A logarithmic law for the velocity- and retention-dependency of the eddy dispersion in chromatographic columns.

Applying the recently introduced patchwork model for porous media, we present a new step forward in the modelling of eddy dispersion in chromatographic columns. The logarithmic law describing the velocity dependency emerging from this patchwork model is supplemented with a retention factor dependency via first principles modelling of the variations in flow resistance and retention capacity caused by the packing disorder. Furthermore, it is shown the derived expression is also able to fit the eddy dispersion originating from the wall effect on the packing.

On the contribution of the top and bottom walls in micro-pillar array columns and related high-aspect ratio chromatography systems.

We report on a steady-state based, and hence highly accurate numerical modelling study of the effect of the top and bottom wall in the current generation of micro-pillar array columns. These have a mesoporous retention layer that not only covers the pillar walls but also the bottom wall. Our results show that the performance of these columns can in general not be improved by also covering the top wall with the same layer, despite the increased column symmetry this approach would offer.

Theoretical computation of the band broadening in micro-pillar array columns.

We have investigated the possibility to establish a theoretical plate height expression for the band broadening in the most widely used micro-pillar array column format, i.e., a cylindrical pillar array wherein the pillar walls and the channel bottom are coated with a thin layer of meso‑porous material.

Minimize Precolumn Band Broadening with Immiscible Solvent Sandwich Injection.

We investigated the possibility of reducing the effect of precolumn band broadening (PreCBB) by sandwiching the sample between two small plugs of an immiscible liquid. It has been found that in cases of severe PreCBB, improvements in peak efficiency can amount up to 20 times for the early-eluting compounds. For smaller degrees of PreCBB, the gain on the efficiency of early-eluting compounds is smaller (order of 50%), yet it is still significant.

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

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.

Moment analysis for predicting effective transport properties in hierarchical retentive porous media.

We report on a new homogenization approach to solve, with drastically improved speed and accuracy, the general advection-diffusion equation in hierarchical porous media with localized diffusion and adsorption/desorption processes, thus opening the way to a much deeper understanding of the band broadening process in chromatographic systems. The proposed robust and efficient moment-based approach allows us to compute the exact local and integral concentration moments and hence provides exact solutions for the effective velocity and dispersion coefficients of migrating solute particles. Innovative to the proposed method is also that it not only produces the exact effective transport parameters of the long-time asymptotic solution, but also their entire transient.

Transient Taylor-Aris dispersion in N-capillary systems: Convergence properties of the band broadening in polydisperse multi-capillary columns with diffusional bridging.

We report on a generic mathematical study of the transient plate height regime in bundles of polydisperse capillaries with diffusional bridging. I.e.

Exact analytical expressions for the band broadening in polydisperse 2-D multi-capillary columns with diffusional bridging.

Using a recent generalization of the Aris dispersion method, we have derived exact analytical expressions for the long-time limit dispersion in 2-D multi-capillary packings with diffusional bridging (binary channel system). Both the plug flow and the parabolic flow case are considered. The expressions are mathematically exact over the entire range of possible values of the degree of polydispersity (σ), the retention equilibrium constant K and the diffusion coefficients in the mobile and stationary zone.

Detailed numerical analysis of the effect of radial column heterogeneities on peak parking experiments with slowly diffusing analytes.

The origin of the peak skewness that can be observed when applying the deconvolution method to isolate the diffusion process from the flow processes for peak parking experiments conducted under conditions of slow radial equilibration and strong trans-column velocity gradients was investigated. Numerical simulations were carried out for a variety of trans-column velocity profiles and a broad range of experimental conditions and system parameters were investigated. Results show that, under the aforementioned conditions, the traditionally employed variance subtraction method displays a consistent error which follows the dynamics of the diffusive relaxation during both the peak parking and the flow steps.

Application of evolutionary algorithms to optimise one- and two-dimensional gradient chromatographic separations.

We report on the performance of three classes of evolutionary algorithms (genetic algorithms (GA), evolution strategies (ES) and covariance matrix adaptation evolution strategy (CMA-ES)) as a means to enhance searches in the method development spaces of 1D- and 2D-chromatography. After optimisation of the design parameters of the different algorithms, they were benchmarked against the performance of a plain grid search. It was found that all three classes significantly outperform the plain grid search, especially in terms of the number of search runs needed to achieve a given separation quality.

The checkerboard model for the eddy-dispersion in laminar flows through porous media. Part I: Theory and velocity field properties.

The additivity assumption underlying Giddings' coupling model for the eddy-dispersion in laminar flows through heterogeneous media is critically analyzed and a potential solution for its non-additivity in the high velocity limit is presented. Whereas the unit cell in Giddings' model only consists of a single velocity bias step, the unit dispersion cell of the newly proposed model comprises two consecutive velocity bias steps. Consequently, the unit cell of this new model allows to account for the occurrence of an internal velocity bias rectification at high reduced velocities and is therefore additive in both the low and high velocity limit.