Foust, A. S., et al. (1979). Principles (1979). Principles of Unit Operations, Operations, 2nd Ed . John Wiley & Sons, Inc., p. 629 – 637. The separation of a dilute slurry by gravity settling into a clear fluid and a slurry of higher solids content is called sedimentation. The mechanism of sedimentation may be best described by observation of what occurs during a batch settling test as solids settle from a slurry in a glass cylinder. Figure 22.18a shows a newly prepared slurry of a uniform concentration of uniform solid particles throughout the cylinder. As soon as the process starts, all particles begin to settle and are assumed to approach rapidly the terminal velocities under hindered-settling conditions. Several zones of concentration will be established (Figure 22.18b). Zone D of settled solids will predominantly predominantly include the heavier faster-settling particles. In a poorly defined transition zone above the settled material, there are channels through which fluid may rise. This fluid is forced from zone D as it compresses. Zone C is a region of variable size distribution and non-uniform concentration. Zone B is a uniformconcentration zone, of approximately the same concentration and distribution as initially. At the top of region B is a boundary above which is clear liquid, region A. If the original slurry is closely sized with respect to the smallest particles, the line between A and B is sharp. As sedimentation continues, the heights of each zone vary as indicated on Figure 22.18b, c, and d. Note that both regions A and D grow larger at the expense of region B. Eventually, a point is reached where B and C disappear and all the solids appear in D; this is referred to as the critical settling point (Figure 22.18e) – that is, the point at which a single distinct interface forms between clear liquid and sediment. The sedimentation process from this point on consists of a slow compression of the solids, with liquid from the boundary layer of each particle being forced upward through the solids into the clear zone. Settling rates are very slow in this dense slurry. The final phase is an extreme case of hindered settling. Equation 22.22 may be used to estimate settling velocities. It accounts for the effective density and viscosity of the fluid but does not account for agglomeration of particles, so that the calculated settling rate may be in considerable error. Equation 22.22:
In a batch-sedimentation operation as illustrated, the heights of the various zones vary with time. The same zones will be present in continuously operating equipment. However, once steady state has been reached (where the slurry fed per unit time to the thickener is equal to the rate of sludge and clear liquor removal), the heights of each zone will be constant. The zones are pictured in Figure 22.19 for a continuous sedimentation.
Industrial sedimentation operations may be carried out batch-wise or continuously in equipment called thickeners. The batch thickener operates exactly like the example cited above. The equipment is nothing more than a cylindrical tank with openings for a slurry feed and product draw-off. The tank is filled with a dilute slurry, and the slurry is permitted to settle. After a desired period of time, clear liquid is decanted until sludge appears in the draw-off. The sludge is removed from the tank through a bottom opening as indicated in Figure 22.20. Figure 22.23 depicts such a layer of concentration c in a batch test. This layer is assumed to be the ratelimiting one, so it may be viewed as rising at a velocity v L. Solids settle into this layer from just above, having concentration (c – dc) and velocity (v + dv) with respect to the column and (v + dv + v L) with respect to the layer. Solids settle out of this layer at a velocity v with respect to the walls a nd (v + v L) with respect to the layer. If the layer is assumed to have a constant concentration of solids, then by material balance: (c – dc)(S)(θ)(v + dv + vL) = (c)(S)(θ)(v + vL) Geankoplis, C. J. (2003). Principles of Transport Processes and Separation Processes. Pearson Education South Asia Pte. Ltd. Determination of settling velocity. In Fig. 14.3-4d, the height z of the clear-liquid interface is plotted versus time. As shown, the velocity of settling, which is the slope of the line, is constant at first. The critical point is shown at point C. Since the sludge vary greatly in their settling rates, experimental rates for each sludge are necessary. Kynch and Talmage and Fitch describe a method for predicting thickener sizes from the batch settling test.
, with slope . At this point, the height is , and is the intercept of the tangent to the curve. The settling velocity is determined by drawing a tangent to the curve in Fig. 14.3-4d at a given time Then:
The concentration is, therefore, the average concentration of the suspension if z, is the height of this slurry. This is calculated by:
( )
3
Where, is the original slurry concentration in kg/m at z0 height and t = 0. This is repeated for other times, and a plot of settling velocity versus concentration is made. Further details of this and other methods of designing the thickener are given elsewhere. These and other methods in the literature are highly empirical and care should be exercised on their use.
