Drag on a sphere in viscoplastic fluids

By virtue of its yield stress, a viscoplastic material in an unsheared state will support an immersed particle for an indefinite period of time. In recent years, this property has been successfiilly exploited in the design of slurry pipelines, as briefly discussed in section 4.3. Before undertaking an examination of the drag force on a spherical particle in a viscoplastic medium, the question of static equilibrium will be discussed and a criterion will be developed to delineate the conditions under which a sphere will either settle or be held stationary in a liquid exhibiting a yield stress. 

The question of whether or not a sphere will settle in an unsheared viscoplastic material has received considerable attention in the literature [Chhabra and Uhlherr, 1988 Chhabra, 1993a]. For the usual case where the sphere is acted upon by gravity, it is convenient to introduce a dimensionless group, Y, which denotes the ratio of the forces due to the yield stress and due to gravity. Neglecting munerical constants, the simplest definition of Y is To 

Using the laser speckle photographic method, Atapattu etal. [1995] measured point velocities in the fluid near a sphere moving at a constant speed 

A china clay suspension has a density of 1050kg/m and a yield stress of 13 Pa. Determine the diameter of the smallest steel baU (density 7750 kg/m ) which will settle under its own weight in this suspension. 

From equation (5.6), the sphere will settle only if F 0.04 — 0.05 

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