Inertial Focusing Of Particles Research Articles

Sheathless inertial particle focusing methods within microfluidic devices: a review.

The ability to manipulate and focus particles within microscale fluidic environments is crucial to advancing biological, chemical, and medical research. Precise and high-throughput particle focusing is an essential prerequisite for various applications, including cell counting, biomolecular detection, sample sorting, and enhancement of biosensor functionalities. Active and sheath-assisted focusing techniques offer accuracy but necessitate the introduction of external energy fields or additional sheath flows. In contrast, passive focusing methods exploit the inherent fluid dynamics in achieving high-throughput focusing without external actuation. This review analyzes the latest developments in strategies of sheathless inertial focusing, emphasizing inertial and elasto-inertial microfluidic focusing techniques from the channel structure classifications. These methodologies will serve as pivotal benchmarks for the broader application of microfluidic focusing technologies in biological sample manipulation. Then, prospects for future development are also predicted. This paper will assist in the understanding of the design of microfluidic particle focusing devices.

Bifurcations and Dynamics in Inertial Focusing of Particles in Curved Rectangular Ducts

Bifurcations and Dynamics in Inertial Focusing of Particles in Curved Rectangular Ducts

Controllable Size-Independent Three-Dimensional Inertial Focusing in High-Aspect-Ratio Asymmetric Serpentine Microchannels.

High-throughput three-dimensional (3D) focusing of cells is the key prerequisite for enabling accurate microfluidic cell detection and analysis. In this work, we develop a high-aspect-ratio asymmetric serpentine (HARAS) microchannel for single-line inertial focusing of particles and cells at the 3D center of the channel. The mechanism of 3D focusing is explored by numerical simulation, and the focusing performances of differently sized particles are characterized experimentally at different flow rates. The results demonstrate the outstanding 3D single-line focusing capability of our HARAS microchannel. In addition, the phenomena of size-independent and position-controllable focusing over wide flow rates are observed. Finally, the applicability of our HARAS microchannel for processing real biological cells is validated by the 3D single-line focusing of A549 cells and MCF-7 cells. Our work overcomes the issue of off-centered focusing of most previous works and provides new insights into the 3D focusing in inertial microfluidics. The proposed HARAS microchannel is extremely easy for mass production and may provide a stable, high-throughput, and position-controllable scheme for subsequent single-cell detection and analysis.

Inertial focusing of particles and cells in the microfluidic labyrinth device: Role of sharp turns.

Inertial, size-based focusing was investigated in the microfluidic labyrinth device consisting of several U-shaped turns along with circular loops. Turns are associated with tight curvature and, therefore, induce strong Dean forces for separating particles; however, systematic studies exploring this possibility do not exist. We characterized the focusing dynamics of different-sized rigid particles, cancer cells, and white blood cells over a range of fluid Reynolds numbers . Streak widths of the focused particle streams at all the turns showed intermittent fluctuations that were substantial for smaller particles and at higher . In contrast, cell streaks were less prone to fluctuations. Computational fluid dynamics simulations revealed the existence of strong turn-induced Dean vortices, which help explain the intermittent fluctuations seen in particle focusing. Next, we developed a measure of pairwise separability to evaluate the quality of separation between focused streams of two different particle sizes. Using this, we assessed the impact of a single sharp turn on separation. In general, the separability was found to vary significantly as particles traversed the tight-curvature U-turn. Comparing the separability at the entry and exit sections, we found that turns either improved or reduced separation between different-sized particles depending on . Finally, we evaluated the separability at the downstream expansion section to quantify the performance of the labyrinth device in terms of achieving size-based enrichment of particles and cells. Overall, our results show that turns are better for cell focusing and separation given that they are more immune to curvature-driven fluctuations in comparison to rigid particles.

Instability of a liquid sheet with viscosity contrast in inertial microfluidics

Flows at moderate Reynolds numbers in inertial microfluidics enable high throughput and inertial focusing of particles and cells with relevance in biomedical applications. In the present work, we consider a viscosity-stratified three-layer flow in the inertial regime. We investigate the interfacial instability of a liquid sheet surrounded by a density-matched but more viscous fluid in a channel flow. We use linear stability analysis based on the Orr–Sommerfeld equation and direct numerical simulations with the lattice Boltzmann method (LBM) to perform an extensive parameter study. Our aim is to contribute to a controlled droplet production in inertial microfluidics. In the first part, on the linear stability analysis we show that the growth rate of the fastest growing mode xi ^{*} increases with the Reynolds number text {Re} and that its wavelength lambda ^{*} is always smaller than the channel width w for sufficiently small interfacial tension Gamma . For thin sheets we find the scaling relation xi ^{*} propto mt^{2.5}_{s}, where m is viscosity ratio and t_{s} the sheet thickness. In contrast, for thicker sheets xi ^{*} decreases with increasing t_s or m due to the nearby channel walls. Examining the eigenvalue spectra, we identify Yih modes at the interface. In the second part on the LBM simulations, the thin liquid sheet develops two distinct dynamic states: waves traveling along the interface and breakup into droplets with bullet shape. For smaller flow rates and larger sheet thicknesses, we also observe ligament formation and the sheet eventually evolves irregularly. Our work gives some indication how droplet formation can be controlled with a suitable parameter set {lambda ,t_{s},m,Gamma ,text {Re}}.Graphical

Pattern Transition on Inertial Focusing of Neutrally Buoyant Particles Suspended in Rectangular Duct Flows.

The continuous separation and filtration of particles immersed in fluid flows are important interests in various applications. Although the inertial focusing of particles suspended in a duct flow is promising in microfluidics, predicting the focusing positions depending on the parameters, such as the shape of the duct cross-section and the Reynolds number (Re) has not been achieved owing to the diversity of the inertial-focusing phenomena. In this study, we aimed to elucidate the variation of the inertial focusing depending on Re in rectangular duct flows. We performed a numerical simulation of the lift force exerted on a spherical particle flowing in a rectangular duct and determined the lift-force map within the duct cross-section over a wide range of Re. We estimated the particle trajectories based on the lift map and Stokes drag, and identified the particle-focusing points appeared in the cross-section. For an aspect ratio of the duct cross-section of 2, we found that the blockage ratio changes transition structure of particle focusing. For blockage ratios smaller than 0.3, particles focus near the centres of the long sides of the cross-section at low Re and near the centres of both the long and short sides at relatively higher Re. This transition is expressed as a subcritical pitchfork bifurcation. For blockage ratio larger than 0.3, another focusing pattern appears between these two focusing regimes, where particles are focused on the centres of the long sides and at intermediate positions near the corners. Thus, there are three regimes; the transition between adjacent regimes at lower Re is found to be expressed as a saddle-node bifurcation and the other transition as a supercritical pitchfork bifurcation.

Inertial migration of aerosol particles in three-dimensional microfluidic channels

In recent years, manipulation of particles by inertial microfluidics has attracted significant attention. However, most studies focused on inertial focusing of particles suspended within liquid phase, in which the ratio of the density of the particle to that of the medium is O(1). The investigation on manipulation of aerosol particles in an inertial microfluidics is very limited. In this study, we numerically investigate the aerosol particle's motion in a 3D straight microchannel with rectangular cross section by fully resolved simulation of the particle–air flow. The air flow is modeled by the Navier–Stokes equations. The particle's motions, including translation and rotation, are governed, respectively, by the Newton's second law and the Euler equations without using any approximation models for the lift and drag forces. The coupled mathematical model is numerically solved by combining immersed boundary with lattice Boltzmann method (IB-LBM). We find that the Reynolds number (Re), the particle's initial position, particle's density and diameter are the influential parameters in this process. The equilibrium positions and their stabilities of aerosols are different from those suspended in liquid.

High-Throughput Particle Concentration Using Complex Cross-Section Microchannels.

High throughput particle/cell concentration is crucial for a wide variety of biomedical, clinical, and environmental applications. In this work, we have proposed a passive spiral microfluidic concentrator with a complex cross-sectional shape, i.e., a combination of rectangle and trapezoid, for high separation efficiency and a confinement ratio less than 0.07. Particle focusing in our microfluidic system was observed in a single, tight focusing line, in which higher particle concentration is possible, as compared with simple rectangular or trapezoidal cross-sections with similar flow area. The sharper focusing stems from the confinement of Dean vortices in the trapezoidal region of the complex cross-section. To quantify this effect, we introduce a new parameter, complex focusing number or CFN, which is indicative of the enhancement of inertial focusing of particles in these channels. Three spiral microchannels with various widths of 400 µm, 500 µm, and 600 µm, with the corresponding CFNs of 4.3, 4.5, and 6, respectively, were used. The device with the total width of 600 µm was shown to have a separation efficiency of ~98%, and by recirculating, the output concentration of the sample was 500 times higher than the initial input. Finally, the investigation of results showed that the magnitude of CFN relies entirely on the microchannel geometry, and it is independent of the overall width of the channel cross-section. We envision that this concept of particle focusing through complex cross-sections will prove useful in paving the way towards more efficient inertial microfluidic devices.

Stability condition of self-organizing staggered particle trains in channel flow

The inertial focusing of particles in channel flow of a Newtonian fluid is studied using the lattice Boltzmann method. The effects of Reynolds number (Re) and blockage ratio (k) on the stability condition of self-organizing staggered particle trains are explored. The results show that, for staggered particle pairs, the particles will move close to each other with a damped oscillatory trajectory and form a steady horizontal spacing eventually. For single-line particle pairs, the inter-particle spacing increases continuously to a larger value for further downstream. Two lines of 12 particles will self-organize the staggered particle trains. The formation of stable staggered particle trains is dependent on Re and k. Particles with low k in the staggered particle trains are more likely to be unstable or fluctuate within a certain range when Re is larger than a critical value. As k increases, the critical values of Re corresponding to the inter-particle spacing with a stable value or a certain range of fluctuation are also increased. The mean particle spacing decreases with increasing k and decreasing Re, and the blockage ratio k has a greater effect on the particle spacing than Reynolds number Re.

Inertial focusing in triangular microchannels with various apex angles.

We consider inertial focusing of particles in channels with triangular cross sections. The number and the location of inertial focusing positions in isosceles triangular channels can change with varying blockage ratios (a/H) and Reynolds numbers (Re). In triangular channels, asymmetric velocity gradient induced by the sloped sidewalls leads to changes in the direction and the strength of the inertial lift forces. Therefore, varying the configuration (specifically, angle) of the triangular cross section is expected to lead to a better understanding of the nature of the inertial lift forces. We fabricated triangular microchannels with various apex angles using channel molds that were shaped by a planing process, which provides precise apex angles and sharp corners. The focusing position shift was found to be affected by the channel cross section, as expected. It was determined that the direction of the focusing position shift can be reversed depending on whether the vertex is acute or obtuse. More interestingly, corner focusing modes and splitting of the corner focusing were observed with increasing Re, which could explain the origin of the inertial focusing position changes in triangular channels. We conducted fluid dynamic simulations to create force maps under various conditions. These force maps were analyzed to identify the basins of attraction of various attractors and pinpoint focusing locations using linear stability analysis. Calculating the relative sizes of the basins of attractions and exhaustively identifying the focusing positions, which are very difficult to investigate experimentally, provided us a better understanding of trends in the focusing mechanism.

Simulation and practice of particle inertial focusing in 3D-printed serpentine microfluidic chips via commercial 3D-printers.

Inertial focusing of particles in serpentine microfluidic chips has been studied over the past decade. Here, a study to investigate the particle inertial focusing in 3D-printed serpentine microfluidic chips was conducted by simulation and practice. A test model was designed and printed using four commercial 3D-printers. Commercial inkjet 3D-printers have shown the best printing channel resolution of up to 0.1 mm. The force analysis of particle inertial focusing in 3D-printed microfluidic chips with large cross-sectional channels was discussed. Important parameters such as the channel curvature and flow velocity were studied by simulation. The optimal channel curvature and flow velocity are 5.9 mm and 480 μL min-1 (Re: 29.8 and De: 4.49) in the 3D-printed microfluidic chips with 0.2 mm × 0.4 mm cross-sectional channels. Under these optimal conditions, particles were well focused in the middle of the channel. Furthermore, two kinds of cancer cells were focused in these 3D-printed serpentine microfluidic chips under the optimal conditions. We envision that this improved study would provide helpful insights into simulating particle inertial focusing in 3D-printed microfluidic chips and promoting 3D-printed microfluidic chips to commercial production.

Bifurcation phenomena on the inertial focusing of a neutrally buoyant spherical particle suspended in square duct flows

Several patterns of inertial particle focusing over a square cross section are experimentally observed for suspension flows through a square duct. A numerical study describes transitions between the focusing patterns in terms of the bifurcation of particle equilibrium positions.

Inertial Focusing and Separation of Particles in Similar Curved Channels

Inertial particle focusing in curved channels has enormous potential for lab-on-a-chip applications. This paper compares a zigzag channel, which has not been used previously for inertial focusing studies, with a serpentine channel and a square wave channel to explore their differences in terms of focusing performance and separation possibilities. The particle trajectories and fluid fields in the curved channels are studied by a numerical simulation. The effects of different conditions (structure, Reynolds number, and particle size) on the competition between forces and the focusing performance are studied. The results indicate that the zigzag channel has the best focusing effect at a high Reynolds number and that the serpentine channel is second in terms of performance. Regarding the particle separation potential, the zigzag channel has a good performance in separating 5 μm and 10 μm particles at ReC = 62.5. In addition, the pressure drop of the channel is also considered to evaluate the channel performance, which has not been taken into account in the literature on inertial microfluidics. This result is expected to be instructive for the selection and optimization of inertial microchannel structures.

Convergence analysis of inertial lift force estimates using the finite element method

We conduct a convergence analysis for the estimation of inertial lift force on a spherical particle suspended in flow through a straight square duct using the finite element method. Specifically, we consider the convergence of an inertial lift force approximation with respect to a range of factors including the truncation of the domain, the resolution of the tetrahedral mesh and the boundary conditions imposed at the (truncated) ends of the domain. Additionally, we compare estimates obtained via the Lorentz reciprocal theorem with those obtained via a direct integration of fluid stress over the particle surface. 
 
 References M. S. Alnaes, J. Blechta, J. Hake, A. Johansson, B. Kehlet, A. Logg, C. Richardson, J. Ring, M. E. Rognes, and G. N. Wells. The FEniCS project version 1.5. Arch. Numer. Software, 3(100):923, 2015. doi:10.11588/ans.2015.100.20553. D. Di Carlo. Inertial microfluidics. Lab Chip, 21:30383046, 2009. doi:10.1039/B912547G. C. Geuzaine and J.-F. Remacle. Gmsh: A 3-d finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Meth. Eng., 79(11):13091331, 2009. doi:10.1002/nme.2579. B. Harding. A study of inertial particle focusing in curved microfluidic ducts with large bend radius and low flow rate. In Proc. 21st Australasian Fluid Mechanics Conference, number 603, 2018. URL https://people.eng.unimelb.edu.au/imarusic/proceedings/21/Contribution_603_final.pdf. B. Harding, Y. M. Stokes, and A. L. Bertozzi. Effect of inertial lift on a spherical particle suspended in flow through a curved duct. J. Fluid Mech., accepted, 2019. URL https://arxiv.org/abs/1902.06848. A. J. Hogg. The inertial migration of non-neutrally buoyant spherical particles in two-dimensional shear flows. J. Fluid Mech., 272:285318, 1994. doi:10.1017/S0022112094004477. K. Hood, S. Lee, and M. Roper. Inertial migration of a rigid sphere in three-dimensional Poiseuille flow. J. Fluid Mech., 765:452479, 2015. doi:10.1017/jfm.2014.739. N. Nakagawa, T. Yabu, R. Otomo, A. Kase, M. Makino, T. Itano, and M. Sugihara-Seki. Inertial migration of a spherical particle in laminar square channel flows from low to high reynolds numbers. J. Fluid Mech., 779:776793, 2015. doi:10.1017/jfm.2015.456. T.-W. Pan and R. Glowinski. Direct simulation of the motion of neutrally buoyant balls in a three-dimensional poiseuille flow. C. R. Mecanique, 333(12):884895, 2005. doi:10.1016/j.crme.2005.10.006. C. Taylor and P. Hood. A numerical solution of the navier-stokes equations using the finite element technique. Comput. Fluids, 1(1):73100, 1973. doi:10.1016/0045-7930(73)90027-3. M. E. Warkiani, G. Guan, K. B. Luan, W. C. Lee, A. A. S. Bhagat, P. Kant Chaudhuri, D. S.-W. Tan, W. T. Lim, S. C. Lee, P. C. Y. Chen, C. T. Lim, and J. Han. Slanted spiral microfluidics for the ultra-fast, label-free isolation of circulating tumor cells. Lab Chip, 1:128137, 2014. doi:10.1039/C3LC50617G. B. H. Yang, J. Wang, D. D. Joseph, H. H. Hu, T.-W. Pan, and R. Glowinski. Migration of a sphere in tube flow. J. Fluid Mech., 540:109131, 2005. doi:10.1017/S0022112005005677. L. Zeng, S. Balachandar, and P. Fischer. Wall-induced forces on a rigid sphere at finite reynolds number. J. Fluid Mech., 536:125, 2005. doi:10.1017/S0022112005004738.

Inertial lateral migration and self-assembly of particles in bidisperse suspensions in microchannel flows

Inertial focusing of particles in microchannels has demonstrated a great potential for a wide range of applications addressing various challenges, such as clinical diagnosis, biological assay, water treatment, etc. Even though numerous theoretical, numerical and experimental studies have been performed to identify the physical mechanisms underlying the migration of particles in confined environments, only a few works, up to now, have been devoted to the effects resulting from the interactions between particles of different sizes in polydisperse suspensions. In this work, high-speed bright-field imaging was used to experimentally analyse the behaviour of model bidisperse suspensions. The influences of bidispersity on (1) the lateral inertial migration of the particles towards equilibrium positions within the channel cross-section and (2) their longitudinal ordering into trains in the flow direction, were investigated under different conditions by varying the Reynolds number, the particles’ size ratios and concentrations. The quantitative measurements and statistical analysis of the experimental data show that the bidispersity can modify not only the lateral migration process but also the sequential particle-ordering phenomenon.

A Minireview on Inertial Microfluidics Fundamentals: Inertial Particle Focusing and Secondary Flow

In 1961, Segre and Silberberg first reported the tubular pinch effect and numerous theoretical studies were subsequently published to explain the inertial particle migration phenomenon. Presently, as fluid mechanics meets micro- and nanotechnology, theoretical studies on intrinsic particle migration and flow phenomena associated with inertia are being experimentally tested and validated. This collective study on the fluid-particle-structure phenomena in microchannels involving fluid inertia is called, “inertial microfluidics”. Beyond theoretical studies, now inertial microfluidics has been gaining much attention from various research fields ranging from biomedicine to industry. Despite the positive contributions, there is still a lack of clear understanding of intrinsic inertial effects in microchannels. Therefore, this minireview introduces the mechanisms and underlying physics in inertial microfluidic systems with specific focuses on inertial particle migration and secondary flow, and outlines the opportunities provided by inertial microfluidics, along with an outlook on the field.

Direct measurement of microscale flow structures induced by inertial focusing of single particle and particle trains in a confined microchannel

Understanding the flow structures induced by inertial focusing of particles is essential in microfluidics-based applications. In spite of numerous studies described in the literature, such microscale flows have, until today, not been subject to quantitative experimental study. This paper describes the construction and validation of a micro-particle image velocimetry-based experimental setup to investigate particle-induced flows in a confined microchannel. The flow structures around a single inertially focused particle are first visualized and quantitatively measured at Reynolds numbers Re from 21 to 525. A ring-like vortex flow is observed to form in front of the particle at Re = 63 owing to an increased particle lag effect, and finally the reverse flow regime is replaced by a vortex flow regime (at Re ≥ 105). This vortex flow produces a strong wall repulsive force and pushes the equilibrium position of the particle toward the channel center. Then, flows induced by both in-line and staggered particle trains are investigated (for 21 ≤ Re ≤ 105). For in-line particle trains, single-vortex flows are present between two neighboring particles on both sides of the channel. For staggered particle trains, two vortices rather than one are present between two neighboring particles at small Re (Re = 21), but this double-vortex flow develops into a single-vortex flow at relatively high Re (Re = 105). The present investigation helps in understanding particle dynamics and the mechanisms of interaction among particles, fluid, and channel walls. The experimental results presented here also provide validation data for further numerical and analytical studies.

High-Reynolds Microfluidic Sorting of Large Yeast Populations

Microfluidic sorting offers a unique ability to isolate large numbers of cells for bulk proteomic or metabolomics studies but is currently limited by low throughput and persistent clogging at low flow rates. Recently we uncovered the physical principles governing the inertial focusing of particles in high-Reynolds numbers. Here, we superimpose high Reynolds inertial focusing on Dean vortices, to rapidly isolate large quantities of young and adult yeast from mixed populations at a rate of 107 cells/min/channel. Using a new algorithm to rapidly quantify budding scars in isolated yeast populations and system-wide proteomic analysis, we demonstrate that protein quality control and expression of established yeast aging markers such as CalM, RPL5, and SAM1 may change after the very first replication events, rather than later in the aging process as previously thought. Our technique enables the large-scale isolation of microorganisms based on minute differences in size (±1.5 μm), a feat unmatched by other technologies.

Particle slip velocity influences inertial focusing of particles in curved microchannels

Size based separation and identification of particles in microfluidics through purely hydrodynamic means has gained significant interest due to a number of possible biomedical applications. Curved micro-channels, particularly spiral micro-channels with rectangular cross-section and the dynamics of particles in such channels have been extensively researched to achieve size based separation of particles. In this paper we present evidence that sheds new light on the dynamics of particles in such curved channels; that a unique particle slip velocity is associated with the focusing positions in the cross sections, which leads to a balance of forces. Our experiments therefore imply that the forces acting on the particle lead to convergence to an attractor in both the physical space (the cross section of the channel) and the slip velocity space.

(Invited) Hybrid Microfluidic Cell Sorting for Rare Cell Isolation

Selective isolation of specific cell subpopulations from highly heterogeneous biological samples is an essential process in various biological studies and clinical applications. The ability to isolate rare cell populations, for example circulating tumor cells, provides unprecedented capabilities for the study of disease progression and better disease assessment. Currently, sorting and isolation of rare cell populations is typically performed using fluorescence-activated cell sorting (FACS) system, a technology developed nearly 60 years ago. These FACS systems are however complex, bulky, and expensive, require highly trained personnel for operation, and may produce bio-hazardous aerosols in open environments. Microfluidics studies the unique behavior and interactions of fluids and particles at the micrometer length scale, typically in confined microscale channels. Microfluidic technology capable of precise cell manipulation thus has great potential to reinvent the next-generation cell sorting technology. We are currently developing two microfluidic cell sorting technologies including high-throughput hydrodynamic cell sorting and high-accuracy acoustic cell sorting. Hydrodynamic cell sorting is using an interesting inertial particle focusing behavior in an intermediate Reynolds number regime (~100 > Re > ~1). We have designed and fabricated a new type of hydrodynamic sorting device with a series of reverse wavy channel structures. These repeated wavy channels produce periodically reversed Dean secondary flow perpendicular to the main flow direction. The hydrodynamic inertial lift force and the Dean drag force scale with the particle size very distinctively, which leads to distinct equilibrium positions of differently sized particles. We have demonstrated the use of this new hydrodynamic sorting device to isolate cancer cells from blood cells without the use of sheath flows. Acoustic cell sorting is developed based on the study of interactions between high-frequency sound waves and microscale particles. In particular, I will discuss a unique design of a focused interdigital transducer (FIDT) structure, which is able to generate a highly localized acoustic field on the order of 25 µm wide. This highly focused acoustic beam has an effective manipulation area size that is comparable to individual micron-sized particles. We have demonstrated the use of this highly localized acoustic field for fluorescence-activated single cell level sorting with sub-millisecond pulses. By combining the two microfluidic cell sorting technologies, we have demonstrated the capability of enriching target cells by 1,000 to 10,000 times, providing a new solution of rare cell isolation.