Sedimentation and Consolidation in Poly-disperse Suspensions

In this paper, the problem of sedimentation and consolidation of poly-disperse suspensions is considered. The solid particles are assumed to be of different densities. If the sediment solids stresses are dropped out of the system equations and using the Richardson and Zaki hindered settling model, it has been found that in the limit, i.e., as time approaches infinity, the fluid is completely displaced to the top of the sediment zone. Furthermore, the species segregate completely with the heavier and coarser particles at the bottom of the sediment and the lighter and finer particles at the top of the sediment. Practical observations do not support these behaviors and physical-ly such behaviors do not exist; consequently, results of this kind in the literature are unrealistic. Here, a mathematical structure of the poly-disperse sedimentation and consolidation problem has been proposed. In this case the compaction zone species solids stresses are introduced in the momentum balance equations of the system. The species solid stresses in the sediment are constrained so that the system equations are consistent, i.e., sedimentation and consolidation of two or more identical species should behave as a mono-disperse system. Such a condition has not been recognized and imposed in some of the studies in the literature, which has led to unreliable results. Two practical forms of species stresses that satisfy the system consistency condition are here proposed. It should be noted that the study of sedimentation and consolidation of poly-disperse suspensions could result in more realistic suspension interfaces compared to mono-disperse suspensions, and could lead to more reliable engineering designs of tailings ponds. Predictions of sedimentation and consolidation in models of poly-disperse suspensions are demonstrated using published data.