## surface modification of pentlandite and serpentine with reagents and magnetite for magnetic separation | springerlink

In this study, selective magnetic coating was employed to separate pentlandite and serpentine. The surface properties of minerals with and without reagents and magnetite were characterized by zeta potential measurements, scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), and vibrating sample magnetometer (VSM). Zeta potentials showed that the surfaces of serpentine and magnetite were both negatively charged with the addition of sodium hexametaphosphate. Thus, serpentine was hardly coated by magnetite due to the electrostatic repulsion between them. The results of SEM and FTIR demonstrated that a magnetic coating of magnetite was observed on the pentlandite rather than on the serpentine. The VSM measurements confirmed that the magnetism of pentlandite was increased significantly due to the selective adsorption of magnetite on its surfaces; therefore, pentlandite was successfully separated from serpentine by magnetic separation. The study shows that selective magnetic coating technology has the alternative potential to separate pentlandite from serpentine.

The authors acknowledge the National Nature Science Foundation of China (51704057), the China Postdoctoral Science Foundation (2017M621153), the Postdoctoral Science Foundation of Northeastern University (20170312), and Fundamental Research Funds for the Central Universities (N170104018).

Lu, J., Yuan, Z., Tong, Z. et al. Surface Modification of Pentlandite and Serpentine with Reagents and Magnetite for Magnetic Separation. JOM 70, 11241129 (2018). https://doi.org/10.1007/s11837-018-2916-y

## minerals | free full-text | the effect of surface charge on the separation of pyrite from serpentine by flotation | html

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## magnetic separation of pentlandite from serpentine by selective magnetic coating | springerlink

In this study, pentlandite was selectively separated from serpentine using magnetic coating technology by adjusting and optimizing pH, stirring speeds, magnetic field intensities, and dosages of sodium hexametaphosphate (SHMP) and sodium oleate (SO). A magnetic concentrate with Ni grade of 20.8% and Ni recovery of 80.5% was attained under the optimized operating conditions. Considering the above, the adsorption behaviors of SHMP and SO and the surface properties of minerals after the magnetic coating were studied by Fourier transform infrared (FTIR) spectroscopy, X-ray diffraction (XRD), and scanning electron microscopy (SEM). The results show that magnetite was preferentially coated on the pentlandite surfaces and sparingly coated on the serpentine surfaces in the presence of SHMP and SO. Furthermore, calculations by Derjaguin-Landau-Verwey-Overbeek (DLVO) theory indicate that the preferential adsorption of magnetite on the pentlandite surfaces is due to the presence of a hydrophobic interaction between the magnetite and pentlandite, which is much stronger than the interaction between magnetite and serpentine.

X.M. Luo, W.Z. Yin, C.Y. Sun, N.L. Wang, Y.Q. Ma, and Y.F. Wang, Improved flotation performance of hematite fines using citric acid as a dispersant, Int. J. Miner. Metall. Mater., 23(2016), No. 10, p. 1119.

D. Li, W.Z. Yin, J.W. Xue, J. Yao, Y.F. Fu, and Q. Liu, Solution chemistry of carbonate minerals and its effects on the flotation of hematite with sodium oleate, Int. J. Miner. Metall. Mater., 24(2017), No. 7, p. 736.

Z.T. Yuan, J.W. Lu, J.T. Liu, L.X. Li, and S.Y. Wang, Enhancement of pentlandite surface magnetism and implications for its separation from serpentine via magnetic separation, Trans. Nonferrous Met. Soc. China, 27(2017), No. 1, p. 204.

Y.P. Lu, M.Q. Zhang, Q.M. Feng, T. Long, L.M. Ou, and G.F. Zhang, Effect of sodium hexametaphosphate on separation of serpentine from pyrite, Trans. Nonferrous Met. Soc. China, 21(2011), No. 1, p. 208.

W.J. Liu, J. Zhang, W.Q. Wang, J. Deng, B.Y. Chen, W. Yan, S.Q. Xiong, Y. Huang, and J. Liu, Flotation behaviors of ilmenite, titanaugite, and forsterite using sodium oleate as the collector, Miner. Eng., 72(2015), p. 1.

Y.S. Gao, Z.Y. Gao, W. Sun, Z.G. Yin, J.J. Wang, and Y.H. Hu, Adsorption of a novel reagent scheme on scheelite and calcite causing an effective flotation separation, J. Colloid Interface Sci., 512 (2018), p. 39.

K.L. Zhao, G.H. Gu, C.L. Wang, X.Y. Rao, X.H. Wang, and X.X. Xiong, The effect of a new polysaccharide on the depression of talc and the flotation of a nickel copper sulfide ore, Miner. Eng., 77(2015), p. 99.

L.H. Xu, J. Tian, H.Q. Wu, W. Deng, Y.H. Yang, W. Sun, Z.Y. Gao, and Y.H. Hu, New insights into the oleate flotation response of feldspar particles of different sizes: Anisotropic adsorption model, J. Colloid Interface Sci., 505(2017), p. 500.

J. Tian, L.H. Xu, H.Q. Wu, S. Fang, W. Deng, T.F. Peng, W. Sun, and Y.H. Hu, A novel approach for flotation recovery of spodumene, mica and feldspar from a lithium pegmatite ore, J. Clean. Prod., 174 (2018), p. 625.

C. Magnet, C. Lomenech, C. Hurel, P. Reilhac, F. Giulieri, A.M. Chaze, J. Persello, and P. Kuzhir, Adsorption of nickel ions by oleate-modified magnetic iron oxide nanoparticles, Environ. Sci. Pollut. Res., 24(2017), No. 8, p. 7423.

P. Roonasi, X.F. Yang, and A. Holmgren, Competition between sodium oleate and sodium silicate for a silicate/oleate modified magnetite surface studied by in situ ATR-FTIR spectroscopy, J. Colloid Interface Sci., 343(2010), No. 2, p. 546.

This work was financially supported by the National Natural Science Foundation of China (No. 51704057), the China Postdoctoral Science Foundation (No. 2017M621153), the Postdoctoral Science Foundation of Northeastern University (No. 20170312), the Fundamental Research Funds for the Central Universities (No. N170104018), and the Open Fund Project of Shaanxi Key Laboratory of Comprehensive Utilization of Tailings Resources, China (No. 2017SKY-WK012).

Lu, Jw., Yuan, Zt., Guo, Xf. et al. Magnetic separation of pentlandite from serpentine by selective magnetic coating. Int J Miner Metall Mater 26, 110 (2019). https://doi.org/10.1007/s12613-019-1704-1

## the role of sodium oleate (naol) in the magnetic separation of pentlandite from serpentine using magnetic coating - sciencedirect

Selective adsorption of NaOL onto the Fe and Ni sites of penlandite surfacesSelective chemisorption of NaOL onto the Fe sites of magnetite surfacesSelective coating of magnetite onto the pentlandite surfaces through hydrophobic interaction.Pentlandite was separated from serpentine using magnetic separation.

The efficient separation of pentlandite from serpentine remains a challenging issue in the processing of nickel sulfide ores. In this study, selective magnetic coating-magnetic separation was employed to separate the pentlandite from serpentine with adding NaOL as a coagulant, which is different from the conventional flotation. The results indicate that it was very effective for their separation. Furthermore, the role of NaOL in the separation was evaluated in detail by means of adsorption tests, zeta potential measurements, Fourier transform infrared (FTIR) spectra analyses, solution chemistry calculations X-ray photoelectron (XPS) spectra analyses, and scanning electron microscopy-energy dispersive spectra (SEM-EDS) analyses. It turns out that NaOL can adsorb selectively onto the surfaces of pentlandite and magnetite through the Ni and Fe sites (serpentine was pre-depressed by sodium hexametaphosphate (NaHMP)) and form the hydrophobic surfaces between the two minerals. As a result, the pentlandite surface was selectively coated by the magnetite fines and then was separated from serpentine using magnetic separation. Therefore, our results provide an alternative technology for their separation and exhibit great potential for further study and applications.

## inertial focusing and separation of particles in similar curved channels | scientific reports

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

The development of inertial microfluidics1 has enabled particle manipulation with improved performance over sheath flow control2 and external force generators3 and has made it possible to miniaturize the devices and simplify the operation4. Segre and Silberberg5 reported the inertial migration of particles in a circular tube in the 1960s, which first brought inertial microfluidics to the attention of researchers. Due to its many advantages, inertial microfluidics has been widely employed for the focusing6, separation7, and fractionation of bioparticles and has been used in other fields. Steerable objects have become more diverse to accommodate particles of different biophysical characteristics (e.g., size8, density, shape9, and deformability) and to precisely control these particles. In addition to straight channels, there are three basic types of microchannel structures: expansion-shrink array channels, spiral channels and serpentine channels. These structures were created to introduce extra inertial effects, such as Dean flow, to achieve more precise manipulation of particles. Among these channel structures, the serpentine channel is arousing the interest of an increasing number researchers because of its small footprint and simple parallelization and the fact that the processing efficiency can be multiplied. The flow pattern in a serpentine channel is more complicated than that in a straight or spiral channel due to the alternating curve geometry. This phenomenon causes the particles to swing along the channel centerline, which is expected to provide an effective means of achieving precise passive particle manipulation.

As early as 2007, Di Carlo4 adopted symmetric and asymmetric serpentine channels to achieve particle focusing in a pioneering work of inertial microfluidic control. Gossett et al.10 found that the channel curvature can result in reduced fluid resistance for microfluidic designs and can be used for low-flow inertial focusing or separation. Toner et al.11 employed serpentine channel particle focusing as a pretreatment step for magnetic separation technology, greatly improving the magnetic separation efficiency. Wang et al.12 achieved focusing and separation of submicrometer particles in a serpentine channel. However, the results of particle-size-dependent separation in asymmetric serpentine channels are not ideal13. Instead, many researchers have realized the separation of particles of different sizes in a symmetric serpentine channel. Zhang et al.14 reported a comprehensive study of the channel structure parameters and flow conditions for inertial particle focusing in symmetrical sinusoidal/serpentine channels. Obzey et al.15 studied a serpentine channel with a curvature angle of 280 to elucidate the basic physical properties of the particle dynamics. In addition to the conventional serpentine channel, researchers also conducted a series of fundamental and applied studies on a square wave channel, which was also named as a serpentine channel in their works. In terms of fundamental mechanisms, Zhang et al.16 provided insights into the role of the centrifugal force in inertial focusing and demonstrated for the first time that a single focusing streak can be achieved in a symmetric serpentine channel. Then, the authors achieved the separation of particles of different sizes based on the difference in the particle lateral focusing positions17. In biomedical applications, Zhangs group18 successfully separated blood cells from plasma with a purity of 99.95% and developed a continuous high-throughput microfluidic WBC separation platform. The purity of the WBCs could be increased to 48%19. In addition, the interaction of the inertial lift force and dielectrophoretic force in a square wave channel was studied20, and a tunable separation method was proposed by an innovative hybrid DEP-inertial microfluidic platform21. All of these studies investigated the application of curved channels in inertial particle focusing, but it should be noted that the above experimental studies could not adequately study the interaction between particles and flows by showing the focusing behavior of the particles. This problem can be solved very well via a numerical simulation. Rasooli et al.22 developed a Lagrangian model using COMSOL Multiphysics to solve the continuous phase and simulate particle trajectories in a spiral microchannel. Jiang et al.23 explored the particle focusing mechanisms of a symmetric serpentine microchannel based on a lattice Boltzmann method. Although the study of inertial focusing in serpentine channels has been successful, the difference in focusing effects in similar curved channels is still unknown.

This paper aims to study the difference in particle focusing effects and separation possibilities in similar curved channel geometries. A zigzag channel, which has not been used previously for inertial focusing studies, is introduced with the serpentine channel and square wave channel to conduct research by numerical simulations. First, a simulation model is verified based on previous experimental results. Then, the particle trajectories and fluid fields are obtained to analyze the particle migration behaviors by considering the competition between the inertial lift forces and Dean drag forces on the particles. Next, the particle focusing effects are investigated by varying the particle size and Reynolds number to determine the desirable focusing conditions. Finally, the separation of particles of two sizes is attempted to explore the functionalities of curved channels.

Since the first application of inertial effects in microfluidics in 2007, many studies have explained the physics of inertial effects in the literature. Particles in a microchannel are subjected to an external force called an inertial lift force (FL), which consists of a shear gradient lift force (FS) and a wall-induced lift force (FW). In Poiseuille flow, due to the curvature of the fluid velocity profile and its interaction with particles, the shear gradient lift force directs particles away from the channel center. As the particles move towards the channel walls, due to the flow field interaction between the particles and the walls, the wall-induced lift force directs particles away from the walls. These opposite lift forces compete with each other over the channel cross-section. When the lift forces in the opposite directions are equal, particles tend to occupy equilibrium positions and form narrow bands. Previous studies have reported critical conditions for achieving inertial focusing: $$\lambda ={{a}}_{{P}}/{{D}}_{{h}} > 0.07$$ and $${R}{{e}}_{{P}}={R}{{e}}_{{C}}\times {({{a}}_{{p}}/{{D}}_{{h}})}^{2} > 1$$4, where ap is the diameter of the particle, Dh is the hydraulic diameter of the channel, and ReP and ReC are the Reynolds numbers of the particle and channel, respectively.

where f, Um and are the fluid density, maximum velocity and dynamic viscosity, respectively. The lift coefficient fL is dependent on the particles position in the channel, the channel Reynolds number, and the aspect ratio of the channel. In most practical applications of microfluidic chips (Re<100), an average fL value of 0.5 is employed to simplify the estimation24. Recently, it has been found that the lift coefficient is associated with the particle position in the channel, which allows Eq. (1) to be simplified based on the position of the particles. The net lift force near the channel center is simplified as

Particle migration can be further controlled by using curved channels1. The fluid passing through a curved passage is subjected to a radially outward centrifugal acceleration, and two counterrotating vortices are formed in the upper and lower halves of the passage, which are called Dean vortices. The magnitude of these secondary flows is quantified by a dimensionless Dean number (De) given by26.

where Uf is the mean fluid velocity and R is the radius of curvature of the channel. In addition to the inertial lift force, particles in a curved channel are also affected by the centrifugal force and Dean drag force due to the channel curvature and the introduction of the Dean flow. However, the particle density used in most experiments is close to or slightly smaller than the density of the surrounding fluid, and the centrifugal force can be ignored10. Therefore, it can be approximated that the particles migrate to an equilibrium position under the combined action of the Dean drag force and inertial lift force. The maximum value of the Dean drag force (FD) can be estimated by the Stokes drag

In addition, the most distinctive characteristic of serpentine channel flow is that the direction of the Dean flow keeps alternating. Recent comprehensive reviews about particle behavior studies in inertial microfluidics can be found elsewhere27. The influence of the channel structure on the three-dimensional position of particles and the magnitude of the dominant force acting on the particles will be discussed in detail later.

A computational model was developed, and the results were compared with the experimental results of Jiang et al.23 to verify the reliability of the model. As specified in their experiments, a serpentine channel with a rectangular cross-section (80m40m) was studied. The flow field was simulated using COMSOL Multiphysics. Since the relationship between the driving force and ReC is calculated from Poiseuilles law, which is defined for a straight channel, ReC in the simulation is higher than the actual value. In the particle distribution comparison for the simulation and experiments, ReC of the simulation was divided by 1.5. A comparison between the simulation and experimental results for large particles (10 m) is shown in Fig.1a. The simulated focusing positions basically match the experimental results except that the focusing positions on one side slightly deviate at a small Reynolds number. The percentage of the estimated deviation was obtained by comparing the distance between the values from the simulation and experiments with the channel width. For large particles, the maximum deviation of the focusing position does not exceed 10%, and the average deviation of the focusing width is 4%, which is acceptable. The simulation results for small particles are also in line with the experimental trend (Fig.1b), but small particles in the experiment are closer to the sidewalls than those in the simulation. Before small particles appear at the channel center, they focus well along the sidewalls. When the majority of small particles are focused at the channel center at higher ReC, a small portion of particles are focused closed to the sidewalls, which causes an increase in the deviation in the focusing position. These small particles may still be trapped by FL when the flow velocity is relatively low (ReC=41.7), leading to a large deviation of approximately 18%. When FD is the dominant force in the channel (ReC=61.1, ReC=83.3), these small particles may flow in the channel vertical center plane and be pushed by the Dean flow further to the sidewalls. Hence, relatively large deviations at higher ReC can still be observed. Nevertheless, our model can predict the particle behavior and the focusing pattern in a fairly consistent manner, except for individual cases.

Comparison between our simulation and Jiangs experiments (adapted from ref.23, permission of RSC Advances) for the particle focusing positions and focusing width in the serpentine channel (a) for the 10m particles and (b) the 5m particles. The plotted error bars indicate the width of the focusing positions.

First, the trajectories of 10 m particles (=0.189) in the zigzag channel were simulated. The lateral focusing positions of the particles at the outlet are shown in Fig.2. The data of the focusing positions and error bars for the particles correspond to mean and standard deviation values. As the channel Reynolds number (ReC) increases from 12.5 to 100 (corresponding to the flow velocity increasing from 15cm/s to 120cm/s), several particle focusing patterns can be observed in the channel. At a lower ReC (ReC=12.537.5), the particles are focused along both sides of the channel. It can be considered that the dominant inertial lift force results in a two-sided focusing phenomenon, because at ReC=37.5, the outer edges of the particle focusing regions are approximately 15 m (19% of the channel width) away from the sidewalls of the channel, which is similar to the reported straight channel inertial equilibrium positions28.

At a higher ReC (ReC>62.5), the particle focusing positions tend to be stable with a width of approximately 12m, which is close to the particle diameter. Therefore, it can be considered that when ReC is greater than 62.5, the particles exhibit a stable focusing state in which individual particles are sequentially arranged. This is because the Dean drag force is much larger than the inertial lift force and dominates the particle migration.

When ReC ranges from 37.5 to 62.5, the particles are in a transition region. In this region, the inertial lift force and the Dean drag force are comparable and compete with each other. The particles occupy the area between the two focusing positions and tend to gradually move close together. The focusing position will approach the channel center symmetrically as ReC increases and eventually form a stable single focusing position, as discussed above. All the simulations in this paper presented a similar tendency with varying ReC.

It is concluded that the simulated channel Reynolds number range can be divided into three regions: (I) a region dominated by the inertial lift force, (II) a transition region, and (III) a region dominated by the Dean drag force. However, the ReC ranges of the three regions will differ for different curved channels and particle sizes.

The migration behavior of the particles is the result of the inertial lift force and Dean drag force in the flow field. To clarify the competition between these two forces, the flow patterns of several cross-sections in three curved channels were obtained, as shown in Fig.3. It is clear that the flow patterns are symmetrical in the vertical direction due to the lack of a curvature variation in the channels in this direction. Thus, only particles in the upper half of the channel are marked in the figure. Observing position 1 of all three channels, the 10 m particles (blue dots) are subjected to a large inertial lift and are found on both sides of the channel centerline. Because of the shear velocity gradient, the particles will first migrate in the vertical channel direction and then in the horizontal direction. In this case, the vertical positions of the 10 m particles are supposed to be outside the zero Dean velocity line at the top and bottom of the channel. Moreover, the 5 m particles (red dots) occupy four characteristic positions in the channel: two positions are closed to the wall regions, where FW is directing the particles to the channel center, and the another two positions are close to the central region, where FS is directing the particles to both sides of the channel. Since FS is caused by the parabolic velocity profile in the channel center and is proportional to the particle size (see Eq. (3)), the vertical component of FS acting on the 5 m particles is weaker than that on the 10 m particles. Therefore, the vertical positions of the 5 m particles are between the two zero Dean velocity lines. Subsequently, the particles have different behaviors due to the different channel structures.

The cross-sectional view of the fluid field at five positions for ReC=50. The left side of the picture is W1, and the right side is W2. The white dotted line represents the zero Dean velocity line. The arrow size of the velocity vector in the figure is normalized.

In the serpentine channel in Fig.3, due to the constant change of the channel curvature, there are always two counterrotating vortices in the top and bottom halves of the channel. This makes the particle focusing process relatively stable. When the particles reach position 1, the velocity maximum is close to W2. The direction of the horizontal component of FS is from the velocity maximum to the channel walls, and FD is directed to W1 (). The direction from W1 to W2 is the positive direction, indicated by +, and the opposite direction is the negative direction, indicated by . The lateral position of the 10 m particles moves towards the channel center, where FS and FD are balanced. With the joint effect of FW and FD, the 5 m particles near the channel walls rapidly migrate to the nearby equilibrium positions. For particles in the central region of the channel, the direction of FD changes along the streamlines, in some positions helping FS to accelerate the particles to the equilibrium and in other positions competing with FS to disturb the particles from their equilibrium. When the particles reach position 2, the serpentine channel smoothly transitions as the particles pass the corner. The velocity maximum is close to the channel center, the direction of FS is always from the velocity maximum to the two sidewalls of the channel, and FD still maintains the previous direction (). Due to the large Dean drag force in the alternating turns and the effect of the inertial lift force, the particles begin to migrate to the final equilibrium position. When the particles reach position 3 (the transition region), the velocity maximum has moved to the channel center, leading to no lift. Due to the abrupt change in the direction of the curvature, the curvature effect can be ignored. Thus, the Dean drag force becomes insignificant (see Eq. (6)). At this point, both the 5 m and 10 m particles have reached equilibrium positions and follow the streamlines until they reach the new velocity profile region. It should be noted that after position 3, the direction of the curvature changes, and whenever the curvature changes, the directions of the forces are opposite. At position 4, the change in the curvature causes the velocity maximum at the channel center to move to the opposite side. The direction of FD also changes to W2 (+), and the particles swing near the equilibrium positions before FD and FS reach equilibrium again.

In the square wave channel, when the particles reach position 1, the particles exhibit similar motion to that in serpentine channels. The difference is that since the square wave channel does not have continuous curvature but is a combination of short straight channels, the velocity vector at position 1 only has a single direction towards W2. When the particles pass through a 90 corner and reach position 2, the direction of FD is towards W1 (). FD increases due to the expansion of the cross-section, and FL decreases. This change will break the balance between FD and FL and cause the particles to fall into the Dean vortex controlled by FD. After passing two corners, the particles reach position 3, and the direction of FD remains towards W1 (). This situation is the same as in the serpentine channel; both the 5 m and 10 m particles migrate close to the equilibrium positions. At position 4, the velocity vector again becomes a single direction towards W1.

In the zigzag channel, when the particles reach position 1, the motion of the particles is similar to that in the other two channels, and the velocity vector is in a single direction towards W2. Similar to the square wave channel, the zigzag channel has a straight structure after each corner, which can be regarded as a short straight channel. At the beginning of the short straight channel (position 3 in Fig.3), the velocity vector will inherit the pattern from the previous corner (two counterrotating vortices). Then, the Dean vortex becomes smaller and eventually forms a single-direction vector (positions 1 and 4 in Fig.3) similar to the inertial lift in the straight channel until the next corner. With the increase in ReC, the particles can pass through the straight region rapidly, and the Dean drag force will dominate. Therefore, the zigzag channel and the square wave channel can perform better under a high Reynolds number. When the particles reach position 2, the zigzag channel has a 60 corner, and the width of the cross-section is almost doubled. When the cross-section width increases, Dh will inevitably increase. According to Eqs (3) and (4), Dh is proportional to FD but inversely proportional to FL. The velocity maximum is close to W2, and the direction of FD is towards W1 (). Both the 5 m and 10 m particles migrate towards W1 under the joint action of the large FD and FL. It is worth noting that the spacing of the equilibrium positions on both sides of the 5 m particles is enlarged. At position 3, both the 5 m and 10 m particles reach equilibrium positions and follow the streamlines until they reach the new velocity profile region. When the particles reach position 4, the velocity maximum is close to W1. Due to the reduction in the Dean drag force, the inertial lift force dominates, so both the 5 m and 10 m particles are offset towards W2. Position 5 is the mirror image of position 2, and the direction of FD is directed towards W2 (+). The final effect is that the secondary flow sweeps small particles towards two-sided walls, facilitating the migration of particles towards the inertial equilibrium positions. Large particles are gradually focused near the centerline of the channel under the action of the large FD and FL at the corner. Then, a new cycle begins, and the particles will reach a stable equilibrium after a few cycles.

To further investigate the difference in the forces acting on the particles, the force variations for the three channels are plotted in Fig.4. The relationship between the inertial lift force and the hydraulic diameter at different positions in the channel are given by Eqs (3) and (4). Equation (3) is the inertial lift force at the channel center, which can be considered as a shear gradient lift force, and Eq. (4) is the inertial lift force at the channel wall, which can be considered as a wall-induced lift force. Therefore, Eqs (3) and (4) can be used to obtain the variation in FS and FW for different channel structures. The directions of FW and FS are fixed, so only the trends of their changes are shown in Fig.4. As the channel cross-section width increases, FW and FS decrease. In addition, the relationship between the Dean drag force and hydraulic diameter obtained by Eq. (6) is also shown in Fig.4. The difference is that the direction of the Dean drag force is indicated by positive (+) and negative () values of the Dean drag force, which is derived from the discussion of the velocity vector. When the channel cross-section increases in size, FD also increases. However, the lift coefficient of these forces varies at every position of the cross-section; hence, it is difficult to obtain the value of the forces. Only the general trends of the forces along the channel are presented in Fig.4. In the serpentine channel, there is no change in the cross-section, so FW and FS remain stable, and FD changes direction due to the channel curvature changes. In the square wave channel, as the particles pass the corner, the cross-section increases in size, FD increases, and FW and FS decrease. After entering the straight section, the cross-section returns to its original size. Therefore, FW and FS will gradually increase and then remain stable, while FD will gradually decrease until the next corner. The development of the force competition in the zigzag channel is similar. However, compared to the square wave channel, the zigzag channel has a greater cross-section extension, and thus the forces exerted on the particles vary more dramatically.

It can be found from the previous discussion that the introduction of the Dean flow does not directly produce particle focusing but acts on the particles together with the inertial lift force to reduce the number of equilibrium positions. The superposition of these two forces is different in different curved channels. To explain the difference, the ratio of the magnitudes of FL to FD29 was given as

The curvature ratio is $${\delta }={{D}}_{{h}}{/}2{R}$$. This relationship suggests that the ratio of FL to FD is strongly dependent on the ratio of ap to Dh. For the same ReC, small particles cannot be focused even when the channel is long enough due to the dominant role of FD, while large particles will be focused quickly.

The competition between FL and FD determines the focusing pattern of particles of different sizes. The variations in the particle focusing width for different channels are shown in Fig.5. It can be found that for the 5 m particles (Fig.5a), when ReC37.5, the particle focusing width in the square wave channel is 510 m narrower than that of the other two channels for the same channel Reynolds number. When ReC is increased to 50 and 75, the inertial lift force has a relatively slight influence on the particle migration in the vertical direction, the particles horizontally swing across the cross-section by the Dean drag force, and the focusing width gradually decreases. However, there are exceptions: the particle focusing width in the zigzag channel suddenly increases at ReC=50. This phenomenon results from the increases in FD due to the extension of the channel cross-section at the corner, as mentioned above. Therefore, the spacing of the equilibrium positions on both sides of the 5 m particles is enlarged due to the joint action of the large FD and FL, which will suddenly broaden the focusing width. Although the square wave channel also has an extension of the channel cross-section, the scale of the extension is small. In Fig.5, the focusing width is slightly larger only at ReC=62.5. When ReC exceeds 75, the trend of the curve for the serpentine channel is different from that for the other two channels. In the serpentine channel, particles begin to spread, and the strong Dean flow drags particles to the sidewall again. The optimal focusing state is achieved at ReC=75. A similar phenomenon cannot be observed for the zigzag and square wave channels. The particles in these channels are still well focused, and the optimal focusing state is achieved at ReC87.5. In comparison, the particles in the zigzag channel are arranged more compactly. It is predicted that particle dispersion will occur at a value of ReC that is large than our simulated Re range due to strong Dean flow. In summary, for the 5 m particles, the zigzag channel is the best choice for a relatively high ReC range, and the serpentine channel is also a good choice for moderate values of ReC.

The relationship between the particle focusing width and the channel Reynolds number for the three curved channels for the (a) 5 m particles and (b) 10 m particles. The dotted line corresponds to the critical channel Reynolds number for particle focusing.

The 10 m particles exhibit similar behaviors in the different channels, as shown in Fig.5(b). When ReC is as large as 100, the 10 m particles in all three channels are well focused. At a low ReC, the particles flow along the two sidewalls under the superposition of FL and FD. If ReC continues to increase, the particles will be focused at the channel center by the strong direction alternation of FD (see Fig.2). When ReC exceeds 50, the focusing width curves of the three curved channels almost overlap. When the channel Reynolds number is high, the dominant effect of FD on large particles is far greater than that of FL, and a single focusing position can be achieved along the channel center. With the increase in ReC, the migration of the 10 m particles from both sides to the center is much faster than that of the 5 m particles. Therefore, it can be seen that the size difference also plays an important role in the focusing pattern, and the large particles are more likely to be focused at the horizontal center of the channel. This is due to the contribution of both FL and FD. On one hand, large particles are slightly closer to the channel center than small particles in the inertial straight channel because of the difference in FL; on the other hand, FD has more influence than FL in terms of a greater effect on large particles than small particles. It also can be seen from Fig.5 that the focusing width decreases sharply as the channel Reynolds number increases, and focusing is achieved after a critical value (defined as the critical channel Reynolds number for particle focusing, ReCC). An exception is that the 5 m particles in the serpentine channel are focused at ReC=75 and then diverge at a higher value of ReC. It should be noted that the ReCC values of the 10 m particles are all smaller than those of the 5 m particles for the same channel. To comprehensively evaluate the focusing performance, the ReCC data for all of the conditions studied here are listed in Table1. The large 10 m particles can be focused within a wide range of ReC (>~60) in all three channels. The threshold of the serpentine channel is 62.5, a relatively lower value. Nevertheless, for the 5 m particles, focusing becomes more difficult than for the large particles. In the serpentine channel, only one ReC (=75) value leads to focusing; in the square wave and zigzag channels, the small particles are focused because the focusing width still decreases at ReC=100. However, the small particles do not reach the desired complete focusing state because of the limitation of the Reynolds number in this study; thus, the ReCC values of the small particles in the square wave and zigzag channels are tentatively set to 100. If the Reynolds number is extended in a later study, a more accurate ReCC value could be obtained.

Another criterion for evaluating the focusing performance of a curved channel is the focusing length. To compare the focusing length under various conditions, the focusing widths of the 5 m and 10 m particles after each structural period are plotted in Fig.6. A critical advantage of a small focusing length is the reduction in the fluidic resistance. The horizontal dotted line indicates that the focusing width tends to be stable, and the particles can be considered to be fully focused. As shown in Fig.6, the 5 m particles tend to focus only after the fifth period within the simulated period numbers, and a stable focusing width cannot be observed. However, the 10 m particles achieve a stable focusing width for all three channels at ReC=75 and 100. Under the same conditions, the large particles are subjected to a greater inertia lift force and are less susceptible to interference by the Dean drag force, so they can achieve focusing more quickly than the small particles. This is consistent with the results of the critical channel Reynolds number. When ReC=75, the curves for the 10 m particles in the serpentine channel and the zigzag channel almost overlap, and the particles in the channels are focused after the fourth period. The particles in the square wave channel are focused after only three periods, with a focusing length of approximately 1.5mm. When ReC=100, the focusing length of the particles for the three channels is shortened to varying degrees. The square wave channel is still superior in terms of the focusing length. Hence, it can be concluded that the large particles can be focused within a shorter focusing length when the flow condition (ReC) is constant, and the square wave channel has advantages over the other two channels for the 10 m particles due to the rapid focusing.

An interesting result of the above focusing characteristics is that the arrangement of particles of different sizes varies across the width of the channel. To show the distribution of particles intuitively, the overlaid ReC maps in Fig.7 graphically show the focusing positions and their deviations for the two sizes of particles for the three curved channels. The particle focusing positions are either distinct and able to be separated or overlapping and unable to be separated. Figure7 shows that the smaller particles occupy both sides of the channel and that the particles have a wider region dominated by the inertial lift force. Correspondingly, the large particles are focused along the channel center, and the width gradually decreases to a single stable focusing line and thereby has a wider region dominated by the Dean drag force. The particles are focused along the channel center, and the width gradually decreases to a single stable focusing line. This contributes to the possibility of separating particles of two sizes.

Focusing positions of the 5 m (red) and 10 m (blue) particles in the three curved channels for various channel Reynolds numbers. The plotted error bars indicate the width of the focusing positions, and the solid legend represents the single point focusing particles.

In the serpentine channel (Fig.7a), the regions of the 5 m and 10 m particles fully overlap. In the square wave channel (Fig.7b) and the zigzag channel (Fig.7c), the 5 m particles migrate to the channel center more slowly than the 10 m particles in the ReC range of 5075. The small particles line up on both sides of the large particles. There is a significant separation distance between the equilibrium regions of the particles of two sizes. In addition, in order to avoid difficulties in controlling the precision of the separation, it was found that the separation distance could not be too small. A distinct 10 m distance can be observed at ReC=62.5 in the zigzag channel (dotted circle in Fig.7c), which corresponds to the optimal separation condition in this study. When ReC continues to increase to 100, the particles are both arranged in a line. The equilibrium regions of the two lines create a certain separation distance again, indicating a separation trend. It should be noted that the separation outlet system needs to be designed carefully for different separation behaviors, namely, three outlets for moderate ReC values and two outlets for high ReC values.

A high Reynolds number will lead to a large pressure drop, causing greater energy consumption and possible sample leakage. Thus, the pressure drop data were extracted to evaluate the channel performance, as shown in Fig.8. The pressure drop of the zigzag channel generally exhibits a smaller pressure drop than the other two channels, which is on average 13.9% less than that of the serpentine channel and 22.7% less than that of the square wave channel. In other words, the overall performance of the zigzag channel is superior to that of the square wave and serpentine channels considering the focusing, separation and pressure drop.

In this paper, a zigzag channel, which has not been used previously for inertial focusing studies, is compared to a serpentine channel and a square wave channel to explore their differences in terms of focusing effects and separation possibilities. From the particle trajectories and fluid fields in the curved channels, the competition between the inertial lift force and the Dean drag force exerted on the particles is illuminated clearly. The channel structures influence the flow velocity profile and the balance between FL and FD, thus producing various focusing and separation behaviors. The results for the focusing width, focusing length and Reynolds number range show that, for small particle focusing, the zigzag channel is the best choice for a high ReC value and the serpentine channel is the second choice for a moderate ReC value. The three curved channels achieve a similar focusing performance for large particles and a high ReC, because the contribution of the Dean drag force is much greater than that of the inertial lift force. In addition, the particle distribution presents a distinct separation possibility. The optimal separation performance appears at ReC=62.5 in the zigzag channel with a separation distance of approximately 10 m. Ultimately, the overall performance of the zigzag channel is superior to that of the square wave and serpentine channels considering the focusing, separation and pressure drop.

The zigzag channel has prospects in focusing and separation applications. Future research should consider finite-size effects in the modeling of the particles. In this research, the interaction between the particles was ignored, as the particles were individually released at each time step and experienced a weak interaction. Particle trains, which are seriously affected by particle interactions, may produce new phenomena in the flow pattern and particle migration. This is our ongoing work. Because of limitations in terms of code complexity and computing resources, it is challenging to obtain quantitative data from numerical simulations. Therefore, our long-term vision includes the development of viable simulation methods.

To analyze and compare the focusing behavior of the particles, the particle trajectories and fluid fields in three curved channels were simulated using the commercial computational fluid dynamics (CFD) software COMSOL Multiphysics 5.3 (Burlington, MA). Structural diagrams of the three curved channels studied in this paper are shown in Fig.9(a,b) describes the structural unit of the channels. As shown in the figure, the length of the channel structural unit is 280 m, and the channel height H and the width W are 40 m and 80 m, respectively. Thus, the channel depth-to-width ratio AR is 0.5. These channels were modeled and simulated by using tetrahedral meshes, and a mesh independence test was conducted. Taking the serpentine channel as an example, the grid number for different meshing methods ranged from 8.98104 to 3.77105, and 2.92105 was selected as the best grid number. The same test was conducted for the other two channels to obtain the best grid number. Each model was solved using the GMRES iterative solver. The element size and quality were adapted based on computer memory restrictions and the actual size of the model for each structure. The densities of the particles and water were both 1000kgm3. The viscosity of water was 1103kgm1s1.

The full Navier-Stokes equations were solved by a laminar flow model using single-phase and incompressible flow assumptions. For an incompressible and steady laminar flow, the governing Navier-Stokes equations can be expressed as $${\rho }({\boldsymbol{u}}\cdot \nabla ){\boldsymbol{u}}=\nabla \cdot [\,-\,{p}{\boldsymbol{I}}+{\mu }(\nabla {\boldsymbol{u}}+{(\nabla {\boldsymbol{u}})}^{{T}})]+{\boldsymbol{F}}$$ and $${\rho }\nabla \cdot {\boldsymbol{u}}=0$$, where the symbols follow the default definition in COMSOL. Then, the particle tracking module was used to predict the particle trajectories in the curved channels, and the particle momentum was given by Newtons second law. The particles experienced a drag force given by Stokes law, which includes a correction factor for the drag force for particles near walls. The drag force was expressed as $${{\boldsymbol{F}}}_{{D}}=6{\pi }{\mu }{{a}}_{{p}}({\boldsymbol{u}}-{\boldsymbol{v}})$$, where is the fluid viscosity, u is the fluid velocity, and v is the particle velocity. The lift force was expressed as $${{\boldsymbol{F}}}_{{L}}={\rho }\frac{{{r}}_{{p}}^{4}}{{{D}}^{2}}{\beta }({\beta }{{G}}_{1}({s})+{\gamma }{{G}}_{2}({s})){\boldsymbol{n}}$$, where rp is the particle radius, n is the wall normal at the nearest point on the sidewall, s is the nondimensionalized distance from the particle to the sidewall, divided by D so that 0

## nanomaterials | free full-text | a novel nanocomposite of activated serpentine mineral decorated with magnetic nanoparticles for rapid and effective adsorption of hazardous cationic dyes: kinetics and equilibrium studies

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Seliem, M.K.; Barczak, M.; Anastopoulos, I.; Giannakoudakis, D.A. A Novel Nanocomposite of Activated Serpentine Mineral Decorated with Magnetic Nanoparticles for Rapid and Effective Adsorption of Hazardous Cationic Dyes: Kinetics and Equilibrium Studies. Nanomaterials 2020, 10, 684. https://doi.org/10.3390/nano10040684

Seliem MK, Barczak M, Anastopoulos I, Giannakoudakis DA. A Novel Nanocomposite of Activated Serpentine Mineral Decorated with Magnetic Nanoparticles for Rapid and Effective Adsorption of Hazardous Cationic Dyes: Kinetics and Equilibrium Studies. Nanomaterials. 2020; 10(4):684. https://doi.org/10.3390/nano10040684

Seliem, Moaaz K., Mariusz Barczak, Ioannis Anastopoulos, and Dimitrios A. Giannakoudakis 2020. "A Novel Nanocomposite of Activated Serpentine Mineral Decorated with Magnetic Nanoparticles for Rapid and Effective Adsorption of Hazardous Cationic Dyes: Kinetics and Equilibrium Studies" Nanomaterials 10, no. 4: 684. https://doi.org/10.3390/nano10040684

## inertial particle separation by differential equilibrium positions in a symmetrical serpentine micro-channel | scientific reports

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This paper presents an inertial microfluidic device with a simple serpentine micro-channel to continuously separate particles with high performance. Separation of micro/nano-particles has a variety of potential applications in biomedicine and industry. Among the existing separation technologies, a label-free technique without the use of antibody affinity, filter or centrifugation is highly desired to ensure minimal damage and alteration to the cells. Inertial microfluidics utilising hydrodynamic forces to separate particles is one of the most suitable label-free technologies with a high throughput. Our separation concept relies on size-based differential equilibrium positions of the particles perpendicular to the flow. Highly efficient separation is demonstrated with particles of different sizes. The results indicate that the proposed device has an integrative advantage to the existing microfluidic separation techniques, taking accounts of purity, efficiency, parallelizability, footprint, throughput and resolution. Our device is expected to be a good alternative to conventional separation methods for sample preparation and clinical diagnosis.

Particle separation has a wide range of industrial, biomedical and clinical applications such as wastewater purification, blood sample preparation and disease diagnosis1. Conventional macro-scale techniques such as physical filter and differential centrifugation have been used for this purpose. However, centrifugation is bulky, expensive, labour intensive and even dangerous because it contains components moving at high speed2,3. Centrifugation is also limited by the heterogeneity of sample source. Furthermore, exposure to a high acceleration will likely alter the immunophenotype4 and viability5 of cells. Physical filters are prone to clogging and frequent cleaning is labour intensive. Thus, a simple, low cost, more efficient and less offensive technique is desired. The recently emerged microfluidic technology is endeavoured to satisfy these demands.

In microfluidics, continuous flow separation and sorting of particles are generally based on two basic concepts: the equilibrium separation and the kinetic separation6,7. In the first concept, particles occupy different property-dependent equilibrium positions; whereas the second concept employs different transport speeds perpendicular to primary flow direction under an applied force field3. According to the manipulation force, particle separation can be categorized as active and passive techniques. Active techniques depend on external force fields8,9,10,11,12,13,14,15. The input flow rate and throughput are rather low because target particles need a long residence time to be exposed to the force field. The auxiliary system supplying the force field further complicates the design, although it may bring flexibility and controllability to the device. In contrast, passive techniques only rely on intrinsic hydrodynamic forces or channel geometry16,17,18,19,20. Passive devices are simple and could provide a much higher throughput. As a passive technique, inertial microfluidics employing inertial migration21 and inertial effects of fluid (secondary flow)20 and particles (centrifugal force)22 under a high flow speed can provide excellent separation efficiency and purity with a massive throughput. Inertial microfluidics is also label-free, which eliminates the need for potentially cell-damaging immunolabelling procedures and promises a cost-effective cell separation method for downstream biological assays23. Generally, there are 6 criteria to evaluate inertial microfluidic separation/sorting device. (i) Footprint. A small device footprint not only reduces the fabrication cost, but also improves the portability. (ii) Throughput. High throughput is essential in processing a large volume of sample and it is actually the main advantage of inertial microfluidics. (iii) Parallelizability. An effective method to amplify the throughput is to pattern parallel channels in the same device. Basically, a microchannel with linear structure (e.g. straight or serpentine) is prone to be parallelised. (iv) Performance. High separation purity and efficiency (or recovery ratio) are important for the downstream application, including enumeration, molecular assay and drug screening, etc. (v) Resolution. The minimum particle property (size, deformability and shape) difference required to achieve effective particle separation. (vi) Complexity. Sheath flow and complicated microchannel structure (e.g. double layer microchannel) are not in favour of fabrication costs and portability. Although great progress in the inertial microfludics has been achieved recently24,25,26,27, so far there is still lack of techniques with an integrative ability to satisfy all the required criteria simultaneously.

There are four basic types of microchannel structures used in inertial microfluidics: straight channel24,28, expansion-contraction array channel29,30, spiral channel26,31 and serpentine channel3. Lee et al. reported a series of particle separation in an expansion-contraction array (CEA) channel, including polystyrene beads of 4m and 10m in diameter32, blood plasma from red blood cells33 and cancer cells from whole blood29. These devices can handle highly concentrated bio-particle samples such as undiluted whole blood (1 109 counts/ml) using a sheath flow. However, the inclusion of a sheath flow will certainly complicate the whole system, diluting the sample and potentially causing contamination. In addition, microvortex-aided trapping and separation in the similar microchannels was also developed27,34,35,36,37. It is believed as one of most size-sensitive separation methods which employs size-selective trapping of microvortex within expansion-contraction chambers24. The group of Di Carlo has conducted a series of investigation on its trapping sensitivity and efficiency by a variety of bio-samples, including cancer cells spiked in blood34, pleural fluids37 and blood sample27 from cancer patients. This device basically works in batch procedures and specifically effective in trapping of rare cells (e.g. CTCs), due to limited capacity in expansion-contraction chambers. Later, Wang et al.36 proposed a modified microvortex-aided device by adding a side outlet in each chamber to continuously siphon larger particles from chambers, facilitating high efficiency and high purity size-based particle separation in a continuous manner. Although with great separation performance achieved, this kind of devices is still facing challenges about separation of smaller particles, as their functional cut-off size is relatively large (15m in diameter34,37 and 20m in diameter36).

Spiral channels were investigated extensively for particle separation by Papautsky's group31,38, Go's group39, Jiang's group40,41 and Han's group26,42,43,44, etc. Kuntaegowdanahalli et al.38 demonstrated continuous separation of three different-sized polystyrene beads (10, 15 and 20m in diameter) with an efficiency of 90% and a throughput of 1 106cells/min. Later, Hou et al.42 employed a similar spiral channel to isolate CTCs from blood and achieved a recovery rate of more than 85%. Apart from that, a clinical validation with positive detection of CTCs from all the blood samples of cancer patients was reported42. At the same time, Guan et al.43 introduced a novel spiral micro-channel with a trapezoidal cross-section and showed a higher separation resolution than those with rectangular cross-section. Later, isolation CTCs from cancer patient blood samples was demonstrated by this slanted spiral micro-channel26 from the same group. A high throughput of 1.7ml/min and increased CTC capture efficiency were achieved. Although the spiral micro-channel has a great potential for real clinical application, its throughput is still limited due to difficulties in parallelisation. A linear channel structure is more preferred for parallelization design.

Mach and Di Carlo28 reported a massively parallelized microfluidic device that passively separates pathogenic bacteria from diluted blood. The device consists of 40 single straight micro-channels placed as a radial array. Each single channel consists of three different cross-sections and uses a unique differential transit time by size-dependent inertial lift forces to obtain cell separation. Zhou et al.24 utilized a more polished design of size and length for their cascaded straight channels. The separation concept is based on their theory of two-stage inertial migration which permits precise prediction of particle or cell position within the micro-channel. A much higher separation efficiency (~ 99%) and purity (~ 90%) were achieved. However, the sizes (width height) of channel cross-section (27m 50m upstream segment, 100m 50m downstream segment for separation of 9.94m and 20m particles) were restrained to provide enough lateral inertial lift force. The small cross section leads to a high fluidic resistance, which needs more power to pump the sample into the microfluidic device. In addition, the channel is relatively long (>36mm) leading to a large device footprint.

In terms of small footprint and easy parallelization, a serpentine channel with linear structure is an optimal choice. A serpentine channel not only is easy to parallelise, but also can achieve focusing and separation within a much shorter length due to the assistance of secondary flow22,45. Unfortunately, little effort has been paid to separate particles by a serpentine channel in inertial microfluidics. Besides a complicated hybrid microfluidic device which combines hydrodynamic size-based deterministic lateral displacement, inertial focusing in an asymmetric serpentine channel and magnetophoresis to separate cancer cells from leukocytes46, only one attempt to develop an inertial filtration device using an asymmetrical serpentine channel was reported3. In this filtration system, large particles were well focused and small particles below a threshold remained unfocused and randomly distributed. Therefore, large particles were completely removed from the mixture, leaving behind small particles with a high purity (90%100%). However, because small particles are still unfocused, plenty of them will enter the reservoirs meant for large particles, leading to undesirable purity (~20%) of large particles collection. Also the recovery efficiency of small particles was low (~56%). Ambitious work is still needed to separate binary particles mixture with high purity and high efficiency.

In order to provide a continuous separation technique with high-throughput, good parallelizability, small footprint and high separation performance, we proposed an innovative inertial microfluidic device which can continuously separate particles based on the size-dependent differential equilibrium positions. The differential focusing phenomenon is partially based on the concept of our previous study47, where both Dean drag force and particle centrifugal force (DC force) dominate particles migration in a serpentine channel. A single focusing streak can be achieved at the centre of the channel. As inertial lift force, Dean drag force and particle centrifugal force scale differently with the particle size. Particles below a certain threshold could be dominated by the inertial lift force and are focused along two sides of the channel. Therefore, a complete separation can be achieved with a proper outlet system. First, we examined the focusing pattern of different-sized particles under varying conditions. The results were placed into the Reynolds number - particle size operation space. After that, the available working area for particle separation can be easily determined. Then, we tested the separation of two pairs of polystyrene particle mixtures (3-m/10-m and 5-m/13-m particles). We achieved a very high purity of both small particles (>99%) and large particles (>90%) after a single separation process at a flow rate of 600l/min. Finally, we successfully demonstrated the separation of biological particles (erythroleukemia cells and 5-m polystyrene particles and human blood cells and erythroleukemia cells) with outstanding performance.

When the flow rate was increased from 100l/min to 1000l/min, three different particle focusing patterns were observed in a serpentine channel. If the flow condition was below a threshold A, particles were focused along the two sides of the channel. The distances between the focused streaks and the side walls were both around 38m (19% channel width), which was close to the reported inertial equilibrium positions in a straight channel25,32,48, so we expected that the observed two-sided focusing is an inertial lift force dominated phenomenon. Under this flow condition (region I in Fig. 1a), inertial lift force was stronger than the DC force and dominated the final equilibrium positions of particles. In our previous test with a straight channel of the same cross section, distinct focusing positions were not apparent even after a channel length of 40mm. This is due to the insufficient inertial lift force to push particles to their inertial equilibrium positions within 40mm length (supplementary Fig. S1a) and maybe a longer channel is needed. While, in a serpentine channel, these focusing positions were obvious within a much shorter channel length of 10mm as shown in supplementary Fig. S1(b). Probably due to the combined effect of Dean flow and centrifuge force, particles can reach stable inertial equilibrium positions more quickly22. When flow condition exceeded a level B (region III in Fig. 1a), we proved in our previous study that the resultant effect of DC force was much greater than the inertial lift force in the serpentine channel and a single focusing position along the channel centre can be achieved47. When the flow was in the region between A and B (region II in Fig. 1a), a transition phenomenon occurred. The inertial lift force and the DC force were of the same order of magnitude and competed against each other. Particles occupied the space between the two streaks and formed a single but wide streak band. The focused streaks approached the channel centre symmetrically as the flow rate increased and finally formed a stable single streak, where DC force began to dominate the movement of particles. The areas of regions I and III depend on the particle size. Generally, large particles have a wider region III and a lower threshold B. Small particles have a wider region I and a higher threshold A. If there is any overlap between these two regions (Ap1 Bp2) for two different particle sizes, the complete separation of particles is possible, according to their differential equilibrium positions along the channel width (Fig. 1b). The size-based separation mechanism proposed in the present paper is built upon the above phenomenon.

(a) Three different particle focusing patterns in a serpentine channel with varying flow conditions, (I) Inertial lift force dominated region with two-sided focusing streaks, (II) transition region with a wide single central focusing band and (III) DC dominated region with a single focusing streak at the channel centre. The error bars indicate the width of the focusing streak. Particle diameter is 10m. (b) Schematic illustration of particle size-based separation concept in a serpentine channel.

In order to determine the working conditions for complete particle separation, particles with a series of sizes were tested in the serpentine channel. Fluorescent streak images of different-sized particles at the outlet are plotted in Figure 2a, which shows that smaller particles had a wider region I and particles were occupying two sides of the channel. A more intriguing phenomenon was that small particles (5m) become unfocused rather than focused into the centre of the channel even at a large Reynolds number (ReC = 160~200), which was different from their large counterparts (8m). Two effects are responsible for this phenomenon. First, mixing effects of Dean vortex were more effective on small particles. Small particles were prone to being retained by the counter-rotating streamlines of a Dean vortex, so that focusing at the centre of the channel is hard to be obtained. Yoon et al.39 demonstrated that particles smaller than 27% of the channel height posed an inward velocity due to the mixing effects in a curved channel. We recently found that this ratio could be as small as 20% in a low-aspect-ratio serpentine channel, due to the suppression on mixing streamlines47. In this work, the channel height was 42m, so particles smaller than 8m were prone to being affected by the mixing effects of Dean flow. Therefore, the theory of Dean drag force and particle centrifugal force (DC force) induced central focusing may be not suitable for these small particles. Second, even at our high testing flow condition, DC force maybe still cannot overcome inertial lift force, so that this defocusing status could remain longer downstream. Unfortunately, it is impossible to scale these forces quantitatively to determine the particle size threshold. Particles are unstable within channel cross-section and their movement speed and direction along channel cross-section is uncertain, causing varying Dean drag force. Moreover, the exact mechanism how Dean drag force and particle centrifuge force collaborate together to fight against inertial lift force is still unclear.

(a) Experimental observation of outlet fluorescent streak images for different-sized particles under various flow conditions; (b) Translation of particle focusing pattern into three standard regions in the channel Reynolds number particles diameter space.

The focusing pattern of different-sized particles was placed into three standard regions and plotted in the channel Reynolds number versus particles size operation map (Fig. 2b), which indicates the available working area for the separation of particles with specific sizes. The operation map shows a distinct overlap between region I of 3m and 5m particles and region III of 10m and 13m particles. The transition threshold A for 3m (A3 = 130) and 5m (A5 = 120) particles was obviously higher than the transition threshold B for 10m (B10 = 107) and 13m (B13 = 90) particles. So it is possible to completely separate particles based on their size-dependent differential equilibrium positions in the serpentine channel, a fact that will be demonstrated in the following sections. The quantitative particle streak position and width under various flow conditions were shown in supplementary Fig. S2. The streak position is not only useful for the determination of the available flow condition, but also important for designing a proper outlet system for particle separation.

A mixture of fluorescent particles with diameters of 3m and 10m were tested in the designed device to demonstrate the concept of complete separation. Figure 3a is a schematic illustration of microchannel structure used for particle separation in the present work. Pillar arrays acting as a filter upstream of the serpentine channel was used to prevent clogging by large debris. A trifurcating outlet system was placed at the end of serpentine channel. For simple handling, the two symmetrical side branches were merged together into a single outlet.

(a) Schematic illustration of the micro-channel structure used for particle separation in this work. A filter upstream of the serpentine channel prevents the channel from being blocked by large debris. A trifurcation outlet system with two symmetrical side branches merged together as a single outlet #2 was used. (b) Superimposed fluorescent images illustrating the distribution and position of the 10-m (pseudo-colored green) and 3-m (pseudo-colored red) particles in different periods of serpentine channel. (c) (i) Fluorescent images of the particle mixture at the outlet of the serpentine channel and (ii) its cross sectional fluorescence intensity profile presents differential equilibrium positions for binary particles. (iii) Pictures of particles suspension before and after processing indicate an effective particle separation in the serpentine channel.

The fluorescent images of particles at different periods in the serpentine channel are shown in Figure 3b. Particles were randomly distributed at the channel inlet [Fig. 3b(i)]. After passing through several serpentine periods, large particles migrated into the channel centre dominated by the DC force, while small particles occupied two sides of the channel due to the dominant inertial lift force [Fig. 3b(ii~v)]. At the end, a three-branch outlet system was used to collect particles from different lateral positions [Fig. 3b(vi)]. Figure 3c(i) shows the distribution and position of 10-m and 3-m particles before the trifurcation. The fluorescence intensity profile clearly demonstrates distinct lateral positions of 10-m and 3-m particles [Fig. 3c(ii)], facilitating particle separation by size. Figure 3c(iii) shows particle suspensions before and after the treatment by the microfluidic device, clearly indicates an effective separation for the particles mixture.

The particles mixture was tested in the microfluidic device with different throughputs to quantitatively evaluate the separation performance. Particle concentration, particle purity (collected target particle number/collected total number24) and separation efficiency (collected target particle number/input target particle number1,49) were measured and shown in Figures 4b~d, respectively. The sample collected from outlet #2 had a very high purity (~99%) of small 3-m particles, due to excellent focusing of larger 10-m particles at the channel centre. However, for collection from outlet #1, purity of large 10-m particles was not as high as expected. The maximum purity was around 88.7%, although this value was much greater than the input purity of 24.2%. The main reason is that small 3-m particles still could not experience enough inertial lift force in the migration process even with the assistance of DC force. There was no distinct single lateral equilibrium position for them, but a wide band area (Fig. 2a). The wide band reduced the separation distance between large and small particles along the lateral direction and increased the possibility of small particles entering outlet #1, finally deteriorated the purity of the collected large 10-m particles. In addition, the separation efficiencies for both large particles and small particles are more than 90% (97.5% for 10-m particles and 92.8% for 3-m particles), which implies that most input particles can be effectively separated and recovered at their corresponding collectors.

(a) Fluorescent images of collections from control and two outlets. The control is particle mixture collected before passing through the serpentine channel. Pseudo-colored green and red dots represent 10m and 3m particles respectively. (b) Particle concentrations from control and two outlets under different processing flow conditions (flow rate or Reynolds number). (c) The purity of particles from two collectors at various flow conditions. (d) The separation efficiency for 3-m and 10-m particles under different flow conditions. Error bars represent the standard deviation of three measurements by hemocytometry.

We also tested the separation of a mixture of 5-m and 13-m particles. Since 5-m particles had a larger size and experienced a much larger inertial lift force (FL) and DC force (FD & Fcent) as well as a faster lateral migration speed than 3-m particles, two narrow focusing streaks along the channel could be observed in Figure 2a. As expected, at the optimal flow rate (600l/min), the purity of large 13-m particles collected at outlet #1 could be as high as 91.6%. Small 5-m particles collected at outlet #2 (Fig. 5c) also achieved a high separation purity of more than 99.2%. The fluorescent images of particles from the control and outlets in the hemocytometer showed the excellent separation performance of our device (Fig. 5a). It should be noted that the purity of collected particles sample is taken from a single process, so it is expected that complete separation with purity of more than 99% could be obtained with a cascading process.

(a) Fluorescent images of collections from control and two outlets. Pseudo-colored green and red dots represent 13-m and 5-m particles respectively. (b) Particle concentrations from control and two outlets under three different processing flow conditions. (c) The purity of particles from two collectors at various flow conditions. (d) The separation efficiency for 5-m and 13-m particles under different flow conditions. Error bars represent the standard deviation of three measurements by hemocytometry.

MEL cells, as a commonly used model of red blood cell biology50,51, are used to investigate molecular events involved in the oncogenesis of erythroleukemias52. Microscopic measurements of 70 randomly selected MEL cells revealed that live MEL cells have a mean diameter ~12.6m with a standard deviation of ~2m. In order to test the separation capacity of our device on biological cells, MEL cells were mixed with 5m polystyrene particles at a ratio of ~1:1 in PBS solution. The mixture was then pumped into the microfluidic device under the optimal flow rate of 600l/min. Beads and MEL cells concentration and purity from input mixture and two collections from outlets were plotted in Figures 6a and 6b. Their bright field and fluorescent images were shown in supplementary Fig. S3. Within our expectations, sample collected from outlet #2 resulted in a very high purity (~98%) of 5-m particles. Also, a high purity of ~94.9% was also achieved for MEL cells obtained from outlet #1. The flow cytometric data (plotted as forward scatter FSC and side scatter SSC) were shown in Figure 6c, which further supports the high separation performance of our device. Additionally, MEL cells were spiked into the human blood sample as a model of circulating tumours cells. The ratio of MEL cells to human blood cells was set as 1:100 and the concentration of the whole cells was around 5 107/ml. The results of separation of MEL cells from human blood cells in a single process were plotted in supplementary Fig. S4. The purity of MEL cells can be improved from 1.25% to 45.4%, indicating an effective isolation and enrichment of MEL cells. And it demonstrated the ability of our device on the separation and isolation of CTCs from cancer patients' blood sample for the diagnosis and prognosis.

(a) Concentrations of 5-m polystyrene beads and MEL cells from control and two outlets under the flow condition of Rec = 120. (b) Purity of 5-m polystyrene beads and MEL cells before and after a single process by the proposed microfluidic device. (c) Flow cytometric data indicate relative concentration of (i) input mixture of 5-m polystyrene beads and MEL cells, (ii) collection from outlet #1 and (iii) collection from outlet #2. The number near the gated group represents the percentage of group number on the total particle events.

Particle separation in the device reported here relies on the overlap area between inertial lift force dominated region (region I) and DC dominated region (region III) for different-sized particles (Fig. 2b). Normally, small particles have a wider region I and large particles have a wider region III. The overlap between these areas is the working space available for particle separation. It should be noted that the particle mixture is assumed to be diluted and particle-particle interaction is negligible. Smaller and larger particles will migrate to their own equilibrium positions without interfering each other. However, in a dense mixture, the interaction and even collision of particles may affect the focusing process and final focusing width.

Examining the transition region II (Fig. 2) more closely, we observed some intriguing phenomena. At the entrance of this region, apart from two-sided focusing streaks, another clear focusing streak arises at the centre of the channel. This central focusing streak is expected to be the initial result of the DC force. From the intensity profile of fluorescent streaks, most particles are located within these three streaks (supplementary Fig. S5). In contrast to the increasing intensity of the central focusing streak, two-sided focusing streaks have decreasing intensity and move closer to the channel centre at an increasing flow rate. The three streaks finally merge together forming a single central focusing streak.

The cut-off size of particles in our device was around 8m, equivalent to 20% of the channel height. Demonstrated size difference for particle separation were 7m (for 3-m and 10-m particles mixture) and 8m (for 5-m and 13-m particles mixture) respectively. Here we defined that the complete separation happened at the overlap of region I and region III (Fig. 2b). In the actual situation, an efficient separation can still be achieved between region I and region II. In the region II, particles are focused to a band at the channel centre, which have not reached complete focusing. If the lateral distance between this focusing band of large particles and two-sided focusing streaks of small particles is large enough, particle separation can still be achieved with carefully tailored trifurcating outlets. For example, under the condition of a channel Reynolds number of ReC = 120 (Fig. 2a), particles with diameter of 8m are focused at the central area of channel with a width of 37m. Under the same flow condition, 5-m particles are focused at the two sides of the channel symmetrically, 58m away from channel centre, with each streak width of about 15m. So the minimum lateral distance between 8-m and 5-m particle streaks is about 32m, which is still sufficient for particle separation using the right outlet geometry. Therefore, the actual size difference for complete particle separation could be much smaller, even less than 3m.

In our work, due to the assistance from secondary flow, inertial focusing can be achieved within much shorter channel length in a serpentine channel than that in a straight channel24, therefore leading to a smaller device footprint. Although the throughput of a single serpentine channel demonstrated here is 600l/min, which is far less than 1.7ml/min for a state-of-the art spiral channel26, it can be easily scaled up by massive parallelization due to its linear structure. For example, a device with eight parallel serpentine channels can reach a throughput of 4.8ml/min (supplementary Fig. S6). In addition, the separation performance (purity and efficiency) is improved greatly than the reported asymmetric serpentine channel3 and even comparable to the most outstanding inertial microfluidic devices24,29,32. After a detailed comparison of existing inertial microfluidic techniques to our work (see supplementary Table S1), we can conclude that our device holds an integrative advantage over existing ones, including excellent separation purity and efficiency, good parallelizability, small footprint and high separation resolution, although it is not significantly superior over the existing ones on specific single criteria.

Challenges of our work. Since the inertial lift force, secondary flow drag and particle centrifugal force are all proportional to particle size, inertial focusing and separation performance is quite sensitive to particle size. In our work, we found that focusing performance of small particles (3-m) is not as good as large particles (10-m). This can be verified by the fluorescent profile of 3-m and 10-m particles at the outlet (Fig. 3c(ii)). The full width at half maximums (FWHM) of 3-m particles is more than 27mm, which is 9 times of its particle diameter, while the corresponding FWHM value for 10-m particles is less than 20m, only 2 times of its particle diameter. The wide distribution of 3-m particles increases the possibility of contamination on large particles collection. That's why the purity of large particle collection is always worse than small particle collection, while the efficiency is often better. In order to acquire high separation performance for both large and small particles, a more efficient way is needed to improve focusing of small particles, e.g. extension of channel length or modification of channel dimension. Additionally, before separation, quite a lot of tests are needed to determine exact thresholds of three focusing patterns for each sized particles, then to determine available flow condition for separation of specific particles mixture. However, this kind of calibration is necessary for all the inertial microfludic devices until the exact mechanism of inertial focusing process is uncovered.

In conclusion, the proposed inertial microfluidic device is expected to be a good alternative for the conventional separation devices. And it promises a cost-effective, label free and robust method for cell preparation and clinical diagnosis.

Based on our previous study of particle inertial focusing47, we implemented a trifurcating outlet at the end of the channel, so that three different particle streaks could be collected in the corresponding branches. The two-sided symmetrical bifurcations were combined to a single outlet to simplify handling. The device with a single serpentine channel has a footprint of 36mm 5mm. The device was fabricated by standard photolithography and soft lithography techniques. The detailed fabricating procedure was given elsewhere53.

Murine erythroleukemia (MEL) cells were maintained in a complete culture medium (RPMI-1640 medium containing 10% fetal calf serum and 2mM L-glutamine) at 37C and 95% air/5% CO2 as previously described54. In order to visualise the trajectory of MEL cells in the microfluidic device, MEL cells were labelled using PKH26 red fluorescent cell linker kit (Sigma-Aldrich, Product No. P9691) according to the manufacturer's instructions as follows. Cell clusters were removed using a 70-m cell strainer (Becton Dickinson, Product No. 352350) and the single cell suspension was washed twice with serum-free RPMI-1640 medium (400 g for 5min at 22C). Cells (2 107) were then resuspended in 1ml of Diluent C (Product No. G8278) and rapidly mixed with 1ml of Diluent C containing 2 106 M PKH26 ethanolic dye solution (Product No. P9691). Immediately following mixing, 2ml of fetal calf serum was added and the mixture was incubated for 1min. The cells were then washed three times in 10ml of complete medium (400 g for 5min at 22C) and finally suspended in the complete medium at ~4.4 106cells/ml.

Fluorescent polystyrene particles were purchased from Thermo Fisher Scientific. Particles with a mean diameter of a = 3.2m (Product No. R0300, CV5%), 4.8m (Product No. G0500, CV5%), 8m (Product No. 363, CV18%), 9.9m (Product No. G1000, CV5%) and 13m (Product No. 364, CV16%) were suspended respectively in deionized (DI) water. Tween 20 (Sigma-Aldrich, Product No. P9416) with 0.1% w/v was added to prevent particles from aggregation. The weight ratio of particles in the suspension was 0.05%. To conduct the separation of polystyrene beads mixtures, two pairs of beads mixture (3-m/10-m beads mixture and 5-m/13-m beads mixture) were prepared in DI water with 0.1% w/v tween. Their concentrations were listed in Figures 4b and 5b. For testing mixture of MEL cells and 5-m polystyrene beads in the proposed device, 5-m polystyrene beads and PKH26-labelled MEL cells were mixed by a ratio of ~ 1:1 and suspended in phosphate-buffered saline (PBS) with a MEL cell concentration of ~2.46 106/ml. The whole blood was donated from a healthy male. The MEL cells were spiked into the whole blood sample, with a ratio of ~1:100 for the separation of MEL cells from whole blood. The mixture was diluted by PBS to the concentration of the whole cells around 7.5 107 counts/ml.

The microfluidic device was placed on an inverted microscope (CKX41, Olympus), illuminated by a mercury arc lamp. Particle suspension was pumped by a syringe pump (Legato 100, KD Scientific). The fluorescent images were observed and captured by a CCD camera (Rolera Bolt, Q-imaging) and then post-processed and analysed using the software Q-Capture Pro 7 (Q-imaging). The exposure time for each frame was kept constant at 100ms. The concentrations of particles and cells were measured by a hemocytometry. The purity of particle suspensions collected from different outlets was calculated from three measurements by hemocytometry. An LSR II flow cytometer (BD Biosciences) was used to further verify the purity from two collections. The flow cytometer data was analysed using FlowJo software (Tree Star).

Li, M., Li, S., Li, W., Wen, W. & Alici, G. Continuous manipulation and separation of particles using combined obstacle-and curvature-induced direct current dielectrophoresis. Electrophoresis 34, 952960 (2013).

Destgeer, G., Lee, K. H., Jung, J. H., Alazzam, A. & Sung, H. J. Continuous separation of particles in a PDMS microfluidic channel via travelling surface acoustic waves (TSAW). Lab Chip 13, 42104216 (2013).

Zhang, J., Li, M., Li, W. H. & Alici, G. Inertial focusing in a straight channel with asymmetrical expansioncontraction cavity arrays using two secondary flows. J. Micromech. Microeng. 23, 085023 (2013).

Friend, C., Scher, W., Holland, J. & Sato, T. Hemoglobin synthesis in murine virus-induced leukemic cells in vitro: stimulation of erythroid differentiation by dimethyl sulfoxide. Proc. Natl. Acad. Sci. U.S.A. 68, 378382 (1971).

This work was partially supported by the University of Wollongong through a UIC grant and China Scholarship Council. Special thanks are given to Ms. Aleta Pupovac for the technical assistance with MEL cell cultures and dye staining.

J.Z., W.L., G.A. and N.T.N. designed research. J.Z. and S.Y. conducted experiments and analysed the data. R.S. contributed reagents and the MEL cell sample and provided technical assistance on flow cytometer test. J.Z., W.L. and N.T.N. co-wrote the manuscript. All the authors have reviewed the manuscript.

Zhang, J., Yan, S., Sluyter, R. et al. Inertial particle separation by differential equilibrium positions in a symmetrical serpentine micro-channel. Sci Rep 4, 4527 (2014). https://doi.org/10.1038/srep04527

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