Inertio-elastic mode instabilities of viscoelastic flow in a periodic channel

This article explores the complex behavior of viscoelastic fluids, specifically those modeled by the Upper Convected Maxwell (UCM) fluid, flowing through periodic channels. It investigates the stability of these flows under both inertial and purely elastic regimes, highlighting the critical roles of the Reynolds number, Weissenberg number, and elasticity number. The study employs advanced numerical methods, such as the Chebyshev spectral collocation method, to analyze the eigenspectrum and stability thresholds. Key findings include the destabilizing effect of the Weissenberg number and the dual role of the elasticity number, which can either stabilize or destabilize the flow depending on its value. The research also reveals how channel geometry, particularly the amplitude and sections of the periodic channel, significantly influences flow stability. By providing detailed insights into the interplay between fluid elasticity and channel geometry, this study offers valuable contributions to the understanding and optimization of viscoelastic flows in complex systems.