Analytical approximation for diffusion-reaction processes in rough pores

¹ Centre de Mathématiques et de leurs Applications Ecole Normale Supérieure de Cachan 94235 Cachan, France
² Departamento de Física, Universidade Federal do Ceará 60451-970 Fortaleza, Ceará, Brazil
³ Laboratoire de Physique de la Matière Condensée, Ecole Polytechnique 91128 Palaiseau, France

Corresponding authors: soares@fisica.ufc.br marcel.filoche@polytechnique.fr bernard.sapoval@polytechnique.fr

Received: 15 December 2000
Accepted: 8 June 2001

Abstract

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