Kynch Theory and Compression ZonesKynch's theories of sedimentation are reinterpreted, modified, and extended to be valid for batch sedimentation in which a zone of compacting sediment forms at the bottom of the column. The development has several steps: First, it is shown that a concentration discontinuity, any part of whose chord plots above the curve on a Kynch plot of settling flux vs. particle concentration, will be unstable and immediately give rise to a different concentration distribution. From this it is deduced that Kynch characteristics, or loci of constant concentration, must propagate either from the origin of a height vs. time plot, or tangentially from the locus of the compression or suspension-sediment discontinuity. A Kynch-like construction is derived to relate the settling rate at the top of the suspension (measured by its subsidence rate) to the concentration arriving at the surface at that time. It makes use of two tangents, one to the settling curve (as in Kynch), and another to the locus of the compression discontinuity. Finally a construction, analagous to that of Talmage and Fitch, is deduced for determining required thickener area.

Three modes or types of sedimentation are recognized in flocculent suspensions: Clarification, in which floccules are separated and settle independently; zone settling, in which floccules are incorporated into some solids structure so that all are constrained to subside at more or less the same rate; and compression or compaction, in which the solids structure is strong enough to exhibit a compressive yield value. Current models for sedimentation in the three moses are reviewed, with particular emphasis on their use thickening presented in the literature derive from a basic partial differential equation for force balance. Models differ in which terms of the equation are disregarded. Several of the theories of compaction are essentially equivalent solutions for the same model, but with different sets of independent variables. and reliability (or lack of it) for sedimentation basin design. Most models ofSedimentation is here defined as the entire process by which particles settle out of fluid suspension. All steps of the process are profoundly affected by interfacial phenomena. Van der Waals or London forces, if not overpowered by electrostatic repulsions (zeta potentials) or fluid-dynamic shear, cause particles to cohere on contact. This gives rise to three different modes or regimes of sedimentation. Which one is followed depends upon the solids concentration, and on the relative tendency of the particles to cohere. The factors are important because they correspond to different sedimentation models or mechanisms.Types of sedimentation are represented paragenetically in Figure 1. The left side represents particles with little tendency to cohere; the right side, those for which interparticle cohesion is strong. The vertical axis represents particle concentration, with more concentrated suspensions at the top.At low concentrations, there occurs a regime called clarification. Particles are, on the average, far apart and free to settle independently, but collisions occur. If the particles then cohere, they grow into clumps, or floccules, whose settling rate increases as they grow. If, on the other hand, they do not cohere, each bumps downward at its characteristic rate. Thus there are two types of settling in clarification: flocculent, and particulate. There is no sharp boundary between the two; one grades gradually into the others. And, it is common practice to modify behavior in this regime by adding flocculants to aid clarification.Clarification behavior is easily recognized in a batch test. Slower settling particles string out behind faster settling ones. The upper layers gradually thin out, or clarify, Settled solids collect at the bottom in a layer whose upper boundary rises as solids settle into it.As particles become more concentrated, crowded closer together, they Enally reach a point where each is in contact with others. If they then have any tendency to cohere, they link into some sort of floc structure. Whether the structure formed is continuous (Fitch 1982(Fitch , 1972 consists of a bed of closely-spaced...

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All classical models for thickening assume one-dimensional continuity. However, the free-settling domain in continuous thickeners is not one-dimensional. Therefore, a two-dimensional model is investigated. The two-dimensional model gives the same values for thickener area demands as the one-dimensional model, but the relationships between batch and steady-state thickening are not the same. Free-settling Kynch characteristics can arise in the continuous operation that do not arise in batch tests. Therefore, design procedures that rely on Kynch theory, such as that of Talmage and Fitch, are not completely valid.A method is developed, based on extrapolating the Kynch or free-settling segment of a batch settling curve, that yields an improved prediction for thickener area demand.principle applies for the amount of solids passing through a Kynch characteristic. Generalized proof of area principleA general proof of the area principle for characteristics is now given:The time dt needed for an element of flow dQ to pass through an element of space bounded by flow lines is shown in Figure 2:The time it takes a characteristic surface to rise from the bottom to the top of the flow element is: