Elastic Turbulence in and Shear Banding in Entangled Polymers and Wormlike Micelles

Highly entangled polymer solutions and wormlike micelles are known to support instabilities in rectilinear geometries. We identify 2D elastic turbulence (ET) in both shear thinning and shear banding rheologies using two numerical models, the Johnson-Segalman and the Rolie-Poly fluid. Both models sustain ET in planar Couette flow (pCf) and planar Poiseuille flow (pPf), both of which are devoid of curvature in their base states. We find a route to this turbulence via a shear thinning linear instability. Within pCf, the ET consists of a number of narrow shear bands with 2D structure that coalesce, split and interact with each other, with the complexity of the state growing with Weissenberg number Wi. Our results suggest that the shear banding plateau seen in experiments on wormlike micelles may be due to this 2D ET state within the high shear branch.