Network modeling of the convective flow and diffusion of molecules adsorbing in monoliths and in porous particles packed in a chromatographic column.

A cubic lattice network of interconnected pores was constructed to represent the porous structure existing in a monolith (continuous bed) or in a column packed with porous chromatographic particles. Expressions were also constructed and utilized to simulate, through the use of the pore network model, the intraparticle interstitial velocity and pore diffusivity of adsorbate molecules in porous chromatographic particles or in monoliths under retained and unretained conditions. The combined effects of steric hindrance at the entrance to the pores and frictional resistance within the pores, as well as the effects of pore size, pore connectivity, nT, of the porous network, molecular size of adsorbate and ligand (active site), and the fractional saturation of adsorption sites (ligands), have been considered. The results for the adsorption systems studied in this work, indicate that the obstruction effects on the intraparticle interstitial velocity, due to (a) the thickness of the immobilized layer of active sites and (b) the thickness of the adsorbed layer, are small and appear to be insignificant when they are compared with the very significant effect that the value of the pore connectivity, nT, has on the magnitude of the intraparticle interstitial velocity. The effective pore diffusion coefficient of the adsorbate molecules was found to decline with increasing molecular size of ligand, with increasing fractional saturation of the active sites or with diminishing pore size, and with decreasing pore connectivity, nT. The results also show that the magnitude of the interstitial fluid velocity is many times larger than the diffusion velocity of the adsorbate molecules within the porous adsorbent particles. Furthermore, the results clearly show that the intraparticle interstitial velocity and the pore diffusivity of the adsorbate increase significantly as the value of the pore connectivity, nT, of the porous medium increases. The results of this work indicate that the pore network model and the expressions presented in this work, could allow one, for a given porous adsorbent, adsorbate, ligand (active site), and interstitial column fluid velocity, to determine in an a priori manner the values of the intraparticle interstitial velocity and pore diffusivity within the monolith or within the porous adsorbent particles as the fractional saturation of the active sites changes. The values of these transport parameters could then be employed in the macroscopic models that could predict the dynamic behavior, scale-up, and design of chromatographic systems. The theoretical results could also have important implications in the selection of a ligand as well as in the selection and construction of an affinity porous matrix.