutive curve of shear stress $\sigma$ as a function of shear rate $\dot{\gamma}$ (for states of homogeneous shear) is monotonic, or has a region of negative slope, $d\sigma/d\dot{\gamma}<0$, which would trigger banding. Attempts to settle the question experimentally via velocimetry of the flow field inside the fluid are often confounded by an instability of the free surface where the sample meets the outside air, known as "edge fracture". Here we show by numerical simulation that in fact even only very modest edge disturbances - which are the precursor of full edge fracture but might well, in themselves, go unnoticed experimentally - can cause strong secondary flows in the form of shear bands that invade deep into the fluid bulk. Crucially, this is true even when the underlying constitutive curve is monotonically increasing, precluding true bulk shear banding in the absence of edge effects.