Modeling and simulation of the dynamic behavior of monoliths. Effects of pore structure from pore network model analysis and comparison with columns packed with porous spherical particles

A mathematical model is presented that could be used to describe the dynami c behavior, scale-up, and design of monoliths involving the adsorption of a solute of interest. The value of the pore diffusivity of the solute in the pores of the skeletons of the monolith is determined in an a priori manner by employing the pore network modeling theory of Meyers and Liapis [J. Chr omatogr. A, 827 (1998) 197 and 852 (1999) 3]. The results clearly show that the pore diffusion coefficient, D-mp, of the solute depends on both the po re size distribution and the pore connectivity, it,, of the pores in the sk eletons. It is shown that, for a given type of monolith, the film mass tran sfer coefficient, K-f, of the solute in the monolith could be determined fr om experiments based on Eq. (3) which was derived by Liapis [Math. Modellin g Sci. Comput., 1 (1993) 397] from the fundamental physics. The mathematica l model presented in this work is numerically solved in order to study the dynamic behavior of the adsorption of bovine serum albumin (BSA) in a monol ith having skeletons of radius r(o)=0.7510(-6) m and through-pores having d iameters of 1.510(-6)-1.8.10(-6) m [H. Minakuchi et al., J. Chromatogr. A, 762 (1997) 135]. The breakthrough curves of the BSA obtained from the monol ith were steeper than those from columns packed with porous spherical parti cles whose radii ranged from 2.50.10(-6) m to 15.00.10(-6) m. Furthermore, and most importantly, the dynamic adsorptive capacity of the monolith was a lways greater than that of the packed beds for all values of the superficia l fluid velocity, V-tp. The results of this work indicate that since in mon oliths the size of through-pores could be controlled independently from the size of the skeletons, then if one could construct monolith structures hav ing (a) relatively large through-pores with high through-pore connectivity that can provide high flow-rates at low pressure drops and (b) small-sized skeletons with mesopores having an appropriate pore size distribution (meso pores having diameters that are relatively large when compared with the dia meter of the diffusing solute) and high pore connectivity, n(T), the follow ing positive results, which are necessary for obtaining efficient separatio ns, could be realized: (i) the value of the pore diffusion coefficient, D-m p, of the solute would be large, (ii) the diffusion path length in the skel etons would be short, (iii) the diffusion velocity, v(D), would be high, an d (iv) the diffusional response time, t(drt), would be small. Monoliths wit h such pore structures could provide more efficient separations with respec t to (a) dynamic adsorptive capacity and (b) required pressure drop for a g iven flow-rate, than columns packed with porous particles. (C) 1999 Elsevie r Science BN. All rights reserved.