Taylor-Couette Instability of Giesekus Fluids: Inertia Effects

Abstract

Taylor-Couette instability of Giesekus fluids is investigated at large gaps using a temporal, linear instability analysis. Having superimposed axisymmetric, normal-mode perturbations to the base flow velocity and stress fields, an eigenvalue problem is obtained which is solved numerically using pseudo-spectral, Chebyshev-based, collocation method. The neutral instability curve is then plotted as a function of the Weissenberg number and also the mobility factor of the Giesekus model. Based on the results obtained in this work, it is concluded that at large gaps, a fluid's elasticity can have a stabilizing or destabilizing effect on the Couette flow depending on the Weissenberg number being smaller or larger than a critical value. The critical Weissenberg number increases by an increase in the gap size, and also by an increase in the mobility factor. Fluid's inertia is identified as the main source of instability.