This study investigates the influence of curvature on the topology and morphology of static plug regions arising at the cessation threshold of viscoplastic flow. By invoking the conservation of angular momentum, a general criterion for the existence of plug regions in curved ducts with arbitrary cross-sections is established. The parametric method is adopted to derive an exact representation of the static plug topology in the curved ducts. Plug configurations and critical Bingham numbers are computed using a simulated annealing algorithm and are validated against three-dimensional numerical simulations and available literature results. The variational formulation shows that a curvature-weighted perimeter-to-area ratio governs the critical condition, linking to weighted Cheeger problems and enabling a unified geometric criterion for identifying plug-free conditions based on duct curvature and cross-sectional geometry. The analysis is carried out for circular, elliptical, and rectangular geometries over a wide range of aspect and curvature ratios. The results identify plug-free regimes in curved elliptical ducts and show that static plugs persist in circular geometries for curvature ratios exceeding 0.382. Regime maps describing plug topology are also constructed, and the boundary of the plug-free regime in the aspect ratio–curvature ratio space is determined analytically for curved elliptical ducts. Despite the complex functional dependence of the exact plug boundaries, they are accurately approximated by elliptical shapes, with errors below 2%. Static plug-free geometries, designed using the proposed curvature-based criteria, can reduce stagnant regions and thrombus formation in curved vessels such as varicose veins, with potential applications in developing low-occlusion vascular grafts.
Mahmood et al. (Mon,) studied this question.