中文   |   English   |   Email Alert
Fig/Tab
Advanced Search
image

Passive Focusing Techniques of Particles in Microfluidic Device

Bingyan Jiang , Tao Peng , Shuai Yuan , Mingyong Zhou

Progress in Chemistry ›› 2021, Vol. 33 ›› Issue (10) : 1780 -1796.

PDF
Progress in Chemistry ›› 2021, Vol. 33 ›› Issue (10) : 1780-1796 DOI: 10.7536/PC200871
research-article
Scan to read & Share
Passive Focusing Techniques of Particles in Microfluidic Device
Author information +
History +
PDF

Abstract

Particle focusing in microfluidic device is a rapidly growing research field due to its wide applications in biology, chemistry, engineering, and medicine. Precise and high-throughput focusing can be a pivotal pretreatment step for counting, detection and separation application. Generally, focusing technologies can be divided into active, passive and sheath-assisted methods. The active and sheath-assisted methods rely on external energy field or sheath flow, which can accurately control the position of particles in microchannel, but require integrating other complex functional elements. Passive focusing uses fluid inertia, viscoelasticity, and other characteristics to control the equilibrium position of particles in the microchannel,and it has been proven to be a powerful tool due to the simplicity, label-free, biocompatible, contact-free, low-cost, and high throughout nature. A large amount of experimental and numerical work has been carried out on the passive focusing technology from the aspects of chip structure, microfluidic characteristics, and particle characteristics. In this review, the fundamental hydrodynamic forces and the basic principles related to the focusing mechanism were firstly briefly introduced and discussed. Then the state of the art of detailed passive focusing methods was presented. At last, the focusing methods were summarized and future development in this field was predicted.

Contents

1 Introduction

2 Hydrodynamic forces and basic principles

2.1 Hydrodynamic forces

2.2 Basic principles for particle passive focusing

3 Inertial focusing techniques

3.1 Inertial focusing in straight microchannels

3.2 Inertial focusing in curved microchannels

3.3 Inertial focusing in multi-staged microchannels

3.4 Micro-vortex induced focusing

4 Elasto-inertial focusing

4.1 Elasto-inertial focusing in straight microchannels

4.2 Elasto-inertial focusing in curved microchannels

5 Application of passive focusing technology in biological particle separation

6 Conclusion and prospects

Graphical abstract

Keywords

particle focusing / passive focusing / microfluidic device / inertial focusing / elasto-inertial focusing

Cite this article

Download citation ▾
Bingyan Jiang, Tao Peng, Shuai Yuan, Mingyong Zhou. Passive Focusing Techniques of Particles in Microfluidic Device. Progress in Chemistry, 2021, 33(10): 1780-1796 DOI:10.7536/PC200871

登录浏览全文

4963

注册一个新账户 忘记密码

1 Introduction

In recent years, microfluidics technology has attracted much attention because it can precisely control the position of microscale or even submicroscale particles in the flow channel[1⇓~3]. Compared with traditional microsystem technology, microfluidics has many advantages, such as time saving, low cost, low consumption and high efficiency[4]. In the past 10 years, microfluidic technology has been developed for many applications, such as particle focusing, particle sorting, fluid mixing, cell stretching and cell trapping[5][6,7][8][9,10][11]. These applications have been widely used in chemical analysis, biopharmaceutical, medical, environmental and other research fields[12][13][14][15][16].
Particle focusing, as a promising technology in microfluidics applications, refers to the random distribution of particles flowing with the fluid in a microchannel.Under the action of transverse migration force perpendicular to the flow direction, the force is balanced at a certain position after transverse motion, showing the phenomenon of orderly arrangement of single or multiple equilibrium positions along the streamline. Focusing can also be used to count and align biological particles, and has been applied to flow cytometry and single cell analysis[17]. Generally, particle focusing on microfluidic chips can be divided into three types according to whether an external energy field and sheath flow are introduced, namely active focusing, sheath flow focusing and passive focusing. Active focusing relies on acoustic vibration, dielectrophoresis, magnetic field, optical field and thermophoretic force to manipulate particle motion and achieve orderly arrangement of particles[18][19][20][21][22]. Sheath flow focusing uses additional sheath flow to squeeze the sample flow to achieve particle focusing in the sample flow[23]. Passive focusing uses the inertia of fluid and the viscoelasticity of non-Newtonian fluid to induce particles to migrate laterally and finally achieve orderly arrangement[24,25][25,26]. Active focusing technology has high flexibility and control accuracy, but the introduction of external energy field requires the integration of additional structures or complex control systems on the microfluidic chip, and the particle fluid needs to maintain a low flow rate to ensure that enough external field force can be obtained to migrate to the focusing equilibrium position in a certain time, so it is difficult to achieve high throughput[27]. Sheath flow focusing can achieve higher flux, but the introduction of sheath flow will increase the number of inlet channels on the chip, and more micropumps are needed to supply sheath flow, which will reduce the integration of microfluidic chips.When used for biological particle focusing, sheath flow may cause sample contamination and dilution[28]. Sheath flow focusing is usually used as a pretreatment step for sorting biological particles, for example, after using sheath flow to focus body fluid samples, surface acoustic waves and fluid viscoelasticity are used to manipulate and sort exosomes[29][30]. Passive focusing does not depend on the external sheath flow and energy field, and uses the inertia force, viscous force and elastic force of the fluid to focus the particles under a specific flow channel structure, so that the integration level of the microfluidic device is effectively improved, and when the microfluidic device is used for focusing biological particles, damage caused by external fluid or external force can be effectively avoided[31,32]. Passive focusing can also achieve particle sorting based on different focusing equilibrium positions, such as cancer cell sorting in whole blood and exosomes sorting in body fluid samples[33][34].
Passive focusing is a continuous, high-throughput, label-free particle manipulation method, which often uses two principles of inertial focusing and elastic-inertial focusing. The most commonly used channel structures in inertial focusing are straight channel, curved channel, curved and straight combined channel structure or straight channel topology[35][36][17,37][38,39]. The spring-inertial focusing has a similar flow channel structure to the inertial focusing, but it uses a viscoelastic fluid medium, so its focusing efficiency, accuracy and principle are different from the inertial focusing. In the particle passive focusing technology, the inertial focusing is usually 2D focusing, that is, the focusing arrangement of particles is realized only in the 2D plane. To obtain the 3D focusing effect, it is usually realized by combining different channel topographies and structures, and the elastic-inertial focusing is usually 3D focusing.
Inertial microfluidics, the application of non-Newtonian fluids in microfluidics, nonlinear microfluidic, sheath flow focusing on microfluidic chips, submicron particle focusing, and particle passive sorting on microfluidic chips have been reviewed in detail.In this paper, the passive focusing technology of polymer particles on microfluidic chips is reviewed, and the development of passive focusing technology in the past 10 years is reviewed in detail[24,25,40,41][26,42,43][44][45][46][47].

2 Hydrodynamic load and focusing principle

2.1 Hydrodynamic load

The focusing process and focusing effect of particles in the microchannel are related to the inertial effect of fluid, the Dean secondary flow effect in the curved channel and the elastic effect of viscoelastic fluid. The hydrodynamic loads related to the inertial effect include the lift induced by particle rotation (Magnus force, FΩ), the lift induced by particle slip and shear motion (Saffman force, FS), the lift induced from the channel wall (FWI) and the lift caused by velocity shear gradient (FSG)[48][49][50][51]. Magnus and Saffman forces are negligible compared to FWI and FSG in most particle passive focusing applications. The hydrodynamic forces associated with secondary flow effects are Dean drag (FD) and elastic effects induce inertial forces on particles near the channel wall (FE). The lateral migration and balance of particles caused by the force can be affected by the three effects alone or by the synergy of the three effects. The forces and dimensionless numbers associated with these effects are described in this section.

2.1.1 Inertial lift

When the fluid inertia is not negligible, the neutrally suspended particles are subjected to a net inertial lift FL, which is the combined force of the FWI and the FSG[52]. Under the action of FWI, the particles move away from the wall of the channel, and the FSG makes the particles move along the direction from the center of the channel to the wall. When FL=0, the particles are in a focused equilibrium position between the wall and the centerline, as shown in Figure 1A. The expression for the net lift FL is:[24,52]
F L = ρ f U 2 m a 4 D 2 H f L ( R c , x c ) ,
Where ρf is the fluid density, Um is the average velocity, a is the particle diameter, and DH is the hydraulic diameter of the flow passage. For a rectangular channel, DH=2wh/(w+h),w and H are the width and height of the channel, respectively. The fL is the lift coefficient, whose value depends on the Rc of the channel Reynolds number and the x c of the particle position in the channel[53].
The dimensionless numbers associated with the net inertial lift are the channel Reynolds number Rc(Re) and the particle Reynolds number R p [52]. The Rc describes the relationship between the inertial and viscous forces, while the Rp introduces the ratio of the particle diameter to the hydraulic diameter of the channel:
R c = ρ f U m D H μ ,
R p = R c a 2 D 2 H = ρ f U m a 2 μ D H ,
Where μ is the dynamic viscosity of the fluid.
Unlike rigid particles, deformable particles induce additional lift when they change shape near the wall. Deformation-induced lift is initially used to calculate the deformation lift of droplets and bubbles in microchannels. The dimensionless numbers used to describe the relative deformation of the droplet are the Weber number ( We = ρ f U m 2 a / σ), the laminar number ( Ca = μ U m a / σh), and the viscosity ratio ( λ d = μ d / μ), where σ is the surface tensor and μd is the dynamic viscosity of the fluid inside the droplet. When Ca increases or the Rp decreases, the lift effect induced by deformation will become obvious, and the expression of the force induced by deformation on the droplet and bubble far away from the wall is:[25,40][54,55]
F L , D = Caμ U m a ( a H ) 3 ( d H ) f ( λ d ) ,
Where d is the distance between the particle and the center of the flow channel. Due to the presence of deformation-induced lift, the equilibrium position of the deformable particles is further from the channel wall than that of the rigid particles, as shown in Fig. 1A[56].

2.1.2 Elastic force induced by viscoelastic fluid medium

When the fluid medium in the microchannel is viscoelastic fluid, the effect of elastic force on particle focusing should be considered. In pressure-driven viscoelastic fluid flow, the first principal stress (N1=σxx-σyy) and the second principal stress (N2=σyy-σzz) have an effect on the lateral migration of particles. The σxx, the σyy, and the σzz are normal stresses in the fluid, pointing to the flow direction, the velocity gradient, and the direction of rotation, respectively. Since dilute viscoelastic fluids are commonly used in microfluidics research, the N2 is negligible compared to the N1[57,58]. In highly concentrated viscoelastic solutions, the N2 becomes significant with increasing shear rate[59]. For a dilute viscoelastic fluid, the elastic force is mainly caused by the inhomogeneous distribution of the N1, as shown in Fig. 1b, and is given by[26,42,60]
F E = C eL a 3 ▽ N 1 = - 2 C eL a 3 η p λ ▽ γ · 2 ,
Where the CeL is the elastic lift coefficient and the ηp is the viscosity of the polymer dissolved in the fluid. The dimensionless number describing the viscoelasticity of a fluid is the Weissenberg number Wi:[61,62]
Wi = γ · λ ,
Where γ · is the characteristic shear rate and λ is the relaxation time. In a rectangular channel, the shear rate is γ · = 2 U m / h, Wi is the 2 λQ / h w 2, and Q is the volumetric flow rate[63].

2.1.3 Secondary flow induced Dean drag

Due to the parabolic velocity distribution and inertia, the fluid flowing through the curved channel forms two counter-rotating vortices in the section perpendicular to the flow, which is called Dean secondary flow, as shown in Fig. 1C. The intensity of the secondary flow is usually characterized by the Dean number De, and the higher the Dean number is, the higher the intensity of the secondary flow is:[64]
De = R c D H 2 δ ,
Where δ is the curvature of the flow channel.
The drag force on particles moving with the secondary flow, i.e. Dean drag force, can be calculated by the Stokes drag force formula:
F D = 3 π μa U D .
The magnitude and direction of Dean drag are determined by the Dean flow distribution at the cross section, and the UD is the Dean secondary flow velocity, which is expressed as[65]
U D ~ 1.8 × 10 - 4 D e 1.63 .

2.1.4 Viscous drag due to fluid flow

In a homogeneous Stokes flow, a viscous drag force, also known as the Stokes drag force, acts on the particle due to the velocity difference between the particle and the fluid, and is expressed as[25,42]
F v = 3 π μa ( U f - U p ) ,
Where the Uf and the Up are the fluid and particle flow rates, respectively.

2.2 Relevant principles for passive focusing of particles

Through a large number of experiments and theoretical derivation, scholars have concluded that in order to design a microfluidic chip to focus particles of a specific size, in order to ensure a good focusing effect, it is necessary to meet the principles such as particle size constraint ratio, particle loading ratio, particle solution concentration and so on.

2.2.1 Particle size constraint ratio principle

Particle focusing based on the principle of inertial microflow needs to satisfy the condition that the particle size constraint ratio is a/DH>0.07, which can ensure that the particle has enough inertial force to achieve lateral migration to the equilibrium position when flowing with the microfluid[31,66,67]. Using the elastic-inertial focusing principle to focus particles, because of the existence of the elastic force, focusing can be realized under the condition of a/DH<0.04 in the curved channel, which makes up for the lack of inertial focusing, but it also needs to reasonably design the particle size constraint ratio[68,69].

2.2.2 Particle loading ratio principle

The balance process of particle inertial focusing is determined by the load ratio Rf=FL/ the F D . When Rf>>1, the inertial lift plays a dominant role, and the particle focusing is the same as the inertial focusing phenomenon in the straight channel[31,67,70]. When Rf<<1, the lateral migration of particles is mainly affected by the Dean drag force and rotates with the Dean vortex. When Rf≈1, particles in the flow channel will obtain a certain equilibrium position, which can be manipulated by controlling the intensity of Dean flow (changing the curvature of the flow channel or the flow rate). The expression for the Rf I[31,71]
R f = F L F D ~ 1 δ a D H 3 R n c ,
The fL is proportional to the R c n, n < 0.
When designing the curved-channel focused microfluidic chip, the Rf should meet the following requirements:[24,40]
R f ≡ a 2 R h 3 > ~ 0.04 ,
R is the maximum radius of curvature in the channel.
In a viscoelastic fluid, the focusing of particles is dominated by the elastic number El, which is the ratio of the Weissenberg number to the Reynolds number, expressed as:[40,72]
El = Wi R c = λμ ( w + h ) ρ f w 2 h ,
The elastic force can be neglected when Wi = El ≈ 0, and the inertial force can be neglected when El ≥ 1. El is determined by the cross-sectional size of the flow channel and the properties of the fluid medium[63]. Both Wi and the Rc are proportional to the flow rate, so the elastic number El is independent of the flow rate.

2.2.3 Concentration Limiting Principles for Particulate Solutions

The position and number of particles in the microchannel are affected by the number of particles per unit length[73]. As the concentration of particles in the fluid increases, the focusing flux will increase, but the interaction between particles becomes significant. When the concentration is too high, the focusing position will appear bending effect, that is, under the influence of the interaction force between particles, particles will produce additional lateral deviation, resulting in bending of the focusing line[74]. Therefore, it is necessary to consider the influence of concentration on the focusing process, and the particle concentration is usually characterized by the percentage of particles per unit length:[24]
φ = a A c V f V p = 6 wh V f π a 2 ,
Where, the Vf is the volume percentage of suspended particles, the Ac is the cross-sectional area of the flow channel, and the Vp is the volume of particles. When φ > 0.5, the interaction between particles should be considered. In most microfluidic focusing applications, the particle solution is diluted, so the interaction is usually ignored.

3 Particle inertial focusing technique

In 1961, Segr Segré et al. Found that suspended particles in a laminar fluid flowing through a cylindrical pipe (diameter ~ 1 cm) were distributed in equilibrium at 0.6 radii from the center of the pipe at the outlet, as shown in Figure 2a.This effect is caused by the lateral migration of particles under the action of inertial lift, which opens up the research field of particle inertial focusing, and the principle of inertial focusing was first combined with microfluidics in 2007[75][31]. In this chapter, the inertial focusing technology of particles is described according to the classification of flow channel structure.

3.1 Inertial focusing in straight channel

Straight channels have been widely used in microfluidic applications due to their simple structure and ease of fabrication. When used for microfluidic focusing, only 2D focusing is usually possible. In the straight channel, the square section (AR = 1, AR = H/w is the depth-width ratio of the channel) and rectangular section (AR > 1 or AR < 1) channels are mostly used. In the straight channel, when the Rp<<1 occurs, the viscous interaction between the fluid and the particles dominates the movement of the particles, and the particles will be mainly affected by the surface drag force and move along the streamline without lateral migration. When Rp≈1, the lateral migration of particles due to inertial lift will become significant and form a focusing phenomenon[31].
The focusing effect of particles in the straight channel is affected by the depth-to-width ratio of the channel, the cross-sectional morphology of the channel, the particle diameter constraint ratio and the flow rate. In the micro-channel with square cross section, the particles are focused on the equilibrium position near the center of the four walls, as shown in Figure 2b. The increase of particle Reynolds number will lead to the increase of FSG, and the equilibrium position will move to the wall[31]. In the rectangular cross section flow channel with AR < 1, the parabolic velocity profile along the broad surface is blunted relative to the narrow surface, and the particles are focused at the focusing position near the center of the broad surface[76]. With the increase of flow velocity, the flow velocity profile along the broad surface returns to a parabolic shape, and the two equilibrium positions along the center of the narrow surface gradually recover under the action of enhanced FSG. The equilibrium position at the broad surface moves toward the wall, and the number of equilibrium positions increases from 2 to 4, as shown in Fig. 2C. The inertial focusing equilibrium process of particles in a straight channel can be explained by a second-order focusing model, as shown in Fig. 2D[35]. In the first stage, the particles are in equilibrium at the position where the FWI and the FSG are equal near the wall of the flow channel.In the second stage, the particles near the wall of the flow channel move to the equilibrium position near the center of the broad surface due to the rotation-induced lift FΩ.
In the application of inertial focusing, the velocity gradient profile in the flow channel changes with the change of the cross-sectional shape of the flow channel, and the focusing characteristics of particles will also be different[77]. Asymmetric velocity profiles with respect to the axis are produced in the trapezoidal cross section channel, and the number of equilibrium points near the trapezoidal wide wall and bottom varies with the slope angle of the top of the trapezoid[78]. In the channel with semicircular cross section, the particles are focused on the center line of the top and bottom surfaces, and the focusing equilibrium position is not affected by the Rp of the particles. In the channel with triangular cross section, the particles are focused near the centerline of the wall, and the number of focusing equilibrium positions increases with the decrease of the vertex angle. As shown in Figure 2e, when the vertex angle is 120 °, AR = 0.4, a single equilibrium position focus near the vertex angle can be achieved[79][80]. Non-spherical particles in the shape of disc and column in the micro-channel will rotate in the flow, and the inertial focusing equilibrium position of the particles is determined by the rotation diameter (the maximum diameter across the center line), and the equilibrium position will be different with different shapes, so the inertial sorting application of non-spherical particles can be realized according to their shapes[81].
Inertial lift is proportional to the fourth :FL~a4 of particle diameter, and inertial focusing is usually more suitable for large micron particles when the flow velocity at the inlet of the channel and the cross section of the channel remain unchanged[82]. The length of the micro-channel is used to ensure the time for the particles to be acted by the inertial force, and the small-size particles need a longer channel length than the large-size particles to ensure enough inertial lift force to achieve balance. When the flow velocity in the channel is kept constant, the size of the channel section decreases, the inertial lift force on particles increases with the sharpening of the flow velocity profile, and the length of the channel required for focusing decreases (FL~ D H - 2)[35]. When focusing on sub-micron particles (0. 1 ~ 1 μm) without increasing the length of the flow channel, the flow channel with small cross-section corresponding to the particle size is needed, which increases the difficulty of channel manufacturing and testing[66]. In the pressure-driven flow, the small size of the cross section is prone to high pressure and blockage (repeated use), so the microfluidic chip is required to have high bonding strength[83][76]. An oscillate microfluidic chip is adopted to switch that flow direction of the particle at a certain frequency, so that the movement distance of the particles in a flow channel with a fixed length and a fixed cross section is increased, and the dependence on the length of the flow channel is weakened. The oscillating microfluidic chip can be used for Rp<0.01 and inertial focusing balance of particles with a/H < 0.07 by controlling the particles to move for a long distance, but it requires a complex external control loop[84].
The structure and focusing principle of straight channel are relatively simple, but the focusing accuracy is low and it is difficult to achieve 3D focusing. In order to obtain good focusing effect, it is necessary to ensure sufficient channel length and flow rate, but it will increase the area of the microfluidic chip and increase the pressure of the chip, which can be solved by introducing curved channels.

3.2 Inertial focusing in a curved channel

The curved channel can effectively improve the compactness of the microfluidic chip, reduce the length of the channel required for focusing, and reduce the fluid resistance and the required driving pressure[85]. In addition to the inertial lift force, the particles in the curved channel are also subjected to Dean drag force, and the additional secondary flow will accelerate the focusing process and reduce the number of focusing equilibrium positions[31]. In order to suppress the mixing effect caused by Dean flow at high flow velocity in a curved channel, a rectangular channel with low AR is often used[86,87]. Particle focusing in a curved channel is usually governed by a dynamic balance between inertial lift and Dean drag. According to the structure of the curved channel, the curved channel for particle focusing can be divided into symmetric serpentine, asymmetric serpentine, spiral and so on.
(1) Focusing in a symmetrical curvature serpentine flow channel
Zhang et al., using a low aspect ratio (AR = 1/5) right-angled transition symmetrical serpentine channel, with negligible inertial lift along the broadside direction, achieved focusing at a single equilibrium position near the center of the channel broadside under the combined action of Dean drag and centrifugal force, as shown in Figure 3A[88]. Shamloo et al. Used numerical simulation method to study the focusing process of right-angled transition serpentine channel driven by centrifugal disk. The focusing balance of particles is affected by Dean drag force, inertial lift force and centrifugal force induced by centrifugal disk. The length of channel required for focusing is related to particle density and transition angle of channel[89]. In the serpentine channel with symmetric fillet curvature transition, the particles are focused at a single or two equilibrium positions depending on the difference in channel section and Reynolds number[31,90]. Yin et al. Found that the curvature and velocity of the flow channel are important parameters affecting the focusing effect through simulation research[91]. Zhang et al. studied the influence of viscosity, flow rate, particle diameter and section size on the focusing effect in the symmetrical serpentine channel, and deduced the parameter coordinate diagram related to the focusing effect, as shown in Figure 3C[92]. The focusing modes of particles can be divided into three types: double equilibrium position focusing, single equilibrium position focusing and non-focusing. The figure can be used to predict the focusing behavior of particles in the symmetrical serpentine microchannel and guide the design of the focusing chip. Özbey et al studied the influence of inertial lift and Dean drag on focusing effect in multi-curvature symmetrical serpentine channel, which provided a basis for clarifying the migration mechanism of particles in inertial microfluidic devices[93].
(2) Focusing in a serpentine channel with asymmetric curvature
Di Carlo et al. First studied the particle focusing in an asymmetric serpentine channel by using the curvature topology of the straight channel[31]. The introduction of asymmetric curvature in a straight channel with square cross section reduces the number of four focusing equilibrium positions to one or two depending on the flow velocity, as shown in Fig. 3B. The particle focusing process becomes more complex as the Rp increases. The asymmetric serpentine microchannel can achieve precise particle focusing, and particles with different diameters have different equilibrium positions, so the channel can be extended to particle sorting and filtration based on size differences[94,95][96,97]. PMDS, which is commonly used to manufacture microfluidic chips, has low elastic modulus and is difficult to withstand high pressure, while Thermoset polyester (TPE) has an elastic modulus of 1000 times that of PDMS and a stiffness higher than that of 1:10 PDMS, so it is more suitable for microfluidic applications with high pressure requirements[98]. Wang et al[99].
The asymmetric serpentine flow channel chip was fabricated by using TPE material and pouring and reverse molding process.The single equilibrium position focusing of sub-micron particles was realized by adjusting the flow rate, which extended the application of inertial focusing principle in sub-micron particles.The chip can also be used to remove micron particles in the mixture of micro-nano particles. Zhou et al. used a series of reversed curved channel structures to generate Dean drag force which is perpendicular to the main flow direction and periodically reversed in direction, forming the hydrodynamic effect of focusing particles. Small particles are focused at double equilibrium positions, while large particles (> 5 μm) are focused at a single equilibrium position. The focusing process is accelerated with the increase of channel Reynolds number[100]. Gossett et al. studied the effect of the asymmetry of the curved channel on the focusing process. With the increase of asymmetry, particles are more likely to focus on a single streamline at low Reynolds number Rc[36].
(3) Inertial focusing in a helical flow channel
The spiral flow channel is compact in structure, and the continuous same curvature can provide stable secondary flow. When Dean drag force is balanced between the FD and the FL, the particles are focused near the inner wall of the flow channel, as shown in Fig. 4A. The time required for the particles to move to the focusing equilibrium position is shortened with the increase of Dean number[70,101]. The FL/FD values of particles with different sizes are different, the focusing position of large particles is closer to the inner wall because of the larger inertial lift, and the focusing position of small particles is far away from the inner wall because of the Dean flow[67]. In the spiral channel with gradually changing width, the particles are focused at two equilibrium positions along the height direction near the inner wall[102]. Martel et al. Have systematically studied the particle focusing effect under the influence of the depth-to-width ratio of the flow channel, and the Dean flow and velocity profile change with the change of the depth-to-width ratio, as shown in Fig. 4B.With the decrease of AR, the inertial lift force along the broad surface in the spiral channel decreases, and the focusing process is dominated by the Dean drag FD, and the lateral focusing equilibrium position of particles can be controlled by regulating the flow rate[103]. Cruz et al. Derived the proportional relationship of flow channel and fluid parameters required for focusing particles of different sizes according to theory, so as to experimentally verify and realize the focusing of sub-micron particles[104,105]. Pai Paiè and others used femtosecond laser modification and chemical etching to process 3D spiral ring microchannels, which can produce high-intensity secondary flow under low channel resistance and accelerate the focusing process of particles compared with planar channel structure, and this processing method can also realize the processing of parallel focusing microchannels for multiple particles[106].
Xiang et al. Proposed a fifth-order model to illustrate the mechanism of the variation of the focusing equilibrium position with flow velocity, as shown in Fig. 4C[107]. With the increase of flow velocity, the equilibrium position changes in the following order: at low flow velocity where the inertia is not negligible, the secondary flow effect is weak, and the lateral movement of particles is first dominated by the inertial lift FL and then focused at the center along the upper and lower broad surfaces[108][31]; When the flow rate increases, the equilibrium position moves to the inner wall of the flow channel and gradually stabilizes at a position close to the inner wall side; When the flow velocity increases again, the FD plays a dominant role, and the lateral equilibrium position of particles moves from the inner wall to the outer wall. Eventually, the Dean flow effect is rapidly enhanced, and the fluid in the flow channel is mixed[67]. Xiang et al. studied the dynamic migration process of particles under different particle size constraint ratios. In the spiral channel with specific size and cross-section morphology, the focusing effect increases with the increase of particle size in the order of no focusing, coarse focusing and precise focusing, and large particles are easier to focus[109]. Guan et al. studied the focusing behavior of particles in the trapezoidal cross section spiral flow channel. The Dean flow with higher intensity is generated near the wide side, which accelerates the capture of particles near the short side. The Dean flow can be strengthened by increasing the trapezoidal inclination[82]. Chen et al. Used 3D printing to process a spiral channel with a similar cross-sectional shape to the river bed, which can be applied to inertial focusing of large particles at a single equilibrium position[110]. Al-Halhouli et Al. Found through experimental research that the single-sided trapezoidal topology of the spiral channel can enhance the focusing effect of small particles (2 μm)[111]. By equidistantly arranging micro-obstacles in the spiral channel, the Dean flow intensity in the channel is enhanced and the focusing process is accelerated, so that the high-flux focusing effect can be achieved, but the introduction of the micro-obstacles increases the fluid resistance and requires the microfluidic chip to have high bonding strength[112]. Martel et al. analyzed the effects of channel Reynolds number Rc, particle size constraint ratio, and channel curvature on the focusing equilibrium position of three sizes of particles, as shown in Figure 4D[113]. Increasing the curvature of the channel not only increases the Dean drag, but also affects the redistribution of the flow profile and the lift force caused by the shear gradient, so that the particles can obtain a new vertical equilibrium position.These results can provide guidance for the design of focused microfluidic chips with curved channels.

3.3 Particle focusing in multi-step flow channel

The inertial focusing balance of particles is different when the cross section shape, size and flow state of the channel are different. By combining the microchannels with different focusing characteristics, the multi-stage control of the focusing balance position can be realized, and the high-precision 3D single balance position focusing can be formed. Oakey et al. proposed a flow channel structure with a straight flow channel with a rectangular cross section and an asymmetric serpentine flow channel in series, as shown in Figure 5A, in which particles in the straight flow channel first move to two equilibrium positions near the center line of the broad surface,When the particles flow through the curved channel, the two equilibrium positions are reduced to one due to the secondary flow, and the focusing behavior of particles in the combined second-order channel is mainly affected by the flow velocity[17]. Zhang et al. combined the high AR rectangular cross section straight channel and the semicircular curved channel periodically, and the two focusing positions near the center of the broad side in the straight channel were reduced to one at the bend to achieve 3D single equilibrium position focusing with high flux[37]. Wang et al. proposed a combined straight channel structure with different rectangular cross sections, as shown in Fig. 5B. By defining the length of the "Y-shaped" outlet at the second step, the hydrodynamic impedance of the channel can be changed to control the flow direction of granular fluid[114]. Particles flowing through the first-order low AR channel are focused at two equilibrium positions near the center of the broad surface, and in the second-order high AR rectangular cross-section channel, the number of two focusing equilibrium positions is reduced to one due to the rotation-induced lift. The device utilizes the focusing characteristics of rectangular cross section flow channels with different aspect ratios to provide a reference for the convenient design of microfluidic focusing, and has the disadvantages that the length of the flow channel is required to be long, and the space size of the chip is increased. Size-based inertial sorting of particles can also be achieved by combining rectangular channels with different aspect ratios[115]. Kim et al. proposed a three-stage straight channel inertial focusing chip with a low AR rectangular section, a triangular section and a semicircular section in turn. Due to the difference of flow velocity profiles in the flow channels of the three sections, the two equilibrium positions of particles in the rectangular section are reduced to one through the triangular and circular sections in turn, thus realizing 3D single equilibrium position focusing[79]. Combinations of flow channels of different cross sections can also be used for size-based inertial sorting[116]. Because the multi-stage channels are connected in series, the focusing effect of particles is affected by the arrangement order of the channels.

3.4 Inertial focusing of particles induced by micro-eddy current

Micro-vortex refers to the fluid vortex that occurs in the micro-channel and can provide a beneficial force for the lateral migration of particles. The micro-vortex can be generated by gradual change of the cross section of the flow channel along the flow direction, expansion and contraction of the flow channel, or arrangement of micro-obstacles in the flow channel. There are generally two types of micro-vortices: those perpendicular to the flow direction and those parallel to the flow direction. In microfluidic focusing applications with micro-vortices, the focusing mechanism of particles is usually a dynamic balance between vortex-induced drag and inertial lift.
Choi et al. studied the particle focusing after the obstacles were arranged at a certain inclination angle in the micro-channel. The micro-obstacles changed the fluid pressure distribution in the straight channel and formed a micro-vortex perpendicular to the flow direction, which induced the particles to produce lateral displacement and focus on the position near the side wall. The focusing depended on the size of the particles and was basically not affected by the flow rate[117]. Choi et al. bonded two PDMS chips with inclined rectangular obstacles with exponentially increasing width in the flow channel. The vertical vortex generated in the flow channel can promote particle focusing, which is more efficient for large particles, and the focusing effect depends on the length of the flow channel[118]. Hsu et al. studied the focusing behavior of particles after arranging chevron-shaped grooves on the top of a straight channel with rectangular cross section. The focusing effect is related to the height of the channel, the size of the channel, the number of grooves and the ratio of groove height to channel height. By manipulating the arrangement of chevron-shaped grooves, particles can obtain a certain lateral focusing position[38]. Chung et al. studied the focusing behavior of particles in the straight channel with cylindrical obstacles, and the channel structure and focusing mechanism are shown in Fig. 6a[119]. After passing through the straight channel with square cross section, the number of four focused equilibrium positions is reduced to one due to the influence of the vertical vortex induced by the cylindrical obstacle when passing through the cylindrical obstacle channel. The introduction of cylindrical obstacles causes high flow resistance, limits the focused flux, and may cause blockages. Chung et al. Used a periodically arranged stepped straight channel, and the number of two equilibrium positions in the low AR rectangular channel was reduced to one under the action of the vertical vortex induced by the tapered channel section. The focusing effect was mainly affected by the number of steps and the concentration of particles[120]. When the step has a certain inclination relative to the channel, the channel width will become a key parameter affecting the focusing performance[121]. Zhao et al. Achieved high flux focusing (≥ 1 mL/min) of 13 μm particles by arranging inclined arc steps in the straight channel[122].
In the microchannel with a rectangular convergent-divergent structure, a horizontal vortex will be generated in the rectangular divergent region, and a vertical vortex will be induced downstream of the cavity due to the inertia of the fluid[123]. Park et al. studied the focusing behavior of particles in a bilateral rectangular converging-diverging channel. As shown in Fig. 6B, due to the action of horizontal and vertical vortexes, the focusing state of particles changes with the increase of flow velocity in the order of non-focusing, double-focusing equilibrium position, non-focusing, single-focusing equilibrium position and non-focusing[39]. Zhang et al. Studied the particle focusing behavior when the straight channel was expanded by a single edge triangle. The large-sized particles were easier to focus, and the difference in focusing state caused by the difference in flow velocity could be used for particle focusing, sorting, and particle capture applications[124].
This chapter provides an overview of inertial focusing methods in different flow channels. Inertial focusing techniques can achieve high throughput, high efficiency, and high precision focusing at a single equilibrium position. Detailed details of each technique are shown in Table 1. At present, most of the studies are still focused on the focusing behavior of particles with different sizes, and the focusing mechanism of the influence of particle shape, deformation characteristics and material characteristics needs to be further explored.

4 Particle elastic-inertial focusing technique

In the viscoelastic fluid, the transverse migration of particles is affected by the elastic effect, and the focusing process is affected by the rheological properties of the fluid and the difference of the first principal stress[60,125]. The shear viscosity of viscoelastic fluid is generally divided into constant viscosity region and shear-thinning region, and particle focusing is usually in the constant viscosity region. The concept of elastic-inertial focusing was first proposed by Yang et al. To explain the focusing mechanism of viscoelastic fluid flow of particles in a square straight channel. Under the combined action of fluid inertia and elasticity, precise focusing at a single equilibrium position can be achieved[126][127,128]. In this chapter, according to the microchannel structure in the microfluidic chip, the particle elastic-inertial focusing technology in the straight channel and curved channel is described respectively.

4.1 Elastic-inertial focusing in straight channel

The focusing behavior of particles in viscoelastic fluids varies with the type of channel section, the ratio of channel depth to width, and the flow velocity. In the microchannel with circular cross section, when the fluid solute is polyethylene oxide (PEO), the randomly distributed particles are firstly focused at the center line by the elastic force gradient at the wall, and with the increase of flow velocity, the FSG and shear thinning effect become significant, and the focused particles are dispersed again. In the elasticity-dominated polyvinylpyrrolidone (PVP) fluid, the particles first migrate to the equilibrium position at the center, and then do not disperse as the flow rate increases[129,130]. The dimensionless numbers related to the bullet-inertial focusing are the elastic number, the channel Reynolds number and the Weissenberg number, among which the Weissenberg number is the most sufficient parameter to evaluate the bullet-inertial focusing efficiency[131]. In the square channel, the randomly distributed particles are focused close to the center line of the four faces (Re > 0, Wi = 0) due to the inertial force only, as shown in Fig. 7A[24,31]; When only subjected to the elastic force of the fluid (Re = 0, Wi > 0), the particles are focused at the four corners and at the position of minimum elastic force at the center line, as shown in Fig. 7B[63,126,132]. When elasticity and inertia are combined (Re > 0, Wi > 0), the particles are focused at a single equilibrium position at the center of the flow channel at a moderate elastic number El, as shown in Figure 7c[126,133,134]. The force on the particles in the viscoelastic microfluid is shown in Figure 7d. The inertia generated by the fluid will destroy the equilibrium position at the four corners. Under the combined action of inertia force and elastic force, the particles at the corners will eventually move to the center of the channel[126]. The square channel increases the vertex angle, and the equilibrium position at the corner moves to the center of the channel due to the increased elastic force[135]. Xiang et al. fabricated PDMS microchannels with circular cross sections using stainless steel and nylon microwires as master molds, which can focus at a single equilibrium position in a wide range of flow rates[136]. By changing the shape of the 3D printing extrusion nozzle, Tang et al realized the production of straight channels with circular, triangular and semi-elliptical sections, in which particles focused on a single equilibrium position near the bottom[137]. Lim et al. reported particle focusing with hyaluronic acid (HA) solution in a square cross section straight channel at extremely high flux (Q = 50 mL/min, Re ~ 10000), the highest flux ever reported[32]. Kim et al. studied the particle focusing in λ-DNA, and found that the focusing flux was enhanced due to the long relaxation time and high elasticity of DNA, but the shear-thinning effect of fluid was more obvious with the increase of flow rate, and the elastic-inertial focusing effect of particles was weakened[138].
Because the first principal stress along the height direction is more significant than that along the width direction in the rectangular channel with low AR, particles will focus on the plane of 1/2 height, and the lateral migration in this plane is mainly affected by the relative magnitude of inertial force and elastic force.When the elastic force is large, the equilibrium position moves away from the wall, and when the inertial lift force is large, the equilibrium position moves toward the wall. There are two focused equilibrium positions in the flow channel with low aspect ratio, as shown in Fig. 7e[139][140]. In the converging-diverging channel, the streamline will bend in the expansion area, and the hoop stress will push the particles to the center line[141]. Yuan et al. studied the elastic-inertial focusing behavior of particles in a single-sided triangular expanding straight channel, and achieved high-precision particle focusing by combining elastic, inertial and secondary flow effects. Non-Newtonian fluids are easier to focus particles than Newtonian fluids[142,143]. Fan et al realized the single equilibrium position focusing of particles by inducing asymmetric elastic force and periodically changing flow velocity profile in a periodically tapered straight channel[144].
Because the elastic force is proportional to the cubic power of the particle diameter, large particles are easier to focus. When used for focusing of sub-micron sized particles, a relatively small channel size is required to ensure the elastic force required to effect particle migration. The Brownian force on the particle is taken into account when the particle size is less than 1 μm in the application of elastic-inertial focusing[60]. Young et al realized the focusing of particles with a diameter of 200 nm under extremely low flux (10 μL/H) by using the principle of elastic-inertial focusing. Particles with a diameter of 100 nm will be randomly dispersed by strong Brownian force. The focusing of submicron particles is affected by elastic force, inertial force and Brownian force[69]. An oscillating microfluidic device was used to inject viscoelastic solution into the microchannel.By switching the flow direction to ensure a long enough particle movement, particles with a size of less than 100 nm could be focused[145]. The elastic-inertial focusing can also be applied to the focusing process of deformable particles, and the deformable particles are subjected to the lifting force induced by deformation, and the lifting force is induced by deformation when the particles are close to the wall of the flow channel,Under the combined influence of deformation lift, inertial force and elastic force, the particles will obtain a certain focusing position, and this kind of focusing method can be used for particle separation based on deformation characteristics[71][146].

4.2 Elastic-inertial focusing in a curved channel

The particle focusing process in the curved channel is affected by the elastic force, inertial force and Dean drag force. The equilibrium position of particle focusing in the spiral channel is determined by the ratio of the FD to the FE, which is proportional to the a2[113]. Unlike the inertial focusing phenomenon, the large-size particles are focused close to the outer wall. The elastic-inertial focusing mechanism in the spiral channel is shown in Figure 8A[68].
A sixth-order model was developed to explain the focusing process in a helical flow channel as a function of flow velocity, as shown in Figure 8B. As the channel aspect ratio AR increases, the focusing becomes more stable, and the time required for particle focusing increases with the curvature. Zhou et al. Found that when the channel parameters are determined, the elastic force acting on particles and the secondary flow in the channel are changed by adjusting the polymer concentration in the viscoelastic solution. By adjusting the flow rate, the focusing of 1 to 3 equilibrium positions of particles of various sizes can be realized. By adjusting the polymer concentration, the separation of sub-micron particles can be realized[34,148]. Xiang et al. Found that when the viscoelastic medium concentration and the channel size are constant, the focusing equilibrium position is mainly determined by the Dean effect. With the increase of the viscoelastic medium concentration, the focusing equilibrium position moves to the outside, and the particles are focused on the center line when the elastic force far exceeds the inertial force[149]. Liu et al. Found that PEO solution with low relative molecular weight has the smallest shear thinning effect and can provide sufficient elastic force, and the viscoelastic medium is used to achieve reliable focusing of nanoparticles (100 nm) in the straight channel[150]. Yuan et al. Have studied the elastic-inertial focusing process of particles in a symmetrical serpentine channel, and the serpentine curvature and elastic effect can reduce the channel length required for particle focusing[151].
This chapter reviews the elastic-inertial focusing technology in different flow channels, which can achieve flexible focusing of particles with a size of 0.1 to 15 μm by adjusting the curvature of the flow channel, the viscoelastic medium and its concentration, and the cross-sectional size of the flow channel (Table 2).However, most of the studies focus on the focusing of rigid polymer particles, and the focusing mechanism combined with the irregular shape and deformation characteristics of particles needs to be further explored.

5 Application of passive focusing in biological particle sorting

Biological particle sorting is of great significance for clinical detection, cell analysis and other applications[152,153]. In the sorting technology based on the principle of microfluidic passive focusing, the sorting method based on size difference can achieve continuous, high-throughput, high-efficiency and label-free sorting process, and has been widely used in biological sample sorting[154]. This chapter mainly introduces the application of biological particle sorting based on the principle of inertial focusing and elastic inertial focusing.
Particle sorting technology based on the principle of inertial focusing is usually realized by using the balance principle between the inertial lift force and Dean drag force on particles. When the mixed particle fluid passes through the flow channel with specific morphology, the force difference caused by the size difference will occupy different focusing equilibrium positions, and the separation can be realized by setting a reasonable bifurcation structure at the outlet. Lee et al. Proposed the technology of inertial sorting of cancer cells in whole blood by using a single-side converging-diverging straight channel[155]. Due to the small size of the cell particles in the whole blood sample, the lateral motion is mainly affected by Dean drag force, while due to the large size of the cancer cells, the lateral motion is dominated by inertial lift force.Under different force conditions, the particles occupy different lateral positions to achieve separation. Hou et al. Used spiral microchannels to separate circulating tumor cells from blood based on size differences[33]. Abdulla et al. Proposed a two-stage serial spiral flow channel step-by-step inertial sorting technology, in which lung cancer cells, breast cancer cells, white blood cells and red blood cells in whole blood are separated step by step in the secondary flow channel, effectively improving the sorting purity and efficiency[156]. Zhang et al. Proposed a method of extracting plasma from whole blood using a serpentine channel[157]. After the cells in the blood flow through the serpentine flow channel, the cells are focused on both sides of the inner and outer walls of the flow channel under the influence of Dean secondary flow and inertial lift, and the blood cells are efficiently removed by setting a specific outlet[158].
The particle sorting technology based on the principle of elastic inertia focusing considers the comprehensive influence of elastic force and inertia force on particles. The existing sorting methods are divided into non-sheathing sorting and sheathing sorting[43]. Liu et al. Proposed a sheathless bullet inertial sorting method for Escherichia coli in a straight channel with rectangular cross section, and the chip can also be used for cell sorting based on size difference[132]. Yuan et al. Proposed a method of extracting plasma by using a single-sided triangular topological channel. Viscoelastic medium PEO was added to the diluted blood sample. Under the action of elastic force and Dean drag force, the blood cells were focused at a specific equilibrium position, thus obtaining highly pure plasma[159]. Yuan et al. Realized the separation process of microalgae and bacteria by using a straight channel. Under the action of the elasticity and inertia of the fluid, the microalgae cells focused on the position near the side wall, and the bacteria focused on the center of the channel[160]. The sheathless separation does not need a complicated flow control process and can realize the particle separation with higher efficiency.
When there is a sheath flow in the channel, the sample fluid can be squeezed and confined to a narrow area near the channel wall by adjusting the velocity ratio between the sheath flow and the sample flow, so as to ensure that the particles are subjected to sufficient elastic force. Zhou et al. Used the method of sorting exosomes by a wavy curved channel[34]. The sheath flow focuses the sample on the side wall, the extracellular vesicles are focused on the center of the channel by a large elastic force, and the small-sized exosomes are kept in the region near the side wall, so that the method can realize efficient and high-purity sorting of exosomes. Faridi et al. Proposed a method for sorting bacteria from whole blood samples in a straight channel, in which large-sized cells at the side wall of the channel are focused at the center of the channel under the action of elastic force, and bacteria move to the outlet along the streamline at the side wall of the channel[161]. Liu et al. Proposed a method of sorting exosomes in a rectangular straight channel. Extracellular vesicles in fetal bovine serum samples were focused on the center of the channel due to the large elastic force at the side wall of the channel, and exosomes with high purity were recovered at the outlet of the side wall streamline[30]. Sheathed sorting can be used for efficient sorting of submicron-sized particles, but the additional sheath flow inlet reduces chip integration.
When both Newtonian and non-Newtonian fluids exist in the flow channel, an interface of the two fluids is formed in the flow channel, and the separation of particles can benefit from the viscoelasticity, elastic-inertia of the fluids and the formed fluid interface[162,163]. Tian et al. Proposed a method for sorting tumor cells from blood using interface microfluidics[164]. A Newtonian fluid flows into the middle of the flow channel, and a non-Newtonian fluid containing a mixed particle sample flows into both sides of the flow channel.Tumor cells close to the side wall pass through the interface and are focused to the center of the flow channel under the action of elastic force and inertial lift force, and blood cells cannot pass through the interface due to insufficient force, thereby forming a sorting effect.
In this chapter, the sorting method of biological particles based on particle passive focusing technology is introduced. Inertial and elastic inertial focusing technologies can achieve efficient sorting of biological particles, and the application details are shown in Table 3. Compared with the inertial separation, the elasto-inertial separation can realize the separation of sub-micron particles, but the control of the concentration and flow rate of the viscoelastic medium is more complex, and its mechanism needs to be further explored.

6 Conclusion and prospect

In this paper, particle passive focusing technology on microfluidic chips is described in detail, including particle focusing migration mechanism, focusing characteristics in different types of channels and focusing behavior under the influence of flow parameters. Passive focusing technology has experienced more than ten years of development, in which the mechanism of inertial focusing has been relatively clear, while the bullet-inertial focusing technology started late, and its theoretical system is not yet perfect, which needs to be explored by scholars. On the basis of summarizing and analyzing the existing research results, the following three prospects are put forward: (1) The mechanism of passive focusing needs to be explored continuously in order to form a more perfect theoretical system; At present, the relevant research is more inclined to rigid spherical particles, if we want to further expand the passive focusing application of biological particles such as exosomes and cancer cells, we need to consider the characteristics of biological particles, such as deformability, irregular shape and bioactivity. (2) The passive control technology of particles can achieve high flux, while the active control can achieve high precision, which combines passive and active control, takes into account the flux and precision of focusing, and improves the efficiency of particle focusing. (3) The passive focusing and detection scheme of particles are integrated on the same chip to form a microfluidic analysis system with integrated pretreatment and detection, which avoids the decentralized operation of the detection process, realizes the high-throughput, automatic and high-precision detection process, and better solves the related practical problems in the fields of biology, chemistry, medical treatment and so on.

References

Publishing order | Descend order by publishing year | Descend order by cited within
[1]

Whitesides G M. Nature, 2006, 442(7101): 368.
[2]

Sackmann E K, Fulton A L, Beebe D J. Nature, 2014, 507(7491): 181.
[3]

Yeo L Y, Chang H C, Chan P P Y, Friend J R. Small, 2011, 7(1): 12.
[4]

Nagrath S, Sequist L V, Maheswaran S, Bell D W, Irimia D, Ulkus L, Smith M R, Kwak E L, Digumarthy S, Muzikansky A, Ryan P, Balis U J, Tompkins R G, Haber D A, Toner M. Nature, 2007, 450(7173): 1235.
[5]

Xuan X C, Zhu J J, Church C. Microfluid.Nanofluidics, 2010, 9(1): 1.
[6]

Lenshof A, Laurell T. Chem.Soc.Rev., 2010, 39(3): 1203.
[7]

Gossett D R, Weaver W M, Mach A J, Hur S C, Tse H T K, Lee W, Amini H, DiCarlo D. Anal.Bioanal.Chem., 2010, 397(8): 3249.
[8]

Lee C Y, Chang C L, Wang Y N, Fu L M. Int.J.Mol.Sci., 2011, 12(5): 3263.
[9]

Gossett D R, Tse H T K, Lee S A, Ying Y, Lindgren A G, Yang O O, Rao J, Clark A T, diCarlo D. PNAS, 2012, 109(20): 7630.
[10]

Benítez J J, Topolancik J, Tian H C, Wallin C B, Latulippe D R, Szeto K, Murphy P J, Cipriany B R, Levy S L, Soloway P D, Craighead H G. Lab Chip, 2012, 12(22): 4848.
[11]

Nilsson J, Evander M, Hammarström B, Laurell T. Anal.Chimica Acta, 2009, 649(2): 141.
[12]

Livak-Dahl E, Sinn I, Burns M. Annu.Rev.Chem.Biomol.Eng., 2011, 2(1): 325.
[13]

Salieb-Beugelaar G B, Simone G, Arora A, Philippi A, Manz A. Anal.Chem., 2010, 82(12): 4848.
[14]

Pamme N. Lab a Chip, 2007, 7(12): 1644.
[15]

Lin Y, Gritsenko D, Feng S L, Teh Y C, Lu X N, Xu J. Biosens.Bioelectron., 2016, 83: 256.
[16]

CrevillÉn A G, Ávila M, Pumera M, González M C, Escarpa A. Anal.Chem., 2007, 79(19): 7408.
[17]

Oakey J, Applegate R W Jr, Arellano E, Carlo D D, Graves S W, Toner M. Anal.Chem., 2010, 82(9): 3862.
[18]

Shi J J, Mao X L, Ahmed D, Colletti A, Huang T J. Lab Chip, 2008, 8(2): 221.
[19]

Demierre N, Braschler T, Muller R, Renaud P. Sens. Actuat.B:Chem., 2008, 132(2): 388.
[20]

Liang L T, Xuan X C. Microfluid.Nanofluidics, 2012, 13(4): 637.
[21]

MacDonald M P, Spalding G C, Dholakia K. Nature, 2003, 426(6965): 421.
[22]

Ross D, Locascio L E. Anal.Chem., 2002, 74(11): 2556.
[23]

Mao X L, Waldeisen J R, Huang T J. Lab a Chip, 2007, 7(10): 1260.
[24]

DiCarlo D. Lab Chip, 2009, 9(21): 3038.
[25]

Zhang J, Yan S, Yuan D, Alici G, Nguyen N T, Ebrahimi Warkiani M, Li W H. Lab Chip, 2016, 16(1): 10.
[26]

Lu X Y, Liu C, Hu G Q, Xuan X C. J.Colloid Interface Sci., 2017, 500: 182.
[27]

Urbansky A, Olm F, Scheding S, Laurell T, Lenshof A. Lab Chip, 2019, 19(8): 1406.
[28]

Chiu Y J, Cho S H, Mei Z, Lien V, Wu T F, Lo Y H. Lab Chip, 2013, 13(9): 1803.
[29]

Wu M X, Ouyang Y, Wang Z Y, Zhang R, Huang P H, Chen C Y, Li H, Li P, Quinn D, Dao M, Suresh S, Sadovsky Y, Huang T J. PNAS, 2017, 114(40): 10584.
[30]

Liu C, Guo J Y, Tian F, Yang N, Yan F S, Ding Y P, Wei J Y, Hu G Q, Nie G J, Sun J S. ACS Nano, 2017, 11(7): 6968.
[31]

Di Carlo D, Irimia D, Tompkins R G, Toner M. PNAS, 2007, 104: 18892.
[32]

Lim E J, Ober T J, Edd J F, Desai S P, Neal D, Bong K W, Doyle P S, McKinley G H, Toner M. Nat.Commun., 2014, 5(1):4120.
[33]

Hou H W, Warkiani M E, Khoo B L, Li Z R, Soo R A, Tan D S, Lim W T, Han J, Bhagat A A S, Lim C T. Sci. Rep., 2013, 3: 1259.
[34]

Zhou Y N, Ma Z C, Tayebi M, Ai Y. Anal.Chem., 2019, 91(7): 4577.
[35]

Zhou J, Papautsky I. Lab Chip, 2013, 13(6): 1121.
[36]

Gossett D R, Carlo D D. Anal.Chem., 2009, 81(20): 8459.
[37]

Zhang Y, Zhang J, Tang F, Li W H, Wang X H. Anal.Chem., 2018, 90(3): 1786.
[38]

Hsu C H, DiCarlo D, Chen C, Irimia D, Toner M. Lab a Chip, 2008, 8(12): 2128.
[39]

Park J S, Song S H, Jung H I. Lab Chip, 2009, 9(7): 939.
[40]

Amini H, Lee W, diCarlo D. Lab a Chip, 2014, 14(15): 2739.
[41]

Xiang N, Zhu X L, Ni Z H. Prog. Chem., 2011, 23: 1945.
[42]

项楠, 朱晓璐, 倪中华. 化学进展, 2011, 23: 1945.).
[43]

Yuan D, Zhao Q B, Yan S, Tang S Y, Alici G, Zhang J, Li W H. Lab Chip, 2018, 18(4): 551.
[44]

Ni C, Jiang D, Xu Y L, Tang W L. Prog. Chem., 2020, 32: 519.
[45]

( 倪陈, 姜迪, 徐幼林, 唐文来. 化学进展, 2020, 32: 519.).
[46]

Stoecklein D diCarlo D. Anal.Chem., 2019, 91(1): 296.
[47]

Lu M Q, Ozcelik A, Grigsby C L, Zhao Y H, Guo F, Leong K W, Huang T J. Nano Today, 2016, 11(6): 778.
[48]

Zhang T L, Hong Z Y, Tang S Y, Li W H, Inglis D W, Hosokawa Y, Yalikun Y, Li M. Lab a Chip, 2020, 20(1): 35.
[49]

Bayareh M. Chem.Eng.Process.Process.Intensif., 2020, 153: 107984.
[50]

Rubinow S I, Keller J B. J.Fluid Mech., 1961, 11(3): 447.
[51]

Saffman P G. J.Fluid Mech., 1965, 22(2): 385.
[52]

Zeng L Y, Balachandar S, Fischer P. J.Fluid Mech., 2005, 536: 1.
[53]

Matas J, Morris J, Guazzelli E. Oil Gas Sci.Technol. Rev.IFP, 2004, 59(1): 59.
[54]

Asmolov E S. J.Fluid Mech., 1999, 381: 63.
[55]

Matas J P, Morris J F, Guazzelli É. J.Fluid Mech., 2004, 515: 171.
[56]

Chan P C H, Leal L G. J.Fluid Mech., 1979, 92(1): 131.
[57]

Stan C A, Ellerbee A K, Guglielmini L, Stone H A, Whitesides G M. Lab Chip, 2013, 13(3): 365.
[58]

Hur S C, Henderson-Maclennan N K, McCabe E R B, DiCarlo D. Lab a Chip, 2011, 11(5): 912.
[59]

Pathak J A, Ross D, Migler K B. Phys.Fluids, 2004, 16(11): 4028.
[60]

Magda J J, Lou J, Baek S G, DeVries K L. Polymer, 1991, 32(11): 2000.
[61]

Feng H D, Magda J J, Gale B K. Appl.Phys.Lett., 2019, 115(26): 263702.
[62]

Leshansky A M, Bransky A, Korin N, Dinnar U. Phys.Rev.Lett., 2007, 98(23): 234501.
[63]

Rodd L E, Scott T P, Boger D V, Cooper-White J J, McKinley G H. J.Non Newton.Fluid Mech., 2005, 129(1): 1.
[64]

Rodd L E, Cooper-White J J, Boger D V, McKinley G H. J.Non Newton.Fluid Mech., 2007, 143(2/3): 170.
[65]

Nam J, Lim H, Kim D, Jung H, Shin S. Lab Chip, 2012, 12(7): 1347.
[66]

Berger S A, Talbot L, Yao L S. Annu.Rev.Fluid Mech., 1983, 15(1): 461.
[67]

Ookawara S, Higashi R, Street D, Ogawa K. Chem.Eng.J., 2004, 101(1/3): 171.
[68]

Bhagat A A S, Kuntaegowdanahalli S S, Papautsky I. Microfluid.Nanofluidics, 2009, 7(2): 217.
[69]

Kuntaegowdanahalli S S, Bhagat A A S, Kumar G, Papautsky I. Lab Chip, 2009, 9(20): 2973.
[70]

Lee D J, Brenner H, Youn J R, Song Y S. Sci.Rep., 2013, 3(1): 3258.
[71]

Young K J, Won A S, Sik L S, Min K J. Lab Chip., 2012, 12: 2807.
[72]

Bhagat A A S, Kuntaegowdanahalli S S, Papautsky I. Lab a Chip, 2008, 8(11): 1906.
[73]

Leal L G. Annu.Rev.Fluid Mech., 1980, 12(1): 435.
[74]

Seo K W, Kang Y J, Lee S J. Phys.Fluids, 2014, 26(6): 063301.
[75]

Humphry K J, Kulkarni P M, Weitz D A, Morris J F, Stone H A. Phys.Fluids, 2010, 22(8): 081703.
[76]

Reece A E, Oakey J. Phys.Fluids, 2016, 28(4): 043303.
[77]

SegrÉ G, Silberberg A. Nature, 1961, 189(4760): 209.
[78]

Ciftlik A T, Ettori M, Gijs M A M. Small, 2013, 9(16): 2764.
[79]

Mashhadian A, Shamloo A. Anal.Chimica Acta, 2019, 1083: 137.
[80]

Moloudi R, Oh S, Yang C, Ebrahimi Warkiani M, Naing M W. Microfluid.Nanofluidics, 2018, 22(3): 1.
[81]

Kim J, Lee J, Wu C, Nam S, DiCarlo D, Lee W. Lab Chip, 2016, 16(6): 992.
[82]

Mukherjee P, Wang X, Zhou J, Papautsky I. Lab Chip, 2019, 19(1): 147.
[83]

Masaeli M, Sollier E, Amini H, Mao W B, Camacho K, Doshi N, Mitragotri S, Alexeev A, DiCarlo D. Phys.Rev.X, 2012, 2(3): 031017.
[84]

Guan G F, Wu L D, Bhagat A A, Li Z R, Chen P C Y, Chao S Z, Ong C J, Han J. Sci.Rep., 2013, 3(1): 1475.
[85]

Wyss H M, Blair D L, Morris J F, Stone H A, Weitz D A. Phys.Rev.E, 2006, 74(6): 061402.
[86]

Mutlu B R, Edd J F, Toner M. PNAS, 2018, 115: 7682.
[87]

Stone H A. Nat.Phys., 2009, 5(3): 178.
[88]

Lee M G, Choi S, Park J K. Appl.Phys.Lett., 2009, 95(5): 051902.
[89]

Yoon D H, Ha J B, Bahk Y K, Arakawa T, Shoji S, Go J S. Lab Chip, 2009, 9(1): 87.
[90]

Zhang J, Li W H, Li M, Alici G, Nguyen N T. Microfluid.Nanofluidics, 2014, 17(2): 305.
[91]

Shamloo A, Mashhadian A. Phys.Fluids, 2018, 30(1): 012002.
[92]

Jiang D, Tang W L, Xiang N, Ni Z H. RSC Adv., 2016, 6(62): 57647.
[93]

Yin P J, Zhao L, Chen Z Z, Jiao Z Q, Shi H Y, Hu B, Yuan S F, Tian J. Soft Matter, 2020, 16(12): 3096.
[94]

Zhang J, Yuan D, Zhao Q B, Teo A J T, Yan S, Ooi C H, Li W H, Nguyen N T. Anal.Chem., 2019, 91(6): 4077.
[95]

Özbey A, Karimzadehkhouei M, Akgönül S, Gozuacik D, Ko塂ar A. Sci.Rep., 2016, 6(1): 1.
[96]

Sun S F, Wang C, Chen Y, Cheng Z D, Cai X Y, Bu E Q. J. Eng. Thermophys., 2017, 38: 1758.
[97]

( 孙思帆, 王超, 陈颖, 成正东, 蔡小燕, 卜恩奇. 工程热物理学报, 2017, 38: 1758.).
[98]

Tang W L, Xiang N, Zhang X J, Huang D, Ni Z H. Acta Phys.Sin., 2015, 64(18): 184703.
[99]

唐文来, 项楠, 张鑫杰, 黄笛, 倪中华. 物理学报, 2015, 64(18): 184703.)
[100]

Di Carlo D, Edd J F, Irimia D, Tompkins R G, Toner M. Anal.Chem., 2008, 80(6): 2204.
[101]

Wang C, Sun S F, Chen Y, Cheng Z D, Li Y X, Jia L S, Lin P C, Yang Z, Shu R Y. Microfluid.Nanofluidics, 2018, 22(3): 25.
[102]

Sollier E, Murray C, Maoddi P, diCarlo D. Lab Chip, 2011, 11(22): 3752.
[103]

Wang L, Dandy D S. Adv.Sci., 2017, 4(10): 1700153.
[104]

Zhou Y N, Ma Z C, Ai Y. Microsyst.Nanoeng., 2018, 4(1): 5.
[105]

Bhagat A A S, Kuntaegowdanahalli S S, Kaval N, Seliskar C J, Papautsky I. Biomed.Microdevices, 2010, 12(2): 187.
[106]

Russom A, Gupta A K, Nagrath S, Carlo D D, Edd J F, Toner M. New J.Phys., 2009, 11(7): 075025.
[107]

Martel J M, Toner M. Phys.Fluids, 2012, 24(3): 032001.
[108]

Cruz J, Hooshmand Zadeh S, Graells T, Andersson M, Malmström J, Wu Z G, Hjort K. J.Micromech.Microeng., 2017, 27(8): 084001.
[109]

Cruz J, Graells T, WalldÉn M, Hjort K. Lab Chip, 2019, 19(7): 1257.
[110]

Paiè P, Bragheri F, DiCarlo D, Osellame R. Microsyst.Nanoeng., 2017, 3(1): 1.
[111]

Xiang N, Yi H, Chen K, Sun D K, Jiang D, Dai Q, Ni Z H. Biomicrofluidics, 2013, 7(4): 044116.
[112]

Xiang N, Chen K, Sun D K, Wang S F, Yi H, Ni Z H. Microfluid.Nanofluidics, 2013, 14(1/2): 89.
[113]

Xiang N, Shi Z G, Tang W L, Huang D, Zhang X J, Ni Z H. RSC Adv., 2015, 5(94): 77264.
[114]

Chen Z Z, Zhao L, Wei L J, Huang Z Y, Yin P J, Huang X W, Shi H Y, Hu B, Tian J. Sens. Actuat.B:Chem., 2019, 301: 127125.
[115]

Al-Halhouli A, Albagdady A, Al-Faqheri W, Kottmeier J, Meinen S, Frey L J, Krull R, Dietzel A. RSC Adv., 2019, 9(33): 19197.
[116]

Shen S F, Tian C, Li T B, Xu J, Chen S W, Tu Q, Yuan M S, Liu W M, Wang J Y. Lab Chip, 2017, 17(21): 3578.
[117]

Martel J M, Toner M. Sci.Rep., 2013, 3(1): 3340.
[118]

Wang X, Zandi M, Ho C C, Kaval N, Papautsky I. Lab Chip, 2015, 15(8): 1812.
[119]

Zhou J, Giridhar P V, Kasper S, Papautsky I. Lab Chip, 2013, 13(10): 1919.
[120]

Kim J A, Lee J R, Je T J, Jeon E C, Lee W. Anal.Chem., 2018, 90(3): 1827.
[121]

Choi S, Park J K. Lab Chip, 2007, 7(7): 890.
[122]

Choi S, Park J K. Anal.Chem., 2008, 80(8): 3035.
[123]

Chung A J, Pulido D, Oka J C, Amini H, Masaeli M, diCarlo D. Lab Chip, 2013, 13(15): 2942.
[124]

Chung A J, Gossett D R, DiCarlo D. Small, 2013, 9(5): 685.
[125]

Song S, Choi S. J.Chromatogr.A, 2013, 1302: 191.
[126]

Zhao Q B, Zhang J, Yan S, Yuan D, Du H P, Alici G, Li W H. Sci.Rep., 2017, 7(1): 41153.
[127]

Lee M G, Choi S, Kim H J, Lim H K, Kim J H, Huh N, Park J K. Appl.Phys.Lett., 2011, 98(25): 253702.
[128]

Zhang J, Li M, Li W H, Alici G. J.Micromech.Microeng., 2013, 23(8): 085023.
[129]

Caserta S, D'Avino G, Greco F, Guido S, Maffettone P L. Soft Matter, 2011, 7(3): 1100.
[130]

Yang S, Kim J Y, Lee S J, Lee S S, Kim J M. Lab Chip, 2011, 11(2): 266.
[131]

Groisman A, Steinberg V. Nature, 2000, 405(6782): 53.
[132]

Groisman A, Steinberg V. Nature, 2001, 410(6831): 905.
[133]

Seo K W, Byeon H J, Huh H K, Lee S J. RSC Adv., 2014, 4(7): 3512.
[134]

Dai Q, Xiang N, Cheng J, Ni Z H, Acta Phys. Sin., 2015, 64: 1.
[135]

( 戴卿, 项楠, 程洁, 倪中华. 物理学报, 2015, 64: 1.).
[136]

Song H Y, Lee S H, Salehiyan R, Hyun K. Rheol.Acta, 2016, 55(11/12): 889.
[137]

Liu C, Xue C D, Chen X D, Shan L, Tian Y, Hu G Q. Anal.Chem., 2015, 87(12): 6041.
[138]

del Giudice F, Romeo G, D'Avino G, Greco F, Netti P A, Maffettone P L. Lab a Chip, 2013, 13(21): 4263.
[139]

Xiang N, Dai Q, Ni Z H. Appl.Phys.Lett., 2016, 109(13): 134101.
[140]

Raoufi M A, Mashhadian A, Niazmand H, Asadnia M, Razmjou A, Warkiani M E. Biomicrofluidics, 2019, 13(3): 034103.
[141]

Xiang N, Dai Q, Han Y, Ni Z H. Microfluid.Nanofluidics, 2019, 23(2): 16.
[142]

Tang W L, Fan N, Yang J Q, Li Z, Zhu L Y, Jiang D, Shi J P, Xiang N. Microfluid.Nanofluidics, 2019, 23(3): 42.
[143]

Kim B, Kim J M. Biomicrofluidics, 2016, 10(2): 024111.
[144]

Won S K, Ran H Y, Joon L S. Appl. Phys. Lett., 2014, 104: 213702.
[145]

Yang S H, Lee D J, Youn J R, Song Y S. Anal.Chem., 2017, 89(6): 3639.
[146]

Cha S, Kang K, You J B, Im S G, Kim Y, Kim J M. Rheol.Acta, 2014, 53(12): 927.
[147]

Yuan D, Zhang J, Yan S, Pan C, Alici G, Nguyen N T, Li W H. Biomicrofluidics, 2015, 9(4): 044108.
[148]

Yuan D, Tan S H, Zhao Q B, Yan S, Sluyter R, Nguyen N T, Zhang J, Li W H. RSC Adv., 2017, 7(6): 3461.
[149]

Fan L L, Wu X, Zhang H, Zhao Z, Zhe J, Zhao L. Microfluid.Nanofluidics, 2019, 23(10): 117.
[150]

Asghari M, Cao X B, Mateescu B, van Leeuwen D, Aslan M K, Stavrakis S, de Mello A J. ACS Nano, 2020, 14(1): 422.
[151]

Yang S, Lee S S, Ahn S W, Kang K, Shim W, Lee G, Hyun K, Kim J M. Soft Matter, 2012, 8(18): 5011.
[152]

Xiang N, Zhang X J, Dai Q, Cheng J, Chen K, Ni Z H. Lab a Chip, 2016, 16(14): 2626.
[153]

Zhou Y N, Ma Z C, Ai Y. Lab Chip, 2020, 20(3): 568.
[154]

Xiang N, Ni Z H, Yi H. Electrophoresis, 2018, 39(2): 417.
[155]

Liu C, Ding B Q, Xue C D, Tian Y, Hu G Q, Sun J S. Anal.Chem., 2016, 88(24): 12547.
[156]

Yuan D, Sluyter R, Zhao Q B, Tang S Y, Yan S, Yun G L, Li M, Zhang J, Li W H. Microfluid.Nanofluidics, 2019, 23(3): 41.
[157]

BankÓ P, Lee S Y, Nagygyörgy V, Zrínyi M, Chae C H, Cho D H, Telekes A. J. Hematol. Oncol., 2019, 12(1): 48.
[158]

Reece A, Xia B Z, Jiang Z L, Noren B, McBride R, Oakey J. Curr. Opin. Biotechnol., 2016, 40: 90.
[159]

Dalili A, Samiei E, Hoorfar M. Anal., 2019, 144(1): 87.
[160]

Lee M G, Shin J H, Bae C Y, Choi S, Park J K. Anal. Chem., 2013, 85(13): 6213.
[161]

Abdulla A, Liu W J, Gholamipour-Shirazi A, Sun J H, Ding X T. Anal. Chem., 2018, 90(7): 4397.
[162]

Zhang J, Yan S, Li W H, Alici G, Nguyen N T. RSC Adv., 2014, 4(63): 33149.
[163]

Zhang J, Yuan D, Sluyter R, Yan S, Zhao Q B, Xia H M, Tan S H, Nguyen N T, Li W H. IEEE Trans. Biomed. Circuits Syst., 2017, 11(6): 1422.
[164]

Yuan D, Zhao Q B, Yan S, Tang S Y, Zhang Y X, Yun G L, Nguyen N T, Zhang J, Li M, Li W H. Lab Chip, 2019, 19(17): 2811.
[165]

Yuan D, Zhang J, Sluyter R, Zhao Q B, Yan S, Alici G, Li W H. Lab Chip, 2016, 16(20): 3919.
[166]

Faridi M A, Ramachandraiah H, Banerjee I, Ardabili S, Zelenin S, Russom A. J. Nanobiotechnology, 2017, 15(1): 1.
[167]

Tian F, Zhang W, Cai L L, Li S S, Hu G Q, Cong Y L, Liu C, Li T J, Sun J S. Lab Chip, 2017, 17(18): 3078.
[168]

Yuan D, Zhang J, Yan S, Peng G R, Zhao Q B, Alici G, Du H J, Li W H. Electrophoresis, 2016, 37(15/16): 2147.
[169]

Tian F, Cai L L, Chang J Q, Li S S, Liu C, Li T J, Sun J S. Lab Chip, 2018, 18(22): 3436.

Funding

National Natural Science Foundation of China (Key International (Regional) Joint Research Program)(51920105008)

Key Research and Development Program of Hunan Province(2019SK2221)

Hunan Provincial Innovation Foundation for Postgraduate(CX20210210)

PDF (18277KB)

3394

Accesses

0

Citation

Detail
Sections
Recommended

/

〈 〉

Address of Editorial Office: No. 33 Beisihuan Xilu, Zhongguancun , Beijing 100190, China
Tel: +86 10 8262 7757
Fax: +86 10 8262 7757
E-mail: progchem@mail.las.ac.cn
http://www.progchem.ac.cn
    • 　
    Copyright © Editorial Office of Progress in Chemistry