Donnan dialysis with ion-exchange membranes .1. Theoretical equation

The transfer of ions through ion-exchange membranes was investigated theoretically for Donnan dialysis. By applying Fick's equation and no electric current to the flux through the ion-exchange membrane on Donnan dialysis, and by changing the valences of feed and drive ions, three kinds of equations were derived: 1) feed ions and drive ions are of equal valence, 2) feed ions are monovalent and drive ions are bivalent, and 3) feed ions are bivalent and drive ions are monovalent. The equations were evaluated by use of a computer by the Runge-Kutta method. The relation between the valence of ions and the characteristic coefficients of the membrane became apparent from the calculated results.