Batch sedimentation

This result follows from the Richardson-Zaki equation. In their original work, Richardson and Zaki (1954) studied batch sedimentation, in particular the settling of coarse solid particles through a liquid in a vertical cylinder with a closed bottom. Richardson and Zaki found that the settling speed uc of the equal-sized particles in the concentrated suspension was related to the terminal settling speed u, of a single particle in a large expanse of liquid by the equation... 

If a tangent is drawn from the point on the abscissa corresponding to the required underflow concentration C , it will meet the if curve at a concentration value CL at which fT has the minimum value (A/v. and will intersect the ordinate axis at a value equal to irTL. The construction is dependent on the fact that the slopes of the tangent and of the iru line are equal and opposite ( uu). Thus, in order to determine both Cl and (An, it is not necessary to plot the total-flux curve (i[Pg.260]

In a batch sedimentation experiment, the sediment builds up gradually and the solids which are deposited in the early stages are those which are subjected to the compressive forces for the longest period of time. In the continuous thickener, on the other hand, all of the particles are retained for the same length of time with fresh particles continuously being deposited at the top of the sediment and others being removed at the same rate in the underflow, with the inventory thus remaining constant. Residence time distributions are therefore not the same in batch and continuous systems. Therefore, the value of tR calculated from equation 5.59 will be subject to some inaccuracy because of the mismatch between the models for batch and continuous operation. 

Wallis, G. B. Third Congress of the European Federation of Chemical Engineering (1962). Symposium on the Interaction between Fluids and Particles, 9. A simplified one-dimensional representation of two-component vertical flow and its application to batch sedimentation. 

Figure 5.4.2 (A) Kinematic shock (B) boundary conditions for kinematic shocks in batch sedimentation.

Figure 5.4.3 Interface positions as a function of time in batch sedimentation of an infinitely dilute suspension.

Figure 5.4.5 Flux curve for batch sedimentation with hindered settling.

Figure 5.4.6 Simple concave downward flux curve with a maximum and no inflection point for batch sedimentation with hindered settling.

Finally, we make mention of a settling method that employs the fact that particles when settling in an inclined tube do so faster than if the tube is vertical. This effect is termed the Boycott effect, after the physician A.E. Boycott, who in 1920 made this observation in connection with the sedimentation of blood cells in a tube. A picture of batch sedimentation in an inclined channel is shown in Fig. 5.4.8. The clarified liquid, suspension, and sediment are modeled as three distinct regions separated by kinematic shocks, as in vertical settling. 

Consider the batch sedimentation of a mixture of particles of two different characteristic sizes but the same density and configuration (concentrations... 

The apparatus may be used for a batch sedimentation by sinq>ly setthng for prescribed periods of time and sanq)ling at all the san le points. An arithmetic average concentration is confuted for all the points above and including the one in question. In this way decantation of supernatant liquid above that point is simulated. 

Figure 14.3-4. Batch sedimentation restdts (a) original uniform suspension, b) zones of settling after a given time, (c) compression of zone D after zones B and C disappear, (d) clear liquid interface height z versus lime of settling.

Moncrieff A.G., 1964. Theory of thickener design based on batch sedimentation tests, Trans IMM, 73, 729-759. 

Mirza and Richardson (1979), based on batch sedimentation experiments with several sized binaries down to E 0.5, concluded that the species interaction effect could be accounted for by the factor applied to the right-hand side of Eq. (127), so that... 

Note that for a monodisperse system. Eg, = e and Eq. (134) reverts back to Eq. (131). Both Eqs. (132) and (134) were able to map features of the binary batch sedimentation data of Richardson and Meikle (1961a) for spheres of different sizes and densities having the same value of /q. 

Figure 4.2.6. Batch sedimentation of a dilute suspension of particles under gravitatiorml force (a) dilute suspension in a vessel at time t = 0 (b) condition at time fi > 0 (c) condition at time t2> h> 0 (d) final ecfuilibrium state.

The nature of these two trajectories changes if batch sedimentation involves a more concentrated suspension (for an introduction, see the general treatment in Probstein (1989) of the subject). First, the settling velocity of an individual particle is reduced due to the close proximity of many other particles. This is due to an increased viscosity of the Uquid, as well as an increased drag force experienced by the particle due to the other particles. The effective settling velocity is less than f/p, for a dilute suspension of the same particle size ... 

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