Rate of diffusion-limited reactions for a fractal aggregate of reactive spheres

On the basis of the mean-field approximation, the "macroscopic" equation simply includes an effective sink term in the diffusion equation for a porous catalyst. Thus, the accuracy of the aforementioned coarse-grained theories should be accessed by the "microscopic" approach based on solving the diffusion equation for the local concentration of the reactant around sinks with appropriate boundary conditions. This paper adopts such a microscopic description to calculate the rate of diffusion-limited reactions for a fractal aggregate of reactive spheres.