Problems and pitfalls in the use of the fick formulation for intraparticle diffusion

Abstract

In this paper attention is focused on intraparticle diffusion of multicomponent gaseous mixtures in macroporous and microporous media. Bulk, Knudsen and surface diffusion will be handled using a unified, consistent, approach, borrowing ideas and concepts developed more than a century ago by James Clerk Maxwell and Josef Stefan. The diffusion equations for bulk and Knudsen equations coincide with the dusty gas model, rediscovered already about five times in history. The walls of the porous adsorbent are modelled as giant dust molecules and in this theory they are accorded the status of pseudo-species. One advantage of this procedure is that the kinetic gas theory may now be used to predict the Knudsen diffusion coefficients. For the description of surface diffusion of multicomponent mixtures a new approach is developed in which the vacant sites are modelled, additionally, as pseudo-speices (craters on the dust “molecules”). Then practical application of the crated dusty gas model is illustrated by considering a number of studies, including (1) single-component sorption; (2) uptake of binary mixtures by zeolites and activated carbon; (3) multicomponent diffusion and chemical reaction within catalyst pellets. The examples discussed in this paper support the contention that the Fick formulation is hopelessly inadequate because it will fail even at the qualitative level to describe the observed experimental phenomena. The Maxwell-Stefan formulation provides a useful tool for solving practical problems in intraparticle diffusion.