Transient shear banding during startup flow: Insights from nonlinear simulations

Abstract

We study the dynamics of shear startup of Johnson–Segalman and non-stretching Rolie-Poly models using nonlinear simulations. We consider startup to shear rates in both monotonic and nonmonotonic regions of the constitutive curve. For the Johnson–Segalman model, which exhibits a shear stress overshoot during startup, our nonlinear simulations show that transient shear banding is absent regardless of whether the startup shear rate is in the monotonic or nonmonotonic regions of the constitutive curve. In the latter case, while there is clearly an inhomogeneity en route to the banded state, the magnitude of the extent of banding is not substantially large compared to that of the eventual banded state. Marked inhomogeneity in the velocity profile is predicted for the nonstretching Rolie-Poly model only if the solvent to solution viscosity ratio is smaller than O(10−3), but its occurrence does not appear to have any correlation with the stress overshoot during startup. The comparison of the present nonlinear results with the results obtained within the framework of linearized dynamics show that nonlinearities have a stabilizing effect and mitigate the divergence of perturbations (as predicted within the linearized dynamics) during shear startup. We argue that the neglect of inertia in the nonlinear simulations is not self-consistent if the solvent to solution viscosity ratio is very small, and that inertial effects need to be included in order to obtain physically realistic results. Furthermore, our study demonstrates a pronounced sensitivity of shear startup in the nonstretching Rolie-Poly model when a random white noise with zero mean is used as the initial perturbation. Finally, this study clearly emphasizes that stress overshoot during shear startup does not always result in transient shear banding, notwithstanding whether the shear rates is in the monotonic or nonmonotonic part of the constitutive curve.