Modelling the relation between the species retention factor and the C‐term band broadening in pressure‐driven and electrically driven flows through perfectly ordered 2‐D chromatographic media

Abstract

The band broadening that can be expected in perfectly ordered cylindrical pillar arrays has been calculated for a wide range of intra-particle diffusion coefficients (D sz ) and zone retention factors (0ok 00 o10) using an in-house-developed computational fluid dynamicsalgorithm. Both pressure-driven and electrically driven (PD and ED) flows are considered. In the case of a large intra-pillar diffusion coefficient (D sz /D mol 5 0.5), the minimal reduced plate height varies between h 5 0.8 (low k 00 ) and h 5 1.2 (high k 00 ), while the C-term range of the Van Deemter curve depends only slightly on k 00 . In the case of a small intra-pillar diffusion coefficient (D sz /D mol 5 0.1), h is nearly independent of k 00 and approximately equals h min 5 1.1, while the C-term band broadening decreases strongly with increasing k 00 . The difference between ED and PD flows in perfectly ordered porous pillar arrays is much smaller than in packed beds, generally only 3% difference around the minimum of the plate-height curve and maximally 10% at high-reduced velocities. The generated data sets were also ideal to verify the accuracy of k 00 and D sz dependency of the general plate height model of chromatography. Determining the values of the geometrical parameters appearing in the model through curve fitting, the average fitting error can be reduced to a value of about 1%.

Predictive model of solute transport with reversible adsorption in spatially periodic hierarchical porous media

“…5. The symbols, solid lines correspond, respectively, to the results of De Wilde et al [28], and our theoretical model. The solid circles and hollow squares correspond, respectively, to D /Dˇ= 0.5 and D /Dˇ= 0.1.…”

“…Current model is capable of capturing the influence of pore geometry on the transport process, hence it is expected that current model will provide accurate results. De Wilde et al [28] numerically calculated the effective diffusion coefficient for solute diffusion in a two-dimensional, ordered circular pillar [28] can be used to check our model. In order to calculate the effective diffusion coefficient by the current model, we need to solve the closure equations.…”

“…In the above, the factor k = V ε int (1 + K)/Vˇis equivalent to the definition of zone retention factor [28] and the vector m is the closure variable as a function of the location in the unit cell A. …”

“…In order to calculate the effective diffusion coefficient by the current model, we need to solve the closure equations. We first reproduce a unit cell of the pillar array geometry reported by De Wilde et al [28] in computer, and then solve the closure equations (Eq. (21)- (26)) to obtain the axial component of the closure variable m x .…”

“…Computational software and hardware advances make it possible to do pore-scale simulation in hierarchical porous media. Some researchers have resorted to direct pore-scale numerical simulations [27][28][29][30]. Simulation results significantly improve our understanding of the solute transport in both macropores and micropores.…”