Onset of transient shear banding in viscoelastic shear start-up flows: Implications from linearized dynamics

We analyze transient dynamics during the shear start-up in viscoelastic flows between two parallel plates, with a specific focus on signatures for onset of banding using Johnson–Segalman, nonstretching Rolie-Poly, and Giesekus models. explore monotonic regions constitutive curves different methodologies: (i) oft-used “frozen-time” linear stability (eigenvalue) analysis, wherein we examine whether infinitesimal perturbations imposed instantaneous stress components (treated as quasisteady states) exhibit exponential growth, (ii) more mathematically rigorous fundamental-matrix approach that characterizes growth via numerical solution time-dependent linearized governing equations, coevolve flow. Our results reinforce hitherto understated point there is no universal connection overshoot subsequent decay base state unstable eigenvalues obtained from frozen-time analysis. It may, therefore, be difficult to subsume occurrence within ambit single model-independent criterion. work also suggests strong transients seen earlier could sensitive small solvent viscosity values considered absence otherwise negligible terms such fluid inertia.