Separation by dialysis using neutral membranes

Dialysis is a membrane process in which a microsolute present in a. feed solution is removed from the feed to a receiving solution of the same phase called the dialysate-, the membrane is such that the macrosolutes 

Let the microsolute (e.g. urea) to be removed from feed be species 1, the feed solution region j =/and the dialysate solution region j = d. Let the feed and the dialysate concentrations of the solute 1 at time t = 0, be C / and 0). We are interested in knowing the 

A total solute balance on the feed side and the permeate side leads to 

Laplace transforms of these two coupled ordinary differential equations will convert the t-domain to the s-domain and yield the following two equations  

After eliminating C f from these two equations, the following equation is obtained for Ci  

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