Drag force on a sphere in steady motion through a yield-stress fluid

We have studied the motion of spheres falling through yield-stress Carbopol gels. We measured the velocity of the falling sphere as a function of time and sphere density. Reproducible results were obtained when the experimental fluids were carefully prepared and homogenized. Three regimes of motion were observed. Spheres of high enough density reached a constant terminal velocity, as in Newtonian fluids. Below a critical density, the sphere came to a complete stop, while in an intermediate regime, the sphere continued to move but with a velocity which steadily decreased with time. We have also carefully characterized the theological behavior of the fluids. The flow regimes observed for the falling sphere are analogous to those observed in creep tests for different applied stress levels. The yielding criterion and the drag force on the sphere obtained from our data are in excellent agreement with the longstanding but previously unconfirmed theoretical predictions of Beris et al.