Catalytic effectiveness of irregular interfaces and rough pores: the 'land surveyor approximation'

摘要

We apply the concept of active zone in Laplacian transport to investigate the steady state mass transfer of a diffusive species towards an arbitrarily irregular catalytic interface. By means of a recently proposed coarse-graining technique, it is possible to compute the reactive flux on the catalytic interface from its geometry alone, without solving the general Laplace problem. As a result, we demonstrate by direct numcrical simulation of molecular diffusion and first-order reaction that this method allows one to predict the catalytic effectiveness of a slit-shaped pore with an arbitrary rough geometry and over a wide range of diffusion-reaction conditions. It is found that, contrary to the traditional pseudo-homogeneous approach, the effect of the irregular morphology at the mesoscopic pore level is modify the reaction rate and not the effective diffusion coefficient. We show that, for all practical situations where the reactant penetration in the pore is significant, a simplified picture of a smooth pore with an effective reactivity K_(eff) can be used to describe the efficiency of a rough pore. Remarkably, K_(eff) is the product of the intrinsic reactivity by a screening factor S, which has an elementary geometrical meaning, namely, the ratio between the real and the apparent surface area.