Separation development in a closed system

Dividing both sides by Ixly Az and taking the limit Az 0, we get 

Assume now that the movement of solute species 1 in the solvent does not affect the movement of solute species 2 and vice versa. Following the derivation of the species balance equation (3.2.2) for i = 1, we may obtain a similar species conservation equation for i = 2  

Tbe solution of these two partial differential equations, subject to appropriate boundary and initial conditions, will yield the concentration profiles for solutes i =1,2 as a function of z and t. 

How each of these two concentration profiles develops along the z-coordinate with time is intimately connected with the nature of the species-specific forces, since the latter determine Ni. Recall from expressions (3.1.27) and (3.1.42), at constant temperature. 

We will find out later that the nature of the profile in the z-direction along the separator is crucial. It can be either continuous or discontinuous, with all sorts of variation with z in either category. 

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