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It is well known that inertia-free shearing flows of a viscoelastic fluidwith curved streamlines, such as the torsional flow between a rotating cone andplate, or the flow in a Taylor-Couette geometry, can become unstable to athree-dimensional time-dependent instability at conditions exceeding a criticalWeissenberg (Wi) number. However, the combined effects of fluid elasticity,shear thinning, and finite inertia (as quantified by the Reynolds number Re) onthe onset of elasto-inertial instabilities are not fully understood. Using aset of cone-plate geometries, we experimentally explore the entire Wi - Rephase space for a series of rate-dependent viscoelastic fluids (quantifiedusing a shear thinning parameter $\beta_P$). We tune $\beta_P$ by varying thepolymer concentration in solutions. This progressively reduces shear-thinningbut leads to finite inertial effects before the onset of elastic instability,thus naturally resulting in elasto-inertial coupling. Transient rheometricmeasurements and flow visualization experiments allow us to investigate theeffects of flow geometry and document the combined effects of varying Wi, Re,and $\beta_P$ on the emergence of secondary motions at the onset ofinstability. The resulting critical state diagram quantitatively depicts thecompetition between the stabilizing effects of shear thinning and thedestabilizing effects of inertia. We extend the curved streamline instabilitycriterion of Pakdel and McKinley 1996 for the onset of purely elasticinstability in curvilinear geometries by using scaling arguments to incorporateshear thinning and finite inertial effects. The augmented condition facilitatespredictions of the onset of instability over a broader range of flowconditions, thus bridging the gap between purely elastic and elasto-inertialcurved streamline instabilities.

Elasto-Inertial Instability in Torsional Flows of Shear-Thinning Viscoelastic Fluids