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. The reason for this is that the local species retardation caused by a retentive layer is much stronger than the pure flow arresting effect of an uncovered wall. At least, this has a crucial impact in high aspect-ratio systems such as micro-pillar array columns because these require a small inter-pillar distance to promote mass transfer together with a large channel depth to enable a sufficiently high flow rate. On the other hand, a notable improvement could be made if micro-pillar array would be produced without having a retentive layer at the bottom. At Péclet number Pe = 50 and aspect ratio AR = 5 for flow-channels, this gain amounts up to about 4.5 h-units at a zone retention factor k'' = 2 and 1.75 h-units at k'' = 16 (gain scales almost linearly with Pe). To verify these results, we also considered another high aspect-ratio system with a simplified geometry: the open-tubular channel with a flat-rectangular cross-section. This led to very similar observations, thus confirming the findings for the micro-pillar array. The results produced in the present study also allow us to conclude that the classic modelling paradigm adopted in chromatography, which is based on the independency and hence additivity of the hCm- and hCs-contributions, can lead to large modelling errors in chromatographic systems with a high aspect-ratio, even when their geometry is so simple as that of a straight open-tubular channel with constant cross-section. Indeed, when both zones are treated independently, the analysis misses how the vertical diffusion through the retentive layer helps suppressing the vertical gradients in the mobile zone. The diffusion through this layer occurs in a ratio of k''Ds/Dm (Dm being the diffusion coefficient in mobile phase zone and Ds being the diffusion coefficient in stationary phase zone), such that at high retention factors this diffusion contribution even becomes the dominant one.

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.

Deep reinforcement learning for the direct optimization of gradient separations in liquid chromatography.

While Reinforcement Learning (RL) has already proven successful in performing complex tasks, such as controlling large-scale epidemics, mitigating influenza and playing computer games beyond expert level, it is currently largely unexplored in the field of separation sciences. This paper therefore aims to introduce RL, specifically proximal policy optimization (PPO), in liquid chromatography, and evaluate whether it can be trained to optimize separations directly, based solely on the outcome of a single generic separation as input, and a reward signal based on the resolution between peak pairs (taking a value between [-1,1]). More specifically, PPO algorithms or agents were trained to select linear (1-segment) or multi-segment (2-, 3-, or 16-segment) gradients in 1 experiment, based on the outcome of an initial, generic linear gradient (ϕstart=0.3, ϕend=1.0, and tg=20min), to improve separations. The size of the mixtures to be separated varied between 10 and 20 components. Furthermore, two agents, selecting 16-segment gradients, were trained to perform this optimization using either 2 or 3 experiments, in sequence, to investigate whether the agents could improve separations further, based on previous outcomes. Results showed that the PPO agent can improve separations given the outcome of one generic scouting run as input, by selecting ϕ-programs tailored to the mixture under consideration. Allowing agents more freedom in selecting multi-segment gradients increased the reward from 0.891 to 0.908 on average; and allowing the agents to perform an additional experiment increased the reward from 0.908 to 0.918 on average. Finally, the agent outperformed random experiments as well as standard experiments (ϕstart=0.0, ϕend=1.0, and tg=20min) significantly; as random experiments resulted in average rewards between 0.220 and 0.283, and standard experiments resulted in average rewards of 0.840. In conclusion, while there is room for improvement, the results demonstrate the potential of RL in chromatography and present an interesting future direction for the automated optimization of separations.

Column-Only Band Broadening in a Porous Shell Radially Elongated Pillar Array Column.

In the quest for better performing separation media for liquid chromatography, micropillar array columns have received great interest over the past years. While previous research was mainly focused around micropillar array columns (µPACs) filled with cylindrical pillars, this contribution discusses µPACs with rectangular pillars, which, for the first time, have been anodized and hence carry a mesoporous shell. We report on a series of on-chip measurements of the band broadening and flow permeability in a µPAC with very wide radially elongated pillars (3·75 µm) and with an interpillar distance (2 µm) between that of the first (2.5 µm) and second generation (1.25 µm) of cylindrical µPACs. Because of the extreme flow path tortuosity, this type of µPAC can produce very large plate numbers over a short distance. Despite the relatively large interpillar distance, we obtain Hmin = 0.26 µm for a nearly unretained component (phase retention factor, k' ≈ 0.24) and Hmin = 0.79 µm for a retained component with k' ≈ 3. The kinetic performance in terms of separation impedance (Ei = 19) is considerably improved compared to cylindrical pillar µPACs (Ei in range 40-50) and is in excellent agreement with the theoretical value for an open tubular channel with a rectangular cross-section (Ei = 18). This shows that rectangular µPACs can be represented as a parallel bundle of interconnected open-tubular channels.

Toward Unrivaled Chromatographic Resolving Power in Proteomics: Design and Development of Comprehensive Spatial Three-Dimensional Liquid-Phase Separation Technology.

Spatial comprehensive three-dimensional chromatography (3D-LC) offers an innovative approach to achieve unprecedented resolving power in terms of peak capacity and sample throughput. This advanced technique separates components within a 3D separation space, where orthogonal retention mechanisms are incorporated. The parallel development of the second- and third-dimension stages effectively overcomes the inherent limitation of conventional multidimensional approaches, where sampled fractions are analyzed sequentially. This review focuses on the design aspects of the microchip for spatial 3D-LC and the selection of orthogonal separation modes to enable the analysis of intact proteins. The design considerations for the flow distributor and channel layout are discussed, along with various approaches to confine the flow during the subsequent development stages. Additionally, the integration of stationary phases into the microchip is addressed, and interfacing to mass spectrometry detection is discussed. According to Pareto optimality, the integration of isoelectric focusing, size-exclusion chromatography, and reversed-phase chromatography in a spatial 3D-LC approach is predicted to achieve an exceptional peak capacity of over 30,000 within a 1-h analysis, setting a new benchmark in chromatographic performance. Expected final online publication date for the Annual Review of Analytical Chemistry, Volume 17 is May 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

An alternative general model for the effective longitudinal diffusion in chromatographic beds filled with ordered porous particles.

The two-zone moment-analysis method for the determination of the dispersion tensor in hierarchical retentive porous media has been adopted to compute and model the effective longitudinal diffusion Deff, or equivalently the B-term band broadening, in chromatographic beds filled with ordered porous particles. On the one hand, this approach offers accurate numerical results for Deff while keeping computational expenses low. On the other hand, it also gives direct insight for the analytical modelling, readily revealings the two main essential quantities (resp. referred to as the mobile-zone and stationary-zone effective diffusion factors γm and γs) that contribute to Deff. Modelling these two main parameters provided us with two new analytical models for Deff: a general one, valid for diluted and concentrated packings and accurate in the whole range of relevant intra-particle diffusion coefficient Dpz, and an approximate one, reliable for diluted packings and accurate also for concentrated packings with low to intermediate values of Dpz. The large advantage of both models is that they do not need any fitting parameter because all the required information is incorporated into the experimentally accessible geometric obstruction factor in the mobile phase originating from the tortuosity of the through-pore space (limiting case of fully solid particles without any retention). These models hence serve as an alternative to the Effective Medium Theory (EMT) models used so far in the literature. To validate the theory, five ordered geometries have been investigated. The accuracy of the general model proposed has been quantified and found to be comparable with that of the 3rd order approximate Torquato model for four geometries, even for macro-porosities close to the close-packing limit. The case of a 2-d triangular array of ellipsoidal particles with different elongations is also investigated to show the general validity and applicability of the models.

Selectivity and Resolving Power of Hydrophobic Interaction Chromatography Targeting the Separation of Monoclonal Antibody Variants.

This study presents a comprehensive investigation of the mechanistic understanding of retention and selectivity in hydrophobic interaction chromatography. It provides valuable insights into crucial method-development parameters involved in achieving chromatographic resolution for profiling molecular variants of trastuzumab. Retention characteristics have been assessed for three column chemistries, i.e., butyl, alkylamide, and long-stranded multialkylamide ligands, while distinguishing column hydrophobicity and surface area. Salt type and specifically chloride ions proved to be the key driver for improving chromatographic selectivity, and this was attributed to the spatial distribution of ions at the protein surface, which is ion-specific. The effect was notably more pronounced on the multialkylamide column, as proteins intercalated between the multiamide polymer strands, enabling steric effects. Column coupling proved to be an effective approach for maximizing resolution between molecular variants present in the trastuzumab reference sample and trastuzumab variants induced by forced oxidation. Liquid chromatography-mass spectrometry (LC-MS)/MS peptide mapping experiments after fraction collection indicate that the presence of chloride in the mobile phase enables the selectivity of site-specific deamidation (N30) situated at the heavy chain. Moreover, site-specific oxidation of peptides (M255, W420, and M431) was observed for peptides situated at the Fc region close to the CH2-CH3 interface, previously reported to activate unfolding of trastuzumab, increasing the accessible surface area and hence resulting in an increase in chromatographic retention.

Comprehensive analysis of the effective and intra-particle diffusion of weakly retained compounds in silica hydrophilic interaction liquid chromatography columns.

A detailed analysis of intra-particle volumes and layer thicknesses and their effect on the diffusion of solutes in hydrophilic interaction liquid chromatography (HILIC) was made. Pycnometric measurements and the retention volume of deuterated mobile phase constituents (water and acetonitrile) were used to estimate the void volume inside the column, including not only the volume of the mobile phase but also part of the enriched water solvent acting as the stationary phase in HILIC. The mobile phase (hold-up) volume accessible to non-retained components was estimated using a homologous series approach. The joint analysis of the different approaches indicated the formation of enriched water layers on the hydrophobic silica mesopore walls with a thickness varying significantly with mobile phase composition. The maximal thickness of the enriched water layers, which corresponded to the minimum void volume accessible to unretained solutes, marked a transition in the retention behavior of the studied analytes. Discrepancies between deuterated solvent measurements and pycnometry were explained by the existence of an irreplaceable water layer adsorbed on the silica surface. Regarding the diffusion behavior in HILIC, peak parking experiments were used to interpret the influence of the acetonitrile content on the effective diffusion coefficient Deff. A systematic decrease in Deff and molecular diffusion Dm was observed with decreasing acetonitrile concentration, primarily attributed to variations in mobile phase viscosity. Notably, Deff/Dm remained nearly unaffected by variations in mobile phase composition. Finally, the effective medium theory was used to make a comprehensive analysis of Dpart/Dm to study the contribution to band broadening when the solute resides in the mesopores. The obtained data unveiled a curvature with a minimum corresponding to conditions of maximum water-layer thickness and retention. For the weakly retained compounds (k' < 0.5) the Dpart/Dm-values were found to be relatively high (order of 0.35-0.5), which directly reflects the high γsDs/Dm-values that were observed (order 0.35-7).

Detailed analysis of the effective and intra-particle diffusion coefficient of proteins at elevated pressure in columns packed with wide-pore core-shell particles.

To determine the efficiency that can be obtained in a packed-bed liquid-chromatography column for a particular analyte, a correct determination of the molecular and effective diffusion coefficients (Dm and Deff) of the analyte is required. The latter is usually obtained via peak parking experiments wherein the flow is stopped. As a result, the column pressure rapidly dissipates and the measurement is essentially conducted at ambient pressure. This is problematic for analytes whose retention depends on pressure, such as proteins and potentially other large (dipolar) molecules. In that case, a conventional peak parking experiment is expected to lead to large errors in Deff. To obtain a better estimate ofDeff, the present study reports on the use of a set-up enabling peak parking measurements under pressurized conditions. This approach allowed us to report, for the first time, Deff for proteins at elevated pressure under retained conditions. First, Deff was determined at a (average) pressure of about 105 bar for a set of proteins with varying size, namely: bradykinin, insulin, lysozyme, ß-lactoglobulin, and carbonic anhydrase in a column packed with 400 Å core-shell particles. The obtained data were then compared to those of several small analytes: acetophenone, propiophenone, benzophenone, valerophenone, and hexanophenone. A clear trend between Deff and analyte size was observed. The set-up was then used to determine Deff of bradykinin and lysozyme at variable (average) pressures ranging from 28 bar to 430 bar. These experiments showed a decrease in intra-particle and surface diffusion with pressure, which was larger for lysozyme than bradykinin. The data show that pressurized peak parking experiments are vital to correctly determine Deff when the analyte retention varies significantly with pressure.

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 meso­porous material. Assuming isotropic diffusion in the shell-layer, it was found that the vertical diffusive transport along the porous shell-layer covering the pillar walls significantly suppresses the band broadening originating from the vertical migration velocity gradients. As the vertical transport in the shell-layer increases linearly with the retention equilibrium constant K, this leads to an anomalous dependency on the retention factor. Indeed, instead of increasing with k'' and following the classic (1+ak''+bk''2)/(1 + k'')2-dependency governing a classic Taylor-Aris system, the variation of the mobile zone mass transfer resistance term hCm in a 3D pillar array with bottom-wall retention goes through a maximum (resp. factor 1.5 (k''=4) and 2 (k''=16) difference between observed and classic Taylor-Aris behaviour). This effect increases with increasing pillar heights and increasing reduced velocities. Because of this complex k''-dependency, it proves very cumbersome to establish a general plate height equation covering all conditions. Instead, a plate height expression was established that is limited up to k''=4, but remains accurate for higher k''-values for cases where the ratio of pillar height over inter-pillar distance remains below 5. It can however be anticipated the proposed analytical model is only valid in a rather limited range around the presently considered external porosity of ε=0.5.

Automated method development in high-pressure liquid chromatography.

Method development in liquid chromatography is a crucial step in the optimization of analytical separations for various applications. However, it is often a challenging endeavour due to its time-consuming, resource intensive and costly nature, which is further hampered by its complexity requiring highly skilled and experienced scientists. This review presents an examination of the methods that are required for a completely automated method development procedure in liquid chromatography, aimed at taking the human out of the decision loop. Some of the presented approaches have recently witnessed an important increase in interest as they offer the promise to facilitate, streamline and speed up the method development process. The review first discusses the mathematical description of the separation problem by means of multi-criteria optimization functions. Two different strategies to resolve this optimization are then presented; an experimental and a model-based approach. Additionally, methods for automated peak detection and peak tracking are reviewed, which, upon integration in an instrument, allow for a completely closed-loop method development process. For each of these approaches, various currently applied methods are presented, recent trends and approaches discussed, short-comings pointed out, and future prospects highlighted.

A perspective on the use of deep deterministic policy gradient reinforcement learning for retention time modeling in reversed-phase liquid chromatography.

Artificial intelligence and machine learning techniques are increasingly used for different tasks related to method development in liquid chromatography. In this study, the possibilities of a reinforcement learning algorithm, more specifically a deep deterministic policy gradient algorithm, are evaluated for the selection of scouting runs for retention time modeling. As a theoretical exercise, it is investigated whether such an algorithm can be trained to select scouting runs for any compound of interest allowing to retrieve its correct retention parameters for the three-parameter Neue-Kuss retention model. It is observed that three scouting runs are generally sufficient to retrieve the retention parameters with an accuracy (mean relative percentage error MRPE) of 1 % or less. When given the opportunity to select additional scouting runs, this does not lead to a significantly improved accuracy. It is also observed that the agent tends to give preference to isocratic scouting runs for retention time modeling, and is only motivated towards selecting gradient scouting runs when penalized (strongly) for large analysis/gradient times. This seems to reinforce the general power and usefulness of isocratic scouting runs for retention time modeling. Finally, the best results (lowest MRPE) are obtained when the agent manages to retrieve retention time data for % ACN at elution of the compound under consideration that spread the entire relevant range of ACN (5 % ACN to 95 % ACN) as well as possible, i.e., resulting in retention data at a low, intermediate and high % ACN. Based on the obtained results, we believe reinforcement learning holds great potential to automate and rationalize method development in liquid chromatography in the future.

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. It has been verified that the presence of the immiscible fluid sandwich does not affect the repeatability of the analysis nor the linearity of the calibration curves used for analyte quantitation. It is also shown that the main effect of the two sandwich plugs is the minimization of the dispersion in the precolumn transfer tubing itself, which makes the method fundamentally different from pure on-column focusing methods such as the performance optimizing injection sequence (POISe) method. It is further demonstrated that both halves of the sandwich are needed, since the beneficial effect is clearly much smaller when only one plug is present. A drawback of the method is that some of the late-eluting peaks are slightly adversely affected by the presence of the sandwich liquid in the case where 127 µm i.d. tubing was used. The mechanism for this peak deterioration effect is at present still unclear but only occurs under gradient conditions and is clearly linked to the size of the sandwich plugs (the smaller the plugs, the smaller the adverse effect) and the internal diameter of the tubing used between the injection valve and the column.

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. 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.

Computational Fluid Dynamics Study of the Dispersion Caused by Capillary Misconnection in Nano-Flow Liquid Chromatography.

It is well known that high-speed/high-efficiency separations in nano-flow liquid chromatography (LC) are very sensitive to the quality of the connections between the column and the rest of the instrument. In the present study, two types of connection errors (capillary misalignment and the occurrence of an inter-capillary gap) have been investigated using computational fluid dynamics. Interestingly, it has been found that large degrees of capillary misalignment (assuming an otherwise perfect contact between the capillary end-faces) can be afforded without introducing any significant dispersion over the entire range of investigated relative misalignment errors (0 ≤ ε/dcap ≤ 75%), even at the largest flow rates considered in nano-LC. On the other hand, when an inter-capillary gap is present, the dispersion very rapidly increases with the radial width Dc of this gap (extra variance ∼Dcn with n even reaching values above 4). The dependency on the gap length Lc is however much smaller. Results show that, when Dc ≤ 30 µm and Lc ≤ 200 µm, dispersion losses can be limited to the order of 1 nL2 at a flow of 1.5 µL/min, which is generally very small compared to the dispersion in the capillaries (20 µm i.d.) themselves. This result also reconfirms that zero-dead volume connectors with a sufficiently narrow bore can in theory be used without compromising peak dispersion in nano-LC, at least when the capillaries can be matched perfectly to the connector in- and outlet faces. The results are also indicative of the extra dispersion occurring inside microfluidic chips or in the connections between a microfluidic chip and the outer world.

On-Chip Comparison of the Performance of First- and Second-Generation Micropillar Array Columns.

Because of its dimensions, the recently introduced micropillar array columns are most suited for high-efficiency liquid chromatography separations in proteomics. Unlike the packed bed columns and capillary-based column formats, the micropillar array concept still has significant room to progress in terms of the reduction of its characteristic size (i.e., pillar diameter and interpillar distance) to open the road to even higher-efficiency separations and their applications. We report here on the on-chip comparison between first-generation (Gen 1) and second-generation (Gen 2) micropillar array columns wherein the pillar and interpillar size have been halved. Because of the on-chip measurements, the observed plate heights H represent the fundamental band broadening, devoid of any extra-column band-broadening effects. The observed reduction of H with a factor of 2 around the uopt-velocity and with a factor of 4 in the C-term dominated regime of the van Deemter-curve is in full agreement with the theoretically expected gain. This shows the pillar and interpillar size reduction could be effectuated without affecting the theoretical separation potential of the micropillar arrays. Compared to Gen 1, Gen 2 offers a 4-fold reduction of the required analysis time around the optimal velocity and about a 16-fold reduction in the C-term-dominated range.

Development of a 3D-Printable, Porous, and Chemically Active Material Filled with Silica Particles and its Application to the Fabrication of a Microextraction Device.

We report on the first successful attempt to produce a silica/polymer composite with retained C18 silica sorptive properties that can be reliably printed using three-dimensional (3D) FDM printing. A 3D printer provides an exceptional tool for producing complex objects in an easy and inexpensive manner and satisfying the current custom demand of research. Fused deposition modeling (FDM) is the most popular 3D-printing technique based on the extrusion of a thermoplastic material. The lack of appropriate materials limits the development of advanced applications involving directly 3D-printed devices with intrinsic chemical activity. Progress in sample preparation, especially for complex sample matrices and when mass spectrometry is favorable, remains a vital research field. Silica particles, for example, which are commonly used for extraction, cannot be directly extruded and are not readily workable in a powder form. The availability of composite materials containing a thermoplastic polymer matrix and dispersed silica particles would accelerate research in this area. This paper describes how to prepare a polypropylene (PP)/acrylonitrile-butadiene-styrene (ABS)/C18-functionalized silica composite that can be processed by FDM 3D printing. We present a method for producing the filament as well as a procedure to remove ABS by acetone rinsing (to activate the material). The result is an activated 3D-printed object with a porous structure that allows access to silica particles while maintaining macroscopic size and shape. The 3D-printed device is intended for use in a solid-phase microextraction (SPME) procedure. The proposed composite's effectiveness is demonstrated for the microextraction of glimepiride, imipramine, and carbamazepine. The complex honeycomb geometry of the sorbent has shown to be superior to the simple tubular sorbent, which proves the benefits of 3D printing. The 3D-printed sorbent's shape and microextraction parameters were fine-tuned to provide satisfactory recoveries (33-47%) and high precision (2-6%), especially for carbamazepine microextraction.

Microfluidic Validation of the Diffusional Bridging Effect Suppressing Dispersion in Multicapillary Flow Systems.

The efficiency of liquid chromatography separations could be strongly improved by changing the current packed bed columns by a bundle of parallel capillary tubes. In practice, however, the polydispersity effect, which emanates from the inevitable small differences in capillary diameter, completely ruins this potential. The concept of diffusional bridging, introducing a diffusive cross talk between adjacent capillaries, has recently been proposed to resolve this. The present contribution provides the first experimental proof for this concept and quantitatively validates its underlying theory. This has been accomplished by measuring the dispersion of a fluorescent tracer in 8 different microfluidic channels with different degrees of polydispersity and diffusional bridging. The observed degree of dispersion reduction agrees very well with the theoretical predictions, hence opening the road to the use of this theory to design a new family of chromatographic beds, potentially offering unprecedented performance.

Influence of Wettability and Geometry on Contact Electrification between Nonionic Insulators.

Contact electrification is an interfacial process in which two surfaces exchange electrical charges when they are in contact with one another. Consequently, the surfaces may gain opposite polarity, inducing an electrostatic attraction. Therefore, this principle can be exploited to generate electricity, which has been precisely done in triboelectric nanogenerators (TENGs) over the last decades. The details of the underlying mechanisms are still ill-understood, especially the influence of relative humidity (RH). Using the colloidal probe technique, we convincingly show that water plays an important role in the charge exchange process when two distinct insulators with different wettability are contacted and separated in <1 s at ambient conditions. The charging process is faster, and more charge is acquired with increasing relative humidity, also beyond RH = 40% (at which TENGs have their maximum power generation), due to the geometrical asymmetry (curved colloid surface vs planar substrate) introduced in the system. In addition, the charging time constant is determined, which is found to decrease with increasing relative humidity. Altogether, the current study adds to our understanding of how humidity levels affect the charging process between two solid surfaces, which is even enhanced up to RH = 90% as long as the curved surface is hydrophilic, paving the way for designing novel and more efficient TENGs, eco-energy harvesting devices which utilize water and solid charge interaction mechanism, self-powered sensors, and tribotronics.

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.