Drag and yielding of rotating bodies in yield-stress fluids

We investigate the settling dynamics of rotating objects in a yield-stress fluid by combining controlled experiments with numerical simulations. Experiments were conducted using cylinders and spheres of varying surface roughness, rotated within a Helmholtz coil and immersed in a Carbopol-based yield-stress fluid. Complementary numerical simulations employed a viscoplastic Herschel–Bulkley model to capture the coupled effects of sedimentation and rotation. To parametrise the problem, we define a dimensionless rotational velocity ModifyingAbove upper Omega With caret Ω ^ ̂ to characterise rotation and the Bingham number ( italic Bi Bi Bi ) to characterise sedimentation. Measurements of the drag coefficient show a strong dependence on both surface roughness and rotation rate. The plastic drag coefficient is found to be inversely related to ModifyingAbove upper Omega With caret Ω ^ ̂ at fixed italic Bi Bi Bi , with rotation effectively reducing the resistance to motion. Flow visualisation reveals that enhanced rotation generates a plastic deformation zone in the orthogonal plane and promotes wall slip; while at low ModifyingAbove upper Omega With caret Ω ^ ̂ , a stagnation-point flow develops in the wake, gradually weakening and disappearing as ModifyingAbove upper Omega With caret Ω ^ ̂ increases. In addition, the plastic drag coefficient decreases with increasing italic Bi Bi Bi and approaches an asymptotic plateau at high