Effects of Particle Shape and Size Distribution on the Transient Solution of the Diffusion Equation

Abstract

THE phenomenon of zeolitic sorption has attracted much attention recently because of the increasing practical importance of synthetic zeolites, both as specific adsorbents and as catalysts. It is customary to correlate kinetic data for the sorption of gases in zeolites in terms of diffusion coefficients, calculated by matching experimental sorption curves to the appropriate transient solution of the diffusion equation. This of course assumes that the diffusivity is independent of concentration but, provided the change in concentration is small, this is a reasonable approximation. For a system of uniform spherical particles of radius r subjected at t=0 to a step change in sorbate concentration, the solution of the diffusion equation is1illustration where mt= mass of sorbate adsorbed or desorbed during time t, m∞=mass of sorbate adsorbed or desorbed as t←∞ and D=diffusivity. It is generally assumed that this expression can be used to represent the sorption curves for zeolites, using a mean equivalent spherical radius to account for the effect of crystal shape2. For short times equation (1) fits the experimental data well, but significant deviations are commonly observed at intermediate and large times. This led Kehat and Heineman3 to conclude that the sorption process is non-Fickian. In this communication we shall show that the deviations from equation (1) observed at intermediate and large times probably arise because the effects of crystal shape and size distribution are neglected in the analysis of the sorption curves. Open image in new window