By virtue of its yield stress, a visco-plastic medium in an unsheared condition has the capacity to support the weight of an embedded particle for an indefinite (or sufficiently long) period of time. Figure 4.1 shows 25 mm gravel particles floating in a Kimberlite slimes slurry of mass density∼1300 kg/m3 and likewise Figure 4.2 shows static air bubbles trapped in a carbopol solution having a yield stress of about 8 Pa. In recent years, this phenomenon has been utilized successfully in the design of long distance slurry pipelines for conveying coarse solids in dense media (Thomas, 1977; Traynis, 1977; Chien and Wan, 1983; Duckworth et al., 1986; Hill and Shook, 1998; Talmon and Huisman, 2005). Similarly, the sedimentation of suspended particles in many household and pharmaceutical products is prevented by inducing a small value of yield stress by addition of suitable thickening agents (Berney and Deasy, 1979; Miller and Drabik, 1984) or in the trapping of dense colloids in gels (Laxton and Berg, 2005). On the other hand, the existence of a yield stress is highly detrimental in effecting liquid-solid separation. Evidently, depending upon the value of the yield stress and the size and density of particle, a particle may or may not settle in a visco-plastic medium under its own weight. Hence, before one can talk about the hydrodynamic aspects of particle motion in such media, it is important to establish the criterion for the movement of a particle in a visco-plastic medium of known density and yield stress. In literature, this aspect is usually referred to as static equilibrium. In contrast to the voluminous literature on the motion of particles in viscous fluids without a yield stress, there have been only a few investigations on the equilibrium and motion of particles in visco-plastic media. Furthermore, the bulk of the literature deals with spherical particles. Table 4.1 provides a listing of the pertinent works in this field. An examination of this table shows that most of the research effort has been directed at the elucidation of three aspects of the particle behavior in visco-plastic media. They are
1. Static equilibrium, and the development of a criterion for the initiation or cessation of motion under the influence of gravity.