 Review
 Open access
 Published:
Current status and further development of deterministic lateral displacement for microparticle separation
Micro and Nano Systems Letters volume 11, Article number: 11 (2023)
Abstract
Deterministic lateral displacement (DLD) is a passive, labelfree, continuousflow method for particle separation. Since its discovery in 2004, it has been widely used in medical tests to separate blood cells, bacteria, extracellular vesicles, DNA, and more. Despite the very simple idea of the DLD method, many details of its mechanism are not yet fully understood and studied. Known analytical equations for the critical diameter of separated particles include only the gap between the columns in the DLD array and the fraction of the column shift. The dependence of the critical diameter on the post diameter, channel height, and a number of other geometric parameters remains unexplored. The problems also include the effect of flow rate and particle concentration on the critical diameter and separation efficiency. At present, DLD devices are mainly developed through numerical simulation and experimental validation. However, it is necessary to find fundamental regularities that would help to improve the separation quantitatively and qualitatively. This review discusses the principle of particle separation, the physical aspects of flow formation, and hydrodynamic forces acting on particles in DLD microchannels. Various analytical models of a viscous flow in an array of cylindrical posts are described. Prospects for further research are outlined.
Introduction
Sorting, separating, isolating, and detecting microparticles are important for a wide range of applications, from chemical processing to clinical diagnostics [1]. Advances in microfluidics have led to revolutionary progress in this field. The problems posed can be solved either with labelbased or labelfree approaches [2]. This review is devoted to labelfree methods that use only the intrinsic properties of separated particles. Labelfree microfluidic sorting is very promising for rapid blood testing and pointofcare blood diagnostics [3]. The separation of microparticles from a suspension can be carried out by active or passive methods [4, 5]. Passive methods utilize only hydrodynamic forces arising in microfluidic channels, while active methods additionally use external physical influences. Active methods include acoustophoresis, electrophoresis, dielectrophoresis, magnetophoresis, optical tweezers, and centrifugation. Passive methods rely on the size, shape, density, and deformability of particles (cells, molecules) and are represented by inertial microfluidics, pinched flow fractionation, hydrodynamic filtration, crossflow filtration, deterministic lateral displacement, gravitydriven separation, viscoelastic microfluidics, and shearinduced diffusion [1, 6]. This review focuses on passive methods, namely, deterministic lateral displacement (DLD).
The DLD method was first published by Huang et al. [7]. Sturm et al. outlined the history of discovery from idea to implementation [8]. The DLD device divides particles into large and small in relation to the critical diameter and concentrates large particles. General advances in DLD are described in a number of recent reviews (e.g., [9, 10]). DLD has especially great potential for biomedical and clinical applications in the separation and isolation of biological microobjects [11], blood cells [12], circulating tumor cells [13,14,15,16,17,18,19,20,21], leukocytes [22], single cells [23], extracellular vesicles [24,25,26,27], submicrometer particles [4], and nanoparticles [10, 28, 29].
For almost two decades, the DLD theory has continuously developed, various DLD devices have been designed, high efficiency and highperformance sorting of particles have been achieved, and the minimum critical diameter approached the nanometer scale. Nevertheless, many questions remain open despite the simple idea and relatively easy practical realization of DLD separation. The nature of the separation mechanisms is still not completely unclear; in particular, the interaction between particles and flow, particles and a microchannel, and between particles requires research. The influence of the microchannel geometry on separation efficiency is not fully understood and studied. The problems also include the effect of flow rate and particle concentration on the critical diameter and a number of others.
The purpose of the review is to identify key challenges that need to be tackled in order to improve the quality and performance of the DLD. The review focuses on the separation of rigid spherical particles on an array of cylindrical posts at a moderate Reynolds number.
Basic of DLD
Principle of separation
The crosssection of a typical DLD device along the median plane between the top and bottom of the channel is shown in Fig. 1, where the flow is directed from left to right. Here and below, the xaxis of the Cartesian coordinate system coincides with the flow. The yaxis is perpendicular to the xaxis and lies in the median plane. The pressure difference causes fluid to move through the array of cylindrical posts. The transverse period of the array (in the ydirection) is λ. The longitudinal period (in the xdirection) is λ*. In most practical cases, λ ≈ λ*. The gap between posts is g. The cylindrical posts are shifted by ελ in each subsequent row so that the pattern is repeated after M shifts. Thus, the flux between two posts is divided into M flow streams with equivalent flow rates and ε = 1/M (in Fig. 1, M = 4). Each stream flows in a zigzag path, from left to right on average. Separated particles are considered spherical and rigid. Small particles follow the same path as the streamlines in a zigzag mode.
Large particles whose radius exceeds the width of the first streamline β, travel in the bump mode (or displacement mode). The velocity profile in each gap between two posts is described by function u(y).
The flow rate equivalence in each streamline is expressed by
Usually, it is assumed that the center of a rigid spherical particle moves strictly along the streamline. If the particle collides with the post, it goes around this obstacle due to mechanical contact and fluid flow. Therefore, the flow is characterized by a very low Reynolds number. Under these assumptions, the solution of Eq. (1) for β gives the critical particle diameter D_{c} = 2β. To calculate the width β and the critical diameter D_{c}, the velocity profile u(y) should be found. The velocity profile depends on the flow regime in the microfluidic channel.
Characterization of flow regimes
DLD devices operate at a constant flow rate or pressure drop for an extended period of time so that a steadystate flow regime is established.
Typical microchannel sizes, fluid properties, and particle parameters are shown in Table 2 (see Appendix) along with a list of designations. These data are used below for estimating flow regimes, velocity profiles, and forces acting on particles.
The Reynolds number (Re) is the ratio of fluid momentum force to viscous shear force for a flowing fluid. The channel Reynolds number (Re_{C}) is expressed as follows [30]
Here ρ_{f} is the fluid density, μ_{f} is the fluid viscosity, U_{Max} is the maximum velocity of the fluid, and D_{H} is the hydraulic diameter of the channel, defined as
where A and P are the area and perimeter of the channel crosssection, respectively.
Fluid moves in the channel with the average velocity \(U_{Ave} = {Q / A}\), where Q is the volume flow rate, \(A = Wh\) is the crosssection area, and W and h are the total width and height of the channel, respectively. The fluid velocity is maximum approximately in the middle of the gap between the posts. Using the assumption that velocity profile u(y) is parabolic, the maximum velocity is
Calculations give U_{Ave} = 0.0521 m s^{−1} and U_{Max} = 0.130 m s^{−1}. Using Eq. (3), the hydraulic diameter of the gap between two posts \(D_H = {{2gh} / {\left( {g + h} \right)}} = 24\) µm. According to Eq. (2), the channel Reynolds number Re_{C} = 3.13. This value belongs to the moderate Reynolds number regime (Re_{C} ≤ 18) [31] and indicates a stable laminar flow in the channel. Dincau et al. [31] stated that there is a lack of comprehensive studies of microscale DLD performance in high and moderate Reynolds number regimes.
Estimation of critical diameter
Inglis et al. [32] greatly simplified the problem and assumed that the flow in the gap between two posts is the plane Poiseuille flow of a viscous fluid between two parallel plates separated by a distance g with noslip boundary conditions.
The parabolic velocity profile u(y) is shown in Fig. 1. Using this profile, Inglis et al. [32] solved Eq. (1) for β and found the critical diameter (Inglis diameter):
where \(w = \left[ {\frac{1}{8}  \frac{\varepsilon }{4} + \sqrt {{\frac{\varepsilon }{16}(\varepsilon  1)}} } \right]^{(1/3)} \left( {  \frac{1}{2}  {\text{j}}\frac{{\sqrt {3} }}{2}} \right)\) and j is the imaginary unit \({\text{j = }}\sqrt {  1}\).
Equation (5) predicts the particle separation into the zigzag and bumping mode but gives an underestimated critical diameter.
Davis et al. [33, 34] separated particles in many devices with different row shift fractions and gaps and found the following empirical formula for critical diameter (Davis diameter):
For the parameters given in Table 2, \(D_C^{Inglis} = 8.12\) µm and \(D_C^{Davis} = 9.97\) µm. Equation (6) is considered more accurate and is often used for the preliminary design of DLD devices.
The wellknown Inglis and Davis diameters explicitly depend only on the gap (g) and shift fraction (ε). Dependence on the post radius (R) and transverse period (λ) is implicit since g = λ – 2R.
It seems clear that the critical diameter also depends on the post radius, the longitudinal period, the channel height, as well as the flow rate, and the particle density. However, to the best of our knowledge, such analytical dependences are absent in the literature. In most cases, dependences of this kind are studied numerically.
In addition to the usual post template (λ ≈ λ*, see Fig. 2A), socalled asymmetrical DLD gaps [35] or doublyperiodic arrays [36] are possible (λ < λ* and λ > λ*, see Fig. 2B, C). Zeming et al. [35] found that in both cases λ < λ* and λ > λ* the critical diameter decreases compared to the conventional geometry λ ≈ λ*, which enhances the separation resolution and throughput. Koens et al. [36] state that a slow viscous flow through a doublyperiodic system has no analytical solution. The rotated array layout was also studied [9] (see Fig. 2D).
The shape of the posts significantly affects the separation of particles (Fig. 3).
In addition to circular posts (Fig. 3A), various other posts have been investigated: square [37, 38] (Fig. 3B), triangular [13, 38,39,40] (Fig. 3C), polygonal [39] (Fig. 3D), airfoil [41] (Fig. 3E), Ishaped [37, 42] (Fig. 3F), Tshaped [42] (Fig. 3G), Lshaped [43] (Fig. 3H), L^{o}shaped [44] and others. Hyun et al. [45] used topologyoptimized posts instead of cylindrical ones (Fig. 3J).
Zhang et al. [38] modeled posts in the shape of a circle, square, rhombus, and triangle, and generalized Eq. (2)
where ξ and ζ are dimensionless geometric coefficients for different post shapes. They encountered difficulties in determining the critical diameter of deformable particles.
Highthroughput of DLD devices
One of the main disadvantages of DLD is its low throughput due to tiny volume [23]. The DLD throughput can be increased in three ways: by parallelizing the microchannel, by increasing the flow velocity, and by increasing the channel height.
Liu et al. [15] connected eight parallel channels into one single chamber, achieving a flow rate of 9.6 mL min^{−1}. Smith et al. [25] integrated 1024 nanoscale DLD arrays on a single chip. The achieved flow rate of 900 µL h^{−1} is high for separating nanometersize particles. Integration of multiple arrays requires a hightech fabrication while the principle of DLD remains the same, as first reported by Huang et al. [7].
Dincau et al. [31] studied the high Reynolds number regime (10 < Re < 60) through numerical simulation and experimental validation to achieve high throughput. The maximum fluid velocity in the channel was about 1.6 m s^{−1} at Re = 60. They demonstrated the formation of vortices behind the cylindrical posts, which, together with posts, create a virtual hydrodynamic shape resembling airfoils. Dincau et al. showed a decrease in the critical diameter as the Reynolds number increases.
The throughput increases proportionately to the channel height at a constant average fluid velocity. Bae et al. [46] investigated the effect of channel height on the critical particle diameter. They showed that the critical particle diameter depends on the height position of the particle. The fabrication of a channel with high posts encounters technological difficulties. The most common material for DLD device fabrication is polydimethylsiloxane (PDMS). In the case of PDMS, the tall posts are very flexible, and it is necessary to find another material and develop an alternative manufacturing technique.
Table 1 gives a summary of reviewed DLD devices for microparticle separation and concentration. This table presents particle sizes and nature, flow rate ranges, and device efficiencies. The summary provides insight into various DLD devices that serve different purposes and separate a wide range of particles under different initial conditions.
The weak point of DLD devices is the inability to adjust the critical diameter during operation. The critical diameter depends on many parameters, so the DLD design should focus on the physical processes between the posts.
Forces acting on the particle
Characterization of particle motion
The particle Reynolds number (Re_{P}) is defined as [30]:
where D_{P} is the particle diameter. Using the parameters given in Table 2, the particle Reynolds number Re_{P} = 0.542. The inertial focusing of particles occurs when the particle Reynolds number Re_{p} ≥ 1 [1, 47]. Thus, shearinduced and wallinduced lift forces have little effect on particles in DLD devices at a moderate channel Reynolds number.
The particle moves in the DLD array along a winding trajectory resembling movement in a serpentine channel. The dimensionless Dean number (De) expresses the ratio of the transverse fluid flow arising due to the curvature of the channel to the longitudinal flow [30]:
where R_{C} is the radius of the channel curvature. The assumption that the radius of the channel curvature is equal to the post radius (R_{C} = R) gives an upper bound of the Dean number, De = 3.43. A low Dean number (De < 40–60) indicates that the flow is completely unidirectional and secondary flows do not occur when the fluid direction changes [48].
Characterization of forces
The hydrodynamic forces acting on a particle can be compared to the Stokes drag force (F_{D}) acting on a stationary particle
Substitution of values from Table 2 gives F_{D} = 12.3 nN. If the particle moves at the fluid velocity, then F_{D} = 0.
As particles flow in the microchannel, they experience shear gradient lift force (F_{S}) and wall interaction lift force (F_{W}), which are expressed as [1, 30, 47]:
where C_{S} and C_{W} are the lift coefficients for the shear gradient force and the wall interaction force, respectively. The lift coefficients C_{S} and C_{W} vary with the Reynolds number and particle position. Calculations using Table 2 give F_{S} = 0.352 nN and F_{W} = 0.0255 nN. The lift forces are comparable to drag forces, so they must be taken into account when designing DLD devices.
The inertia of a particle moving along a curved path causes a centrifugal force (F_{C}) [49]:
The assumption that the curvature radius is equal to the post radius (R_{C} = R) gives F_{C} = 0.0885 nN.
Analytical models of fluid flow
Flow between two parallel plates
The plane Poiseuille flow of a viscous fluid is pressureinduced flow created between two infinitely long parallel plates (see Fig. 4B). In this problem, the Navier–Stokes equations are reduced to a linear ordinary differential equation of the second order with respect to the ycomponent of the velocity u:
where p is the pressure. The pressure gradient is constant, dp/dx = const. The ycomponent of velocity is zero at the channel walls. The resulting analytical solution to Eq. (5) is given as
The ycomponent of the velocity v equals zero, \(v = 0\).
The parabolic velocity profile (15) was used to solve Eq. (1) and determine the Inglis critical diameter (5).
Poiseuille flow in rectangular pipes
The flow in a rectangular pipe is a more realistic model of flow in the gap between two posts (see Fig. 4B). The analytical solution of the Poiseuille flow in the rectangular pipe over range − a ≤ y ≤ a and − b ≤ z ≤ b is expressed as follows [50, 51]:
where µ is the dynamic viscosity and p is the hydrostatic pressure.
Bae et al. [46] used Eq. (16) to numerically solve the following equation for β:
The solution shows that the critical diameter depends on the particle position in the channel along the zcoordinate, D_{C}(z) = 2β(z). This conclusion was confirmed experimentally.
Flow perpendicular to array of cylinders, Happel’s model
In addition to analytical solutions for fluid velocity in the y direction (“Flow between two parallel plates” section) and a twodimensional velocity distribution in the y–z plane (“Poiseuille flow in rectangular pipes” section), solutions are also known for a twodimensional velocity distribution in the x–y plane (see Fig. 5).
The flow field in an array of parallel cylinders oriented perpendicular to the flow direction at low Reynolds numbers has been studied for a long time. The periodic structure can be represented by a unit cell (see Fig. 5, Unit cell). This is a more accurate model than the flow between two parallel plates. In 1959, Happel [52] derived the stream function equation for such a system. Happel considered the cylinder array moves in a stationary liquid with a constant velocity (see Fig. 5, Happel’s model).
The Stokes approximation for 2D steady motion takes the form of a biharmonic equation
where Ψ is the stream function such that in cylindrical coordinates (r, θ) the velocity components (u_{r}, u_{θ}) are given by
The vorticity ω is given by
Happel assumed that the normal velocity and shear stress on the outer surface of the cylindrical shell are zero. The nonslip conditions are satisfied on the inner surface.
and
where c is the radius of the unit cell for the Happel’s model.
A general solution to Eq. (18) is
where C, D, E, and D are arbitrary constants that can be determined using boundary conditions (22) and (23). Under such conditions, the stream function is expressed as
where α is the volume fraction occupied by cylinders, α = R^{2}/c^{2}.
Sangani and Acrivos model
Sangani and Acrivos [53] extended the Happel's model to the square unit cell (see Fig. 5, Model of Sangani and Acrivos). The Stokes flow is described by Eq. (18). The boundary conditions are
The solution for the vorticity is given by
and the solution for the stream function is
where A_{1}, …, A_{n}, B_{1}, …, B_{n} are arbitrary constants determined by the boundary conditions. To find these constants, N points on the lines ED and DC are chosen, in which Eqs. (27) and (28) are to meet the boundary conditions. The boundary conditions on the lines AE and BA are satisfied automatically. Satisfaction of the boundary conditions at N points leads to forming a system of 2N linear algebraic equations. The arbitrary constants are determined by the solution of this system. Usually, N = 25–50 is sufficient for a good approximation of the vorticity and stream function.
Numerical simulation and experimental verification
In most works, the authors used the following DLD device design strategy. First, they estimated the parameters of the DLD array using Eq. (6), the Davis diameter. Second, they carried out several iterations of numerical simulation and experimental verification to achieve satisfactory results. Thus, in all works, optimization was carried out, and, in one way or another, the influence of various parameters on the final result was studied.
However, only in a few works, any parameter was varied within wide limits to study the mechanism of its influence on the critical diameter and separation efficiency.
Beech [54] and Holm [55] studied the effect of channel height on the flow profile and critical diameter using 3D finite element modeling. Bae et al. [46] studied this effect by analytical methods and experimental verification. Additionally, Beech investigated the effect of post diameter on the flow profile when the device height and gap are kept constant. Kim et al. [56] numerically studied the postsize variation and developed detailed theories of DLD for nanometer particle focusing. Similar works should be carried out in the future.
Conclusions and perspectives
A review of the literature shows that deterministic lateral displacement remains a very attractive method for separating and sorting particles. Active development of more and more new devices continues. Increasing the throughput of devices and the efficiency of particle separation, the separation of micron and submicron particles, and the separation of highly concentrated particles and particles of similar sizes are challenging problems.
Therefore, the following tasks become important for the study:

1.
A more detailed understanding of the DLD particle separation mechanism.

2.
Influence of the post diameter, channel height, row and column shift fractions, and transverse and longitudinal periods of the posts array on the critical diameter.

3.
Physical aspects of flow formation and the hydrodynamic forces acting on particles in DLD microchannels.

4.
Effect of high flow rate and particle concentration on the critical diameter and separation efficiency.

5.
Very accurate separation of close particle sizes.

6.
Topology optimization of the post shape to reduce device clogging and improve separation efficiency.

7.
Separation of soft and flexible particles of various shapes.
With the solution of these tasks, DLD will reveal its tremendous potential in the future.
Availability of data and materials
Not applicable.
References
Zhou J, Mukherjee P, Gao H, Luan Q, Papautsky I (2019) Labelfree microfluidic sorting of microparticles. APL Bioeng 3:041504. https://doi.org/10.1063/1.5120501
Lee S, Kim H, Yang S (2023) Microfluidic labelfree hydrodynamic separation of blood cells: recent developments and future perspectives. Adv Mater Technol 8:2201425. https://doi.org/10.1002/admt.202201425
Lu N, Tay HM, Petchakup C, He L, Gong L, Maw KK, Leong SY, Lok WW, Ong HB, Guo R, Li K, Ho H, Hou HW (2023) Labelfree microfluidic cell sorting and detection for rapid blood analysis. Lab Chip 23:1226–1257. https://doi.org/10.1039/D2LC00904H
Zhang T, Hong ZY, Tang SY, Li W, Inglis DW, Hosokawa Y, Yalikun Y, Li M (2020) Focusing of submicrometer particles in microfluidic devices. Lab Chip 20:35–53. https://doi.org/10.1039/C9LC00785G
Zhang Y, Zheng T, Wang L, Feng L, Wang M, Zhang Z, Feng H (2021) From passive to active sorting in microfluidics: a review. Rev Adv Mater Sci 60:313–324. https://doi.org/10.1515/rams20200044
Bayareh M (2020) An updated review on particle separation in passive microfluidic devices. Chem Eng Process 153:107984. https://doi.org/10.1016/j.cep.2020.107984
Huang LR, Cox EC, Austin RH, Sturm JC (2004) Continuous particle separation through deterministic lateral displacement. Science 304:987–990. https://doi.org/10.1126/science.1094567
Sturm JC, Cox EC, Comella B, Austin RH (2014) Ratchets in hydrodynamic flow: more than waterwheels. Interface Focus 4:20140054. https://doi.org/10.1098/rsfs.2014.0054
Salafi T, Zhang Y, Zhang Y (2019) A review on deterministic lateral displacement for particle separation and detection. NanoMicro Lett 11:77. https://doi.org/10.1007/s4082001903087
Hochstetter A, Vernekar R, Austin RH, Becker H, Beech JP, Fedosov DA, Gompper G, Kim SC, Smith JT, Stolovitzky G, Tegenfeldt JO, Wunsch BH, Zeming KK, Krüger T, Inglis DW (2020) Deterministic lateral displacement: challenges and perspectives. ACS Nano 14:10784–10795. https://doi.org/10.1021/acsnano.0c05186
Tang H, Niu J, Jin H, Lin S, Cui D (2022) Geometric structure design of passive labelfree microfluidic systems for biological microobject separation. Microsyst Nanoeng 8:62. https://doi.org/10.1038/s4137802200386y
Catarino SO, Rodrigues RO, Pinho D, Miranda JM, Minas G, Lima R (2019) Blood cells separation and sorting techniques of passive microfluidic devices: from fabrication to applications. Micromachines 10:593. https://doi.org/10.3390/mi10090593
Loutherback K, D’Silva J, Liu L, Wu A, Austin RH, Sturm JC (2012) Deterministic separation of cancer cells from blood at 10 mL/min. AIP Adv 2:042107. https://doi.org/10.1007/s104040100635y
Liu Z, Huang F, Du J, Shu W, Feng H, Xu X, Chen Y (2013) Rapid isolation of cancer cells using microfluidic deterministic lateral displacement structure. Biomicrofluidics 7:11801. https://doi.org/10.1063/1.4774308
Liu Z, Zhang W, Huang F, Feng H, Shu W, Xu X, Chen Y (2013) High throughput capture of circulating tumor cells using an integrated microfluidic system. Biosens Bioelectron 47:113–119. https://doi.org/10.1016/j.bios.2013.03.017
Okano H, Konishi T, Suzuki T, Suzuki T, Ariyasu S, Aoki S, Hayase M (2015) Enrichment of circulating tumor cells in tumorbearing mouse blood by a deterministic lateral displacement microfluidic device. Biomed Microdevices 17:59. https://doi.org/10.1007/s1054401599647
Au SH, Edd J, Stoddard AE, Wong KH, Fachin F, Maheswaran S, Haber DA, Stott SL, Kapur R, Toner M (2017) Microfluidic isolation of circulating tumor cell clusters by size and asymmetry. Sci Rep 7:2433. https://doi.org/10.1038/s41598017011503
Zhu S, Jiang F, Han Y, Xiang N, Ni Z (2020) Microfluidics for labelfree sorting of rare circulating tumor cells. Analyst 145:7103–7124. https://doi.org/10.1039/D0AN01148G
Bayareh M, Mohammadali R, Usefian A (2021) Cancer cell separation using passive mechanisms: a review. Chall Nano Micro Scale Sci Technol 9:48–62. https://doi.org/10.22111/cnmst.2021.36975.1202
Kang H, Xiong Y, Ma L, Yang T, Xu X (2022) Recent advances in micro/nanostructure array integrated microfluidic devices for efficient separation of circulating tumor cells. RSC Adv 12:34892–34903. https://doi.org/10.1039/D2RA06339E
Liu X, Ma L, Yan W, Aazmi A, Fang M, Xu X, Kang H, Xu X (2022) A review of recent progress toward the efficient separation of circulating tumor cells via micro/nanostructured microfluidic chips. View 3:20210013. https://doi.org/10.1002/VIW.20210013
Pariset E, Parent C, Fouillet Y, François B, Verplanck N, RevolCavalier F, Thuaire A, Agache V (2018) Separation of biological particles in a modular platform of cascaded deterministic lateral displacement modules. Sci Rep 8:17762. https://doi.org/10.1038/s41598018349588
Hochstetter A (2020) Labonachip technologies for the single cell level: separation, analysis, and diagnostics. Micromachines 11:468. https://doi.org/10.3390/mi11050468
Santana SM, Antonyak MA, Cerione RA, Kirby BJ (2014) Microfluidic isolation of cancercellderived microvesicles from hetergeneous extracellular shed vesicle populations. Biomed Microdevices 16:869–877. https://doi.org/10.1007/s105440149891z
Smith JT, Wunsch BH, Dogra N, Ahsen ME, Lee K, Yadav KK, Weil R, Pereira MA, Patel JV, Duch EA, Papalia JM, Lofaro MF, Gupta M, Tewari AK, CordonCardo C, Stolovitzky G, Gifford SM (2018) Integrated nanoscale deterministic lateral displacement arrays for separation of extracellular vesicles from clinicallyrelevant volumes of biological samples. Lab Chip 18(24):3913–3925. https://doi.org/10.1039/C8LC01017J
Meng Y, Asghari M, Aslan MK, Yilmaz A, Mateescu B, Stavrakis S, deMello AJ (2021) Microfluidics for extracellular vesicle separation and mimetic synthesis: recent advances and future perspectives. Chem Eng J 404:126110. https://doi.org/10.1016/j.cej.2020.126110
Havers M, Broman A, Lenshof A, Laurell T (2023) Advancement and obstacles in microfluidicsbased isolation of extracellular vesicles. Anal Bioanal Chem 415:1265–1285. https://doi.org/10.1007/s00216022043623
Wunsch BH, Smith JT, Giford SM, Wang C, Brink M, Bruce RL, Austin RH, Stolovitzky G, Astier Y (2016) Nanoscale lateral displacement arrays for the separation of exosomes and colloids down to 20nm. Nat Nanotechnol 11:936–940. https://doi.org/10.1038/nnano.2016.134
Xie Y, Rufo J, Zhong R, Rich J, Li P, Leong KW, Huang TJ (2020) Microfluidic isolation and enrichment of nanoparticles. ACS Nano 14:16220–16240. https://doi.org/10.1021/acsnano.0c06336
Martel JM, Toner M (2014) Inertial focusing in microfluidics. Ann Rev Biomed Eng 16:371–396. https://doi.org/10.1146/annurevbioeng121813120704
Dincau BM, Aghilinejad A, Hammersley T, Chen X, Kim JH (2018) Deterministic lateral displacement (DLD) in the high Reynolds number regime: highthroughput and dynamic separation characteristics. Microfluid Nanofluid 22:59. https://doi.org/10.1146/10.1007/s1040401820789
Inglis DW, Davis JA, Austin RH, Sturm JC (2006) Critical particle size for fractionation by deterministic lateral displacement. Lab Chip 6:655–658. https://doi.org/10.1039/B515371A
Davis JA, Inglis DW, Morton KJ, Lawrence DA, Huang LR, Chou SY, Sturm JC, Austin RH (2006) Deterministic hydrodynamics: taking blood apart. Proc Natl Acad Sci USA 103:14779–14784. https://doi.org/10.1073/pnas.0605967103
Davis JA (2008) Microfluidic separation of blood components through deterministic lateral displacement. Ph.D. Thesis, Princeton University
Zeming KK, Salafi T, Chen CH, Zhang Y (2016) “Asymmetrical deterministic lateral displacement gaps for dual functions of enhanced separation and throughput of red blood cells. Sci Rep 6:22934. https://doi.org/10.1038/srep22934
Koens L, Vernekar R, Krueger T, Lisicki M, Inglis DW (2023) The slow viscous flow around doublyperiodic arrays of infinite slender cylinders. arXiv:2301.12774. https://doi.org/10.48550/arXiv.2301.12774
Zeming KK, Ranjan S, Zhang Y (2013) Rotational separation of nonspherical bioparticles using Ishaped pillar arrays in a microfluidic device. Nat Commun 4:1625. https://doi.org/10.1038/ncomms2653
Zhang Z, Henry E, Gompper G, Fedosov DA (2015) Behavior of rigid and deformable particles in deterministic lateral displacement devices with different post shapes. J Chem Phys 143:243145. https://doi.org/10.1063/1.4937171
Loutherback K, Chou KS, Newman J, Puchalla J, Austin RH, Sturm JC (2010) Improved performance of deterministic lateral displacement arrays with triangular posts. Microfluid Nanofluid 9:1143–1149. https://doi.org/10.1007/s104040100635y
Xiang N, Wang J, Li Q, Han Y, Huang D, Ni Z (2019) Precise sizebased cell separation via the coupling of inertial microfluidics and deterministic lateral displacement. Anal Chem 91:10328–10334. https://doi.org/10.1021/acs.analchem.9b02863
Dincau BM, Aghilinejad A, Chen X, Moon SY, Kim JH (2018) Vortexfree highReynolds deterministic lateral displacement (DLD) via airfoil pillars. Microfluid Nanofluid 22:137. https://doi.org/10.1007/s1040401821603
Ranjan S, Zeming KK, Jureen R, Fisher D, Zhang Y (2014) DLD pillar shape design for efficient separation of spherical and nonspherical bioparticles. Lab Chip 14:4250–4262. https://doi.org/10.1039/C4LC00578C
Zeming KK, Sato Y, Yin L, Huang NJ, Wong LH, Loo HL, Lim YB, Lim CT, Chen J, Preiser PR, Han J (2020) Microfluidic labelfree bioprocessing of human reticulocytes from erythroid culture. Lab Chip 20:3445–3460. https://doi.org/10.1039/C9LC01128E
Liu Z, Huang Y, Liang W, Bai J, Feng H, Fang Z, Tian G, Zhu Y, Zhang H, Wang Y, Liu A, Chen Y (2021) Cascaded filter deterministic lateral displacement microchips for isolation and molecular analysis of circulating tumor cells and fusion cells. Lab Chip 21:2881–2891. https://doi.org/10.1039/D1LC00360G
Hyun JC, Hyun J, Wang S, Yang S (2016) Improved pillar shape for deterministic lateral displacement separation method to maintain separation efficiency over a long period of time. Sep Purif Technol 172:258–267. https://doi.org/10.1016/j.seppur.2016.08.023
Bae JH, Zhbanov A, Yang S (2022) Effect of channel height on the critical particle diameter in a deterministic lateral device. Micro Nano Syst Lett 10:20. https://doi.org/10.1186/s40486022001636
Amini H, Lee W, Di Carlo D (2014) Inertial microfluidic physics. Lab Chip 14:2739–2761. https://doi.org/10.1039/C4LC00128A
Nazari N, Yun W, Kovscek AR (2023) The motion of long bubbles in microchannels using a meterlong, rectangular capillary on a chip. J Colloid Interface Sci 638:149–160. https://doi.org/10.1016/j.jcis.2023.01.073
Zhang J, Li W, Li M, Alici G, Nguyen NT (2014) Particle inertial focusing and its mechanism in a serpentine microchannel. Microfluid Nanofluid 17:305–316. https://doi.org/10.1007/s1040401313066
White FM, Majdalani J (2022) Viscous fluid flow, 4th edn. McGrawHill Companies Inc, New York
Fukuchi T (2011) Numerical calculation of fullydeveloped laminar flows in arbitrary crosssections using finite difference method. AIP Adv 1:042109. https://doi.org/10.1063/1.3652881
Happel J (1959) Viscous flow relative to arrays of cylinders. AIChE J 5:174–177. https://doi.org/10.1002/aic.690050211
Sangani AS, Acrivos A (1982) Slow flow past periodic arrays of cylinders with application to heat transfer. Int J Multiph Flow 8:193–206. https://doi.org/10.1016/03019322(82)900295
Beech JP (2011) Microfuidics separation and analysis of biological particles. Lund University: Lund. https://lup.lub.lu.se/record/2198801
Holm S (2018) Microfuidic cell and particle sorting using deterministic lateral displacement. Department of physics. Lund University, Lund. https://lup.lub.lu.se/record/bc57504b53494a1a82835eee9343c80e
Kim SC, Wunsch BH, Hu H, Smith JT, Austin RH, Stolovitzky G (2017) Broken flow symmetry explains the dynamics of small particles in deterministic lateral displacement arrays. Proc Nat Acad Sci USA 114:E5034–E5041. https://doi.org/10.1073/pnas.1706645114
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This work was supported by a GIST Research Project grant funded by the GIST in 2023 and a National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2021R1A2C3008169).
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AZ make contributions to the conception and design of the work and analysis and interpretation of data and have drafted the work; YSL make contributions to the conception and design of the work and substantively revised draft; SY supervised this research, evaluated and edited the manuscript. All authors read and approved the final manuscript.
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Appendix
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Zhbanov, A., Lee, Y. & Yang, S. Current status and further development of deterministic lateral displacement for microparticle separation. Micro and Nano Syst Lett 11, 11 (2023). https://doi.org/10.1186/s4048602300175w
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DOI: https://doi.org/10.1186/s4048602300175w