How do the HSDM and Boyd's model compare for estimating intraparticle diffusion coefficients in adsorption processes

Adsorption kinetics is a key-issue for a successful activated carbon selection and design of the treatment system. Crucial predictive aspects are the determination of the diffusion coefficients and the establishment of the controlling adsorption step. Several kinetic models have been developed and two of the most frequently used, the homogeneous surface diffusion model (HSDM) and the Boyd's model, were applied to microcystins, and particularly MC-LR adsorption. Different initial MC-LR concentrations and carbons (particle diameter, porosity), yielding diverse Biot numbers (Bi), were tested. The model outcomes were compared, namely the Boyd's effective intraparticle diffusion coefficient (D-i) with the HSDM surface diffusion coefficient (D-s), as well as the Bi and Boyd's criteria to establish the controlling adsorption step, which constitute a novel approach. Very good HSDM fittings were achieved with a constant diffusion model (D-s independent of MC-LR surface concentration). D-i was similar to D-s whenever Boyd plots intercepted the origin. The Biot limit above which it may be considered that intraparticle diffusion is the rate limiting step depended on the carbon. A lower limit was observed for smaller carbons.