First-order kinetics in fractal catalysts: Renormalization analysis of the effectiveness factor

By applying Input/Output renormalization and the Green function formalism to the discrete formulation of transport phenomena on graphs, we develop exact recursion for the effectiveness factor for first-order reaction in a fractal porous catalyst. The scaling of the effectiveness factor vs the Thiele modulus is obtained in the case of finitely ramified fractals and discussed in detail. Crossover phenomena in hierarchical and heterogeneous fractal pore-network models and renormalization recursion for integral quantities are also analyzed