Do well-entangled polymer fluids form steady shear bands
In plain words
Some theories predict that a strongly entangled polymer fluid, when sheared, splits into bands flowing at different speeds. Experiments disagree on whether this really happens or is caused by slip at the walls and edge failure.
Precise statement
In startup and steady simple shear of linear polymer solutions and melts with $Z=M/M_e$ above about 50, determine whether the steady constitutive curve $\sigma(\gamma_{\mathrm{dot}})$ is non-monotonic and steady shear banding occurs, as tube models with weak convective constraint release predict, or whether reported banding (particle-tracking velocimetry, from 2006 on) is transient or caused by wall slip and edge fracture.
What would settle it
Velocimetry in geometries free of edge fracture and wall slip, across $Z$ and $\gamma_{\mathrm{dot}}$, showing persistent or absent steady banding, consistent with rheometric data.