Derivation of the Differential Equations 11 and

Because of the mixed conductivity of the anodic film, the Faradaic process at the anode splits into two, i.e. at the inner junction (metal/film) and the outer one (film/electrolyte). 

Let us denote the ionic current part as a. Then, at current I and in a lime interval of dt the quantity of deposit 

At the outer junction, (1 - a)Idt Coulombs of electricity are consumed at the same time to oxidise the portion of the film substance d//exu and the portion of the intermediate transferred from the bulk by the flux is 

To determine the flux, Nemst model of stationary diffusion with linear distribution of the concentration across the layers of the constant thickness is used, and the concentration of the intermediate is assumed to be zero, i.e. the anode discharge proceeds at limit current condition. Then 

The differential equation (Eq. 5.11) is obtained by combination of the equation for the material balance of the film substance 

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