Mathematical aspects of deactivation processes of rough catalytic surfaces

The progressive deactivation of catalytic surfaces, either by parallel or serial fouling, is a key problem in heterogeneous catalysis. A mathematical model of the deactivation of a catalytic reactor is presented. It is shown that this dynamical model can be turned into the study of the steady-state non-linear response of the same system but for a virtual species. This mapping of the problem permits to obtain analytical results such as the duration of the reactor or its total production. As an example, one shows how a fractal surface would respond in such a deactivation process. Finally, a way to control the time dependency of the reactor production is suggested.