Mathematical modelling and simulation of adsorption processes at spherical microparticles

Abstract

A model for the adsorption process at spherical microparticles under transient diffusion conditions has been developed and solved using numerical simulation. This model allowed us to demonstrate that the system is controlled by two main dimensionless parameters: the adsorption rate constant ka' and the saturation parameter beta. Analytical models for the adsorption process at spherical microparticles under steady-state mass transport conditions have been derived. These models use previously developed empirical relationships for the calculation of the mass transfer coefficient (kc). The properties of the system were studied for both the case where mass transport is described by diffusion only and the case where it is the result of a coupled diffusion/convection process. These mathematical tools were then used to analyse the results obtained for the uptake of CuII by glassy carbon powder modified with the monomer L-cysteine methyl ester and to extract a minimum value for the adsorption rate constant which was found to be of the order of 10(-4) cm s(-1).