Influence of nonlinear reaction kinetics

The parametric areas of five regimes are identified for two values of the diffusion ratio. Typical radial concentration profiles associated with each physical picture are also shown. In this case, the boundary for the kinetically controlled regime is given by the value of the Damkohler number so that the effectiveness factor is kept, for example, above 0.9. Since in this case conversion in the channel is negligible, the reactant concentration distribution at the interface with the coating is uniform and close to the inlet value. 

The same cannot be said under mass transfer control, where the surface distribution of concentration and reaction rates included in the Thiele modulus also depend on the mass transfer problem in the channel. This only happens for nonlinear kinetics and gives origin the distinction between an overall regime (with low wall concentration but still allowing for strong gradients to develop in the coating) and a purely interphase resistance (where channel concentration is so low that the effectiveness factor may even approach 1). 

The development of the correlation for the effectiveness factor in Section 8.2.3 also allows the accurate description of 

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