First order approximation for coupled film and intraparticle pore diffusion to model sorption/desorption batch experiments

A simple first order approximation was derived to model sorption/desorption kinetics of hazardous compounds in batch experiments based on a coupled film and intraparticle diffusion model. The solution is accurate enough to replace infinite series expansions needed in analytical solution for intraparticle diffusion and it accounts for the mass transfer shift from diffusion in the external aqueous boundary layer to the intraparticle pore space. With increasing distribution coefficient (K_d) and intraparticle particle porosity (ε) or decreasing Sherwood number (Sh) this mass transfer shift from film diffusion to intraparticle pore diffusion is delayed. The simple first order approximation equation allows analyses of mass transfer resistances and calculation of characteristic times which is relevant for the planning of batch experiments. The proposed solution is verified by a semi-analytical solution in Laplace space for fractional mass uptakes in the solid phase at equilibrium ranging from 50% to 91%, representing scenarios typically encountered in batch experiments.