Stability analysis of viscoelastic fluid flow between two parallel plates, modeled by linear and exponential Phan–Thien–Tanner models

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Abstract
A temporal linear stability analysis of three-dimensional viscoelastic fluid flow between two parallel plates is performed using the linear and exponential forms of the Phan–Thien–Tanner (LPTT and EPTT) constitutive models. The study systematically investigates the influence of key dimensionless parameters—Reynolds number (Re), Weissenberg number (Wi), viscosity ratio (βnn), spanwise wavenumber (β), elongational parameter (ε), and mobility parameter (ξ)—on the onset of flow instability. Neutral stability curves in the α−Re plane are constructed to delineate stable and unstable regions for a wide range of these parameters. The results show that, for both models, two-dimensional waves (β=0) are found to be the most unstable mode. An increase in the Weissenberg number consistently destabilizes the flow, while a higher viscosity ratio (larger solvent fraction) has a strong stabilizing effect. The influence of the elongational parameter, ε, is shown to be model-dependent, exhibiting a destabilizing effect in the LPTT model and a more complex, dual role in the EPTT model that reverses from destabilizing at low Wi to stabilizing at high Wi. The mobility parameter, ξ, is consistently destabilizing for both models. A direct comparison reveals that the LPTT model consistently predicts a larger unstable region than the EPTT model, highlighting that the choice of the constitutive stress function is a critical factor in determining flow stability characteristics.
Funding Information
  • Centros de Pesquisa, Inovação e Difusão, Fundação Amazônia Paraense de Amparo à Pesquisa (2013/07375-0)
  • Conselho Nacional de Desenvolvimento Científico e Tecnológico (001)

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