1ST-ORDER REACTION DIFFUSION KINETICS IN COMPLEX FRACTAL MEDIA

The analysis of transport phenomena with chemical reaction in disordered media requires a detailed characterization of the geometrical structure of the medium. This can be performed by means of fractal geometry, introducing two basic exponents: the fractal and the fracton dimension. Nevertheless, while a statistical analysis of diffusion processes is fairly well established, the definition of mean field approximation for reaction-diffusion phenomena in complex fractal media is still an open question. Starting from the O'Shaugnessy-Procaccia model for diffusion in statistical radially symmetric media, this paper analyzes two models for first-order reaction valid for disordered structure and porous catalysts. The first is based on a generalized Smoluchowski relation and can be applied to diffusion-limited kinetics. In the second the kinetic rate is assumed to be proportional to the density of reacting sites of the medium (uniform kinetics). The steady-state solutions are found in closed form, and the description of steady-state regime is discussed, introducing the concepts of filling factor, which coincides in Euclidean structures with the effectiveness factor, of filling ratio and of stirring factor. In this work attention is focused on the steady-state condition.