THE PRESSURE-DROP CREATED BY A BALL SETTLING IN A QUIESCENT SUSPENSION OF COMPARABLY SIZED SPHERES

Measurements are reported of the pressure differences Delta P existing at large distances above and below a ball settling along the axis of a circular cylinder filled with an otherwise quiescent viscous Newtoni an liquid in which identical particles, comparable in size to the sett ling ball, are suspended. The suspensions ranged in solids volume frac tion phi from 0.30 to 0.50 and consisted of 0.635 cm diameter spheres density-matched to the suspending oil. The settling balls varied in di ameter from 0.1318 to 1.27 cm, resulting in particle Reynolds numbers always less than about 0.4 based upon ball diameter and the effective viscosity of the suspension. For the moderately concentrated suspensio n (phi = 0.30), the product of Delta P with the cross-sectional area A of the containing cylinder was observed to be equal to twice the drag force D on the settling sphere, in accord with theory. In the more co ncentrated suspension (phi = 0.50) this product was found to be slight ly, but significantly, less than twice the drag on the settling sphere . It is speculated that this lower pressure drop may result from the p resence of one or more of the following phenomena: (i) migration of th e falling ball off the cylinder axis; (ii) apparent slip of the suspen sion at the cylinder wall; (iii) blunting of the otherwise Poiseuillia n parabolic velocity profile, the latter phenomenon being known to occ ur during the creeping flow of concentrated suspensions through circul ar tubes. Incidental to the suspension experiments, for a homogeneous fluid we verify the classical theoretical formula for the off-axis pre ssure drop when the sphere settles at a non-concentric position in the cylinder.