Perfectly mobile equilibria the mean diffusion coefficient

1 Perfectly mobile equilibria the mean diffusion coefficient 

We consider again the simple equilibrium of eqn. (178). At first sight, diffusion being the only mode of mass transport, it may seem that Fick s second law, formulated in eqn. (19b), can be applied to the concentrations of both O and OLp. However, it is easily argued that this would conflict with the equilibrium condition in eqn. (178) unless the diffusion coefficients D0 and D0Lp are equal [147], Therefore the proper expressions are 

The extra term dcQ /dt = — dc0hp jdt corresponds to the increase of c0 per unit time due to the tendency of the system to maintain the equilibrium relation 

In fact, dc0/dt equals the very small value of the difference kpcOL — kpcQ that is virtually zero. It could be decided to neglect this so-cafled source term , but it is much more appropriate to combine eqns. (181a) and (181b) in such a way that (i) the source term is eliminated and (ii) an equation in terms of the total concentration c0t is obtained. To this end, the mean diffusion coefficient is introduced, in this case defined as [11,147] 

It should be noted that it is not always possible to solve the problem of unequal diffusion coefficients in such a rigorous way [147]. 

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