Impact of transversal vortices on the performance of open-tubular liquid chromatography.

Open-Tubular Liquid Chromatography (OTLC) is currently limited by two shortcomings, namely the low ratio of adsorbing area to the channel volume and the large values of the Height Equivalent of the Theoretical Plate (HETP) due to Taylor-Aris dispersion. Previous work focusing on axial dispersion of nonadsorbing solutes showed how it is possible to tame the Taylor-Aris effect by inducing transversal velocity components acting alongside the main pressure-driven axial flow. We here analyze the impact of transversal flow on the separation resolution in OTLC, where simultaneous equilibrium adsorption at the channel walls is superimposed to the analyte transport in the mobile phase. A three-dimensional steady flow generated by the combination of a pressure-driven flow and an electroosmotically-induced transversal flow is used as case study. Flows geometries possessing regular and chaotic streamlines are created by axially-invariant and periodically-alternate arrangements of the electrodes along the channel walls, respectively. By enforcing Brenner's macrotransport approach, we predict the column length achieving a prescribed level of resolution as a function of the Péclet number and of the species affinity towards the stationary adsorbing phase. Results show that the presence of transversal flows can lower sensitively the dependence of the column length on the Péclet number. Flows possessing chaotic streamlines prove the most efficient choice at large eluent velocities and low values of the column adsorption constant.

Shape-Enhanced Open-Channel Hydrodynamic Chromatography.

Hydrodynamic chromatography (HDC) is a well-established analytical separation method for the size separation of nano- and microparticles and large molecular weight solutes such as synthetic polymers and proteins. We report on a theoretical study showing that the separation resolution of open-tubular HDC can be significantly enhanced by changing the cross-sectional shape of the separation channel. By enforcing Brenner's macro-transport approach, we provide theoretical/numerical evidence showing how the shape of the cross section influences quantitatively both the selectivity and the axial dispersion of the suspended particles in HDC. The separation performance of square-, triangle-, and star-shaped channel cross sections is compared to that of a cylindrical capillary over three decades of the particle Péclet number in terms of the minimal separation length and time to obtain the unit resolution of a two-particle mixture. Enhancement factors up to 400% are found in the case of triangular shapes, with the best performing case being the 70.6° angle, which can be obtained by KOH etching of bulk silicon.

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.

Taming Taylor-Aris dispersion through chaotic advection.

Taylor-Aris dispersion represents an undesired phenomenon in pressure-driven liquid chromatography, often responsible for the unchecked increase of the Height Equivalent of the Theoretical Plate (HETP) when high throughput operating conditions are sought. Previous work on the subject showed how it is possible to contain the augmented dispersion in empty microchannels by inducing cross-sectional velocity components yielding an overall helical structure of the flow streamlines. Here, we explore the possibility of further reducing axial dispersion by devising flow conditions that give rise to chaotic streamlines. A three-dimensional steady flow generated by the combination of a pressure-driven Poiseuille flow and an electroosmotically-induced spatially periodic flow is used as a case study. Brenner's macrotransport approach is used to predict the axial dispersion coefficient of a diffusing solute in flows possessing regular, partially chaotic and globally chaotic kinematic features. Accurate Lagrangian-stochastic simulations of particle ensembles are used to validate the predictions obtained through Brenner's paradigm. Our findings suggest that the Taylor-Aris phenomenon can be altogether suppressed in the limit of globally chaotic kinematics. A theoretical interpretation of this outcome is developed by combining macrotransport theory with established results of the spectral approach to mixing in advecting-diffusing chaotic flows.

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

In a recent article [Analytical Chemistry, 93(17), 6808-6816 (2021)], an unconventional device configuration enforcing a Brownian sieving mechanism was proposed as proof of concept for the efficient implementation of microcapillary hydrodynamic chromatography (MHDC). In this article, we perform a thorough analysis of the device geometry and of operating conditions, in order to single out the optimal configuration maximizing separation resolution. Brenner's macro-transport theory provides the technical picklock to perform the search for the optimum over a wide choice of device geometries and for a range of values of the particle Péclet number covering most conditions encountered in practical implementations of MHDC. Specifically, effective transport coefficients defining the dynamics of the suspended phase are obtained by the solution of a two-dimensional steady-state advection-diffusion equation defined onto the channel cross-section. The eigenvalue/eigenfunction structure of the associated transient problem is exploited in order to quantify the timescale for reaching the macro-transport regime conditions. Based on this timescale and on the effective transport parameters, an estimate of the column length necessary to achieve a prescribed level of separation resolution is obtained. We identify device geometry and operating conditions where the capillary length is shrunk down by a factor above ten compared to the standard MHDC configuration. Lagrangian stochastic statistics of particle ensembles are used to validate the results obtained through Brenner's macro-transport approach. The method proposed can be readily generalized to other classes of device geometries enforcing the same Brownian sieving mechanism.

Brownian Sieving Effect for Boosting the Performance of Microcapillary Hydrodynamic Chromatography. Proof of Concept.

Microcapillary hydrodynamic chromatography (MHDC) is a well-established technique for the size-based separation of suspensions and colloids, where the characteristic size of the dispersed phase ranges from tens of nanometers to micrometers. It is based on hindrance effects which prevent relatively large particles from experiencing the low velocity region near the walls of a pressure-driven laminar flow through an empty microchannel. An improved device design is here proposed, where the relative extent of the low velocity region is made tunable by exploiting a two-channel annular geometry. The geometry is designed so that the core and the annular channel are characterized by different average flow velocities when subject to one and the same pressure drop. The channels communicate through openings of assigned cut-off length, say A. As they move downstream the channel, particles of size bigger than A are confined to the core region, whereas smaller particles can diffuse through the openings and spread throughout the entire cross section, therein attaining a spatially uniform distribution. By using a classical excluded-volume approach for modeling particle transport, we perform Lagrangian-stochastic simulations of particle dynamics and compare the separation performance of the two-channel and the standard (single-channel) MHDC. Results suggest that a quantitative (up to thirtyfold) performance enhancement can be obtained at operating conditions and values of the transport parameters commonly encountered in practical implementations of MHDC. The separation principle can readily be extended to a multistage geometry when the efficient fractionation of an arbitrary size distribution of the suspension is sought.

Combining Electrostatic, Hindrance and Diffusive Effects for Predicting Particle Transport and Separation Efficiency in Deterministic Lateral Displacement Microfluidic Devices.

Microfluidic separators based on Deterministic Lateral Displacement (DLD) constitute a promising technique for the label-free detection and separation of mesoscopic objects of biological interest, ranging from cells to exosomes. Owing to the simultaneous presence of different forces contributing to particle motion, a feasible theoretical approach for interpreting and anticipating the performance of DLD devices is yet to be developed. By combining the results of a recent study on electrostatic effects in DLD devices with an advection-diffusion model previously developed by our group, we here propose a fully predictive approach (i.e., ideally devoid of adjustable parameters) that includes the main physically relevant effects governing particle transport on the one hand, and that is amenable to numerical treatment at affordable computational expenses on the other. The approach proposed, based on ensemble statistics of stochastic particle trajectories, is validated by comparing/contrasting model predictions to available experimental data encompassing different particle dimensions. The comparison suggests that at low/moderate values of the flowrate the approach can yield an accurate prediction of the separation performance, thus making it a promising tool for designing device geometries and operating conditions in nanoscale applications of the DLD technique.