Analytical approximation for diffusion-reaction processes in rough pores

The concept of an active zone in Laplacian transport is used to obtain an analytical approximation for the reactive effectiveness of a pore with an arbitrary rough geometry. We show that this approximation is in very good agreement with direct numerical simulations performed over a wide range of diffusion-reaction conditions (i.e., with or without screening effects). In particular, we nd that in most practical situations, the effect of roughness is to increase the intrinsic reaction rate by a geometrical factor, namely the ratio between the real and the apparent surface area. We show that this simple geometrical piece of information is sufficient to characterize the reactive effectiveness of a pore, in spite of the complex morphological features it might possess.