Abstract
Much of the theory of gravity sedimentation has been based on the work of Coe and Clevenger (1916) and Kynch (1952). They provided methods for obtaining rates of sedimentation in batch, static tests which are presently used for design of continuous thickeners. Kynch assumed that a first order partial differential equation controlled the entire sedimentation process. His equation was based on: (1) continuity balance; and (2) sedimentation velocity being a unique function of solid particulate concentration. A general solution was presented in the form of volume fraction of solids Ο~s~ = f(x β vt). During the constant rate fall of the upper interface, the boundary condition of uniform initial concentration combines with the Kynch equations to adequately describe the sedimentation phenomena. Kynch ignored the sediment rising from the bottom of the settling chamber, and assumed that the characteristics y = x β vt originated at the origin of coordinates (height, time) during the first falling rate period. The characteristics actually originate at the surface of the rising sediment where the upward liquid velocity affects the rate of fall of the particulates. New equations have been derived based upon the assumption that the characteristics emanate from the rising sediment.