Indices of separation for binary systems

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

All three quantities, the mole fraction x,j, the mass fraction Uij and the atom fraction aip vary between the limits of 0 and 1. When their value is 1, we have pure species i in region j. The closer their value is to 1, the greater is the purity of the region (fraction or phase) in the ith species. 

On the other hand, the mole ratio Xy and the abundance ratio Xy vary between 0 and 00, the latter value indicating only pure species i in region j. Thus, the upper limits of the two sets of quantities xy, Uy, ay and Xy, X ) have radically different values, although all of these quantities indicate the level of purity of the ith species in the given /th region in their own ways. 

Sometimes the initial binary mixture to be separated is not a uniform mbcture as in vessel A, but instead has two regions whose compositions are characterized as Xif and Xif corresponding toy =/i,/2- Note that these regions are such that region/i usually has more of species 1, whereas region /2 has more of species 2. The total and ith component mass balances in such a case lead to 2 2 

The simplest separation indices are the distribution ratio (or capacity factor) k y, the distribution coefficient iqi and the equilibrium ratio K(  

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