  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.
