2026 Yadav Polymer Elastic Instability

The centre-mode elastic instability, prevalent in rectilinear flows of dilute polymer solutions, allows dynamic states to emerge even in the absence of inertia. This study demonstrates that this instability can be significantly enhanced with a nonuniform spatial distribution of polymers in the base flow. We analyze a polymer-laden stream positioned between streams of pure solvent, focusing on the influence of localized polymer concentration in promoting instability. A linear stability analysis, applied to periodic Kolmogorov flow under the Stokes limit, reveals that localizing polymers near the maximum of the velocity profile promotes the centre-mode instability, while a concentration at this maximum shear suppresses it. As polymer loading increases, the neutral stability curve transitions, exhibiting a double-lobe structure that leads to a reduction in the critical Weissenberg number. Our energy analysis indicates that destabilization arises from elastic feedback forces related to polymer concentration gradients. The findings highlight the relevance of localized polymers to channel flow situations, where concentrating polymers near the centerline markedly enhances the centre-mode instability.