Segregation fraction

From Eqs. (7-1) and (7-2), it follows that the separation factor is purely based on the compositions of the entering and exit streams regardless of their flows. Another measure of the separation efficiency of a membrane process is the extent of separation proposed by Rony [1968]. In the context of applying this index of separation efficiency between two comfionents, it is assumed that there is no difficulty in separating the third component Thus the segregation fractions, fiy, are obtained from the molar flow rates of the permeate and retentate streams on the basis of only two components. The extent of separation is defined as the absolute value of a determinant of a binary separation matrix consisting of the segregation fractions as follows ... 

In cross segregation, on the other hand, the separating surfaces between the segregated fractions are oriented perpendicularly to the direction of movement. In this case the segregated fractions arrive at the discharge points completely separated at different times, and there are no chances of remixing at the discharge point. 

Following the segregation fraction Yy for nonisotopic systems, one can define the segregation fraction Yfj of an isotopic mixture as... 

Instead of considering only the separation of particles from one another, consider now the separation of all particles (species 2) from the fluid (species 1) feed or the elimination of liquid from the solid-rich underflow (region 2). Instead of the segregation fractions defined by (2.4.8), we will have... 

We assume that Kii, Vi and V2, and therefore Hn, are independent of the specific number of contacts. Assume the original phase (which becomes the rafSnate after the process) containing the solute i isj = 2 the total number of moles of solute z originally in this phase is m. As the first volume Vi of the extractant is brought in, the segregation fractions after equilibration are given by... 

If we now carry on a third contact by bringing in fresh V"i to contact V2 after second contact (having a total number of moles mtfi] of species z), the molar distribution now consists of m,i(3), mj2(3), where (zztii(3) -I- mj2(3)) = zna(2). Therefore, based on these three contacts, the segregation fractions are... 

If we define the segregation fraction after second contact based on the original amount of solute ml in phase 2 (raffinate), then... 

The fraction of solute (macrosolute) left in the feed/reten-tate (f ) liquid is the segregation fraction, given by... 

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