Brownian sieving enhancement of microcapillary hydrodynamic chromatography. Analysis of the separation performance based on Brenner's macro-transport theory

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

The exact moment approach (EMA) is adopted to predict, without any fitting parameters, the plate height curves for polystyrene microparticles of different sizes in micropillar array columns performed by hydrodynamic chromatography. The EMA allows us to decouple the contribution of horizontal and vertical dispersion terms and thus investigate the influence of pillar height and interpillar distance on separation performance. In the convection-controlled regime, we found that axial dispersion is mainly controlled by the vertical dispersion term, the latter being due to the flow-arresting top and bottom walls. This vertical contribution can be estimated from the axial dispersion in rectangular, open tubular channels formed between the pillars. Henceforth, plate height curves can be accurately predicted by simply adding the estimated vertical term to the horizontal dispersion term evaluated from 2D simulations. This finding allowed us to understand that, to improve separation performance, it is advisible to decrease the interpillar distance (expected result) and decrease the pillar height (counterintuitive result).

On the modelling of the effective longitudinal diffusion in bi-continuous chromatographic beds

We report on the possibility to extend to bi-continuous packings the two models for the effective longitudinal diffusion Deff, or B-term band broadening, recently proposed for discontinuous chromatographic beds. In bi-continuous packings, like monolithic columns, solutes experience a connected end-to-end pathway in both the mobile and stationary zones, as opposed to discontinuous packings, wherein the stationary adsorptive zone is distributed over a set of isolated elements. Since it is unclear whether a densely packed bed of spherical particles should be treated as a continuous or a bi-continuous medium, this extension is also crucial to fully understand the behaviour of packed particle beds. The proposed models for the effective longitudinal diffusion Deff originate from the adoption of the Two Zone Moment Analysis (TZMA) method by which Deff can be expressed as a linear combination of two essential quantities γm and γs, referred to as effective zone-diffusion factors. In the present work we propose two analytical models for γm and γs that now cover both the discontinuous and the bi-continuous case. To validate the theory, several bi-continuous packings are investigated, including the tetrahedral skeleton model (TSM), six different Triple Periodic Minimal Surface (TPMS) monoliths and randomly packed beds of spheres. For all of these, the models provide highly accurate results for Deff over a wide range of porosities and zone retention factors k″. The comparison with literature experimental data for both monolithic silica columns and columns packed with fully porous and porous-shell particles is also presented.

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. The analysis of the transient behaviour can be used, for example, to properly identify the time and length scales needed to achieve the macro-transport conditions. If the hierarchical porous media can be represented as the periodic repetition of a unit lattice cell, the method only requires the solution of the time-dependent advection-diffusion equations for the zeroth order and first-order exact local moments, exclusively on the unit cell. This implies an enormous reduction of the computational efforts and a significant improvement of the accuracy of the results when compared to the direct numerical simulation (DNS) approaches which require flow domains that are long enough to achieve steady-state conditions, and hence often cover tens to hundreds of unit cells. The reliability of the proposed method is verified by comparing its predictions with DNS results, in one, two and three dimensions, in both transient and asymptotic conditions. The influence of top and bottom no-slip walls on the separation performance of chromatographic columns with micromachined porous and nonporous pillars is discussed in detail.

50-Fold Reduction of Separation Time in Open-Channel Hydrodynamic Chromatography via Lateral Vortices

Despite its relatively long history, open-channel hydrodynamic chromatography (OC-HDC) still represents a niche technique for determining the size distribution of particle suspensions. Practical limitations of this separation method ultimately arise from the low eluent velocity that is necessary to contain the adverse increase of analyte bandwidth caused by Taylor-Aris dispersion. Because of the micrometric size of the channel cross section, the low eluent velocity translates into order of pL-per-minute flow rates, which introduce a challenge for both the injection and the detection systems. In this article, we provide theoretical/numerical evidence illustrating how a sizable reduction of the Taylor-Aris effect can be obtained by triggering cross-sectional vortices alongside the main pressure-driven axial flow. As a case study, we consider a square channel geometry where the lateral vortices are created by DC-induced electroosmosis. The analysis of particle separation is based on the classical excluded-volume macrotransport approach, which allows to derive the average particle velocity and the axial dispersion coefficient from the solution of two stationary advection-diffusion problems defined onto the channel cross section. We find that lateral vortices can enhance the separation efficiency quantitatively, e.g., by reducing the separation time of a two-species mixture by a 50-fold factor compared to standard OC-HDC.