Differential stage separation

Two types of differential stage separation are illustrated in Fig. 12.10. In type A the stream being removed in small portions is depleted in the desired component, while the remaining stream becomes progressively enriched in this component the concentration of... 

Equations relating the flow rates and compositions of feed and product streams in differential separation processes, first derived by Lord Rayleigh [Rl] for batch distillation, are often called the Rayleigh distillation equation. We shall derive some of these relationships for type B differential stage separation, using the nomenclature shown in Fig. 12.11. 

Figure 12.11 Nomenclature for type B differential stage separation.

In this form it can be seen that a is greater than a, and becomes much greater as B approaches unity. Thus, differential stage separation may be used to enhance the difference in composition attainable in simple stage separation. 

For type A differential stage separation, a similar derivation leads to... 

Equations for Large Stage Separation Factors. The preceding results have been obtaiaed with the use of equation 2 and by replacing the finite difference, by the differential, chc/ dn both of which are vaUd only when the quantity (a — 1) is very small compared with unity. However,... 

Since the residual solution is saturated at 90% recovery, an additional yield does not affect the work. In the paper previously referred to (5), the work for single-stage separation is plotted vs. per cent recovery but the values are considerably lower, especially at the higher yields, than the ones reported here. As no details on the method were given in the previous paper, the authors are unable to explain the discrepancy. The value for 0% is obviously the same for both the differential and single-stage processes. 

Extraction equipment can be classified by function as providing discrete stages or continuous differential contact. Separation may be by gravity alone or by centrifugal force. Additional energy may be applied to control drop size, either by mechanical agitation or pulsation. This classification is shown in Table 1, along with major examples of available equipment. 

Such a simple cascade, with an infinite number of stages each performing an infinitesimal amount of separation, is equivalent to type A differential st e separation. Equation (12.51) is equivalent to the form of the Rayleigh equation (12.35), when one recognizes that w in the simple cascade is equivalent to the heads separation factor 0 in differential stage enrichment, and a in the simple cascade is equivalent to the local separation factor a. ... 

A. Crystalline Lens. For this tissue, the various stages of differentiation are separated in space. Epithelial cells are in a stage of predifferentiation. Protodifferenti-... 

We now turn from liquid-liquid extraction to solid-liquid extraction. In more casual terms, we turn from extraction to leaching. As expected, we can use the same ideas of differential and staged separations to handle this case as well. We begin with target separations, we list separation equipment, and we then describe differential and staged leaching. The summary leads to the case of unsteady-state leaching, a transitional case best handled by parallels with the analysis of adsorption in the next chapter. 

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