A diffusion limited sorption kinetics model with polydispersed particles of distinct sizes and shapes

We propose a numerical model to compute spatial and temporal variations of the dissolved and sorbed phase concentrations within porous particles of different sizes and shapes that undergo dynamic mass transfer with the surrounding bulk concentration. The model accommodates intra-particle reversible sorption kinetics, film resistance at particle surfaces, and first-order decays in both intra- and extra-particle aqueous volumes. The model allows consideration of mixtures of polydispersed particles of distinct sizes and shapes. A finite-difference formulation of the model provides quantification of novel uptake terms that determine magnitudes of mass transfer between extra-particle aqueous phase and the particles. The model also allows consideration of non-linear irreversible site-limited intra-particle surface reactions for identical particles of spherical, cylindrical, and rectangular geometries. Applications for several examples illustrate the general behavior. Experimental data of iodine concentrations from a wastewater sample were well represented by the pore-diffusion model with site-limited sorption.