Steady-state drag in Herschel–Bulkley yield-stress fluids

When a sphere is drawn through a yield-stress liquid, a surrounding fluidized region is generated near its surface. To investigate the spatial dimensions and contours of this region, we moved steel spheres through tubes of varying diameters filled with Herschel–Bulkley fluid. By measuring how the drag force on the sphere changes with container size, we indirectly assessed the extent of the fluidized area around the moving sphere, finding that the region expands roughly linearly with increasing velocity. For direct visualization, poppy seeds were dispersed throughout the non-Newtonian fluid, and particle tracking, together with particle image velocimetry, was used to map the structure of the fluidized region as a steel sphere traversed the medium. This inexpensive set-up and experiment offers a way for educators to introduce their students to Stokes' law, non-Newtonian fluids, and complexity of motion of a sphere in non-Newtonian fluids.