Viscoelastic Taylor-Couette Instability of Shear Banded Flow

We study numerically shear banded flow in planar and curved Couette geometries. Our aim is to capture two recent observations in shear banding systems of roll cells stacked in the vorticity direction, associated with an undulation of the interface between the bands. Depending on the degree of cell curvature and on the material's constitutive properties, we find either (i) an instability of the interface between the bands driven by a jump in second normal stress across it or (ii) a bulk viscoelastic Taylor-Couette instability in the high shear band driven by a large first normal stress within it. Both lead to roll cells and interfacial undulations but with a different signature in each case, thereby suggesting that the roll cells in each of the recent experiments are different in origin.