Elastic Turbulence in Highly Entangled Polymers and Wormlike Micelles

We show theoretically that an initially homogeneous planar Couette flow of a concentrated polymeric fluid is linearly unstable to the growth of two-dimensional (2D) perturbations, within two widely used constitutive models: the Johnson-Segalman model and the Rolie-Poly model. We perform 2D direct nonlinear simulations of both models to show that this instability leads to a state of elastic turbulence comprising several narrow shear bands that dynamically coalesce, split, and interact. Importantly, we show that this 2D instability arises not only in fluids that have a nonmonotonic constitutive curve and therefore show shear banding in 1D calculations, but also in shear thinning fluids with a monotonic constitutive curve, for which an initially homogeneous base state is stable to 1D perturbations. For the former category, the high shear branch of the constitutive curve is unstable to 2D instability in both models, so the high shear band may be turbulent. In the Rolie-Poly model, the low shear branch is also likewise unstable. Our Letter provides the first simulation evidence for elastic turbulence in highly entangled polymeric fluids. It also potentially explains rheo-chaotic states seen experimentally in shear banding wormlike micelles. We additionally demonstrate elastic turbulence within both models in the planar Poiseuille geometry.