Drag and Yielding of Rotating Bodies in Yield-Stress Fluids

Abstract

Abstract

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 parameterize the problem, we define rotation rate to characterize rotation and the Bi to characterize sedimentation. Measurements of the drag coefficient show a strong dependence on both surface roughness and rotation rate. Flow visualization reveals that enhanced rotation generates a plastic deformation zone in the orthogonal plane and promotes wall slip, while at a stagnation point flow develops in the wake, gradually weakening and disappearing as rotation increases. In addition, the plastic drag coefficient decreases with increasing Bi and approaches an asymptotic plateau at high Bi. Numerical simulations reproduce the general scaling of drag with and but consistently underpredict experimental values, likely due to wall slip and nonlinear effects such as the stagnation point flow not present in the model. The onset of sedimentation (yield limit) was also measured and found to increase with increasing rotation and to depend on surface roughness. Finally, simulations highlight scaling relations for drag coefficient, providing new insight into the interplay of sedimentation, rotation, and viscoplastic rheology.