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We analyze transient dynamics during shear start-up in viscoelastic flowsbetween two parallel plates, with a specific focus on the signatures for theonset of transient shear banding using the Johnson-Segalman, non-stretchingRolie-Poly and Giesekus models. We explore the dynamics of shear start-up inmonotonic regions of the constitutive curves using two different methodologies:(i) the oft-used `frozen-time' linear stability (eigenvalue) analysis, whereinwe examine whether infinitesimal perturbations imposed on instantaneous stresscomponents (treated as quasi steady states) exhibit exponential growth, and(ii) the more mathematically rigorous fundamental-matrix approach thatcharacterizes the transient growth via a numerical solution of thetime-dependent linearized governing equations, wherein the linearizedperturbations co-evolve with the start-up shear flow. Our results reinforce thehitherto understated point that there is no universal connection between theovershoot and subsequent decay of shear stress in the base state and theunstable eigenvalues obtained from the frozen-time stability analysis. It maytherefore be difficult to subsume the occurrence of transient shear bandingduring shear start-up within the ambit of a single model-independent criterion.Our work also suggests that the strong transients during shear start-up seen inearlier work could well be a consequence of consideration of the limit of smallsolvent viscosity in the absence of otherwise negligible terms such as fluidinertia.

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