Equation for Separation Potential

The fact that the total internal flow rate in a close-separation, ideal cascade is given by Eq. (12.142) may be derived without solving explicitly for the individual internal flow rates by the following development, due originally to P. A. M. Dirac. This procedure is valuable in showing the fundamental character of the separation potential and the separative capacity, and provides a point of departure for the treatment of multicomponent isotope separation. 

We consider a close-separation, ideal cascade Wiose external streams have molar flow rates Xif (positive if a product, negative if a feed), and compositions X/t expressed as mole fraction. Let us look for a function of composition x ), to be called the separation potential, with the property that the sum over all external streams, to be called the separative capacity D, 

In a close-separation, ideal cascade 6i =, so that the total flow leaving the rth stage is 

When the separation potential satisfies (12.172), the separative capacity of a single stage in a close-separation cascade operated at a cut of (M = 1V) from Eq. (12.170) is 

We shall now show that the separative capacity of the entire cascade, D, is given by 

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K constant in equation for separation potential of multicomponent mixture X separation parameter defined by Eq. (12.244)... 

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