THE FALLING OF SPHERES THROUGH BINGHAM FLUIDS

The fall of spheres through bentonite clay dispersions has been monitored using an ultrasound technique. It was found that the spheres accelerated to a characteristic terminal velocity in a given fluid; this characteristic velocity was also shown to be a function of other experimental variables, in particular the diameter of the sphere and its density. From these velocity data an equivalent Stokes drag coefficient is introduced and computed, and a Bingham number is calculated. This Bingham number provides a quantitative description of the rheology of these fluids and the parameter includes the yield stress and plastic viscosity. These data were obtained using a conventional rotational viscometer. The measured interrelationship between the Stokes coefficient and the Bingham number agrees closely with data generated by the use of a finite-element analysis published elsewhere [A.N. Beris, J.A. Tsampoulos, R.C. Armstrong and R.A. Brown, J. Fluid Mech., 158 (1985) 219]. However, small but significant systematic deviations were noted between the finite-element predictions and the experimental results. The source of this systematic discrepancy is uncertain but most likely arises because the response of the fluid is not perfectly Bingham in its rheological character.