The Rate Equation for Film Diffusion

The derivation of the rate equation used subsequendy for film diffusion controlled ion-exchange processes in homogeneous systems is oudined briefly below, since it is needed later for initiation of the description of 

Here p denotes the chemical potential, z the signed valencies of the ions, F the Faraday number and 9 the electrical potential. The flow of solvent is zero in the SF frame. The electrical current density has to vanish, i.e., 

Since no electrical field is applied, (p is the diffusion potential originating from the different mobilities of the ions in the film. The ionic flows are obtained by substituting Eq. (4) in Eq. (1) as shown 

For an 1 1 electrolyte the measurable chemical potentials pj3 and P23 are equated to their inaccessible single ion chemical potentials p, as shown 

The solvent fixed flows of the two electrolytes can then be written as 

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