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.

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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.

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 crosssectional 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 excludedvolume 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.

Experiments have shown that a suspension of particles of different dimensions pushed through a periodic lattice of micrometric obstacles can be sorted based on particle size. This label-free separation mechanism, referred to as Deterministic Lateral Displacement (DLD), has been explained hinging on the structure of the 2D solution of the Stokes flow through the patterned geometry, thus neglecting the influence of the no-slip conditions at the top and bottom walls of the channel hosting the obstacle lattice. We show that the no-slip conditions at these surfaces trigger the onset of off-plane velocity components, which impart full three-dimensional character to the flow. The impact of the 3D flow structure on particle transport is investigated by enforcing an excluded volume approach for modelling the interaction between the finite-sized particles and the solid surfaces. We find that the combined action of particle diffusion and of the off-plane velocity component causes the suspended particles to migrate towards the top and bottom walls of the channel. Preliminary results suggest that this effect makes the migration angle of the particles significantly different from that obtained by assuming a strictly two-dimensional structure for the flow of the suspending fluid.

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 opentubular 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 Pećlet 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.

Particles ranging in size from a few nanometers (exosomes or viruses) to a few micrometers (bacteria or red blood cells) can be sorted using a size-based separation process. One of the simplest techniques is provided by hydrodynamic chromatography (HDC) which typically requires long channels to achieve adequate resolution. A new separation mechanism based on a Brownian sieving effect coupled with HDC has recently been proposed to overcome these limitations. An efficiency improvement of up to 2000 % has been predicted for a two-size mixture. The aim of this work is to study and optimize a modified geometry useful for obtaining the simultaneous separation of a three-size diluted suspension. The results suggest a significant performance improvement, up to 3000 %, over the standard HDC.