Wagner pseudo-steady state approximation

We can see in section 7.4.1 that a system is a pseudo-steady state one if there is no accumulation of matter at any point, which is translated by writing that the change of matter amount is null. 

We will examine how the pseudo-steady state is written for diffusion through an increasing layer. We will reason in the case of a one-way diffusion according to a 

Indicate by Q the concentration in diffusing species at as X-coordinate and by C, the concentration at X2 as X-coordinate. These two concentrations are maintained constant (fixed by interfacial equilibriums, for example). The two interfaces are mobile in consequence of the growth of the layer. Write the material balance of the amount of diffusing species in the layer. Using the pseudo-steady state condition, we get 

The terms and take into account the thickness variation of the 

The gradient of concentration in the layer is independent of the X-cooidinate and thus 

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We can consider two manners of dealing with this problem. The first one is due to Danckwerts PAN 50] based on the resolution of the laws of Pick and the second is the pseudo-steady state approximation of Wagner. 

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