Shear banding in polymer solutions

The current theoretical belief is that the steady-state shear banding in viscoelastic liquids requires a non-monotonic constitutive relationship between shear stress and shear rate. Although existing rheological studies conclude that the constitutive equation for entangled polymers is monotonic, recent experimental evidence suggests shear banding can nevertheless occur in polymer solutions. In this work, we predict, for the first time, steady state shear banding with a realistic monotonic constitutive theory for polymeric liquids. The key is that a proper account must be taken of the coupling of polymer stress to polymer concentration. We also predict multiple steady states at some shear rates as seen experimentally, with shear banding if the flow is ramped quickly enough from rest, but homogeneous linear shear flow otherwise.