Agglomerate Model of Electrocatalysis

according to Eq. (84) for an electrochemical reaction, pO+ n e qR, the divergences for species O and R within an agglomerate is given by 

For a ijth-order anodic reaction then we have 

For a linear case, in which reaction order q= 1, Eq. (89) gives the analytical solution 

we define the dimensionless total cuirent density as 

The total current density of one agglomerate sphere can also be evaluated by 

For an arbitrary reaction order, q 0. 1, the approximate forms of general solutions of Eq. (31) can be used for the solutions to Eq. (89) as long as the reaction order n and Thiele modulus j are replaced by q and co respectively. The expressions of concentration A and effectiveness factor 7 for a gth-order reaction, by using m term approximating can be obtained as Eqs. (39) and (40) above. 

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