We use the FENE-P constitutive model to revisit the hoop-stress-driven linear instability in viscoelastic Taylor-Couette flow, considering both inertialess and inertial regimes. The FENE-P model is appropriate for dilute polymer solutions, with the finite extensibility of the polymer leading to shear thinning of both viscosity and the first-normal-stress coefficient. Shear thinning weakens elastic effects and is generally expected to stabilize the hoop-stress mode (HSM), as suggested by the Pakdel-McKinley scaling criterion. Our numerical results confirm this expectation for small values of the ratio of the gap width to the radius of the inner cylinder $(\epsilon <1)$. Unexpectedly, for $\epsilon >1$, finite-extensiblity-induced increase in shear rates at the inner rotating cylinder results in a destabilizing effect on the HSM. We compare our theoretical predictions with relatively recent experimental observations on viscoelastic Taylor-Couette flow for a range of elasticity numbers $\left(E\right)$ with $\epsilon \in [0.25-0.4]$. In this regime, the experimental results for the onset of instability are well predicted both by the Oldroyd-B and FENE-P (with experimentally realistic polymer extensibility parameter values) models, with finite extensibility playing only a secondary role. Our theory predicts that for very dilute solutions with $\beta =0.98$, the hoop-stress instability is suppressed for realistic values of extensibility parameters. Overall, we show that the predictions of the FENE-P model will be qualitatively different from those of the Oldroyd-B model both for very low $\epsilon \text{"s}$ (suppression of HSM) and for $\epsilon >1$ (destabilization of HSM). Further, we also show that the FENE-P predictions for the instability onset are in significant disagreement with experiments carried out using highly concentrated polymer solutions, underscoring the need for the use of more realistic rheological models appropriate for such systems.

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• Flow instability
• Complex fluids
• Non-Newtonian fluids