  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 find 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 information is sufficient to characterize the reactive
effectiveness of a pore, in spite of the complex morphological features it
might possess.
