Nonadditivity and Nonlinearity of Mobile and Stationary Zone Mass Transfer Resistances in Chromatography

Abstract

Using a two-zone moment analysis (TZMA) method based on Brenner’s generalized dispersion theory for two-dimensional (2D) and three-dimensional (3D) periodic media, we investigated the mechanisms for dispersion in particulate media for liquid chromatography. This was done using a set of plate height data covering an unprecedented wide range of retention factors, diffusion coefficients, and velocities, all computed with unequaled accuracy. Applying Giddings’ additivity test, based on alternatingly making the diffusion coefficient in the mobile and stationary zones infinitely large, the dispersion data clearly indicate a lack of additivity. Although this lack could be directly understood by identifying the existence of multiple parallel mass transfer paths, the additivity assumption interestingly overestimates the true C term band broadening (typically by more than 10%, depending on conditions and dimensionality of the system). However, Giddings originally asserted the occurrence of parallel paths would always lead to an underestimation of the dispersion. The origin of the lack of additivity is analyzed in detail and qualitatively explained. Finally, we also established a generic framework for the modeling of the effect of the reduced velocity and the retention coefficient on the C term in ordered chromatographic media. This led to the introduction of a new expression for the mobile zone mass transfer term, which, unlike the currently used literature expression, contains the complete k″ dependency.

An In-Depth Investigation of Micropillar Array Columns for the Separation of Finite-Sized Particles by Hydrodynamic Chromatography

“…Equations – are valid for a tracer particle as well, although they strongly simplify by enforcing w 0 = 1/Vol­(Ω) . The advantage of eq has already been extensively exploted for the analysis of dispersion properties in partition and adsorption chromatography. − The velocity field, the stationary pdf w 0 , and the b-field in the unit cell are obtained by the Finite Element Method in Comsol Multiphysics. Numerical details are listed in the SI.…”

Prediction of Plate Height Curves of Porous-Shell Pillar Array Columns Micro-Pillar Array Columns

“…Consequently, it necessitates the application of more complex homogenization approaches [22][23][24][25][26][27][28][29][30] that can handle and exploit the periodic structure of the unit cell. Recently, a new homogenization approach, named two-zone moment analysis (TZMA), has been proposed and rigorously validated [31][32][33][34][35][36], for application in chromatographic systems. The TZMA approach is a novel homogenization strategy, alternative to volume averaging techniques [37][38][39][40][41], aimed at significantly enhancing the speed and precision in addressing the general advection-diffusion equation within hierarchical porous media featuring diffusion and adsorption-desorption processes.…”