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Cite this: DOI: 10.1039/c4lc00367e

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Configurations and control of magnetic fields for manipulating magnetic particles in microfluidic applications: magnet systems and manipulation mechanisms Quanliang Cao, Xiaotao Han* and Liang Li The use of a magnetic field for manipulating the motion of magnetic particles in microchannels has attracted increasing attention in microfluidic applications. Generation of a flexible and controllable magnetic field plays a crucial role in making better use of the particle manipulation technology. Recent

Received 25th March 2014, Accepted 22nd April 2014 DOI: 10.1039/c4lc00367e www.rsc.org/loc

advances in the development of magnet systems and magnetic field control methods have shown that it has great potential for effective and accurate manipulation of particles in microfluidic systems. Starting with the analysis of magnetic forces acting on the particles, this review gives the configurations and evaluations of three main types of magnet system proposed in microfluidic applications. The interaction mechanisms of magnetic particles with magnetic fields are also discussed.

1 Introduction Manipulation of magnetic particles in solution using magnetic fields is an effective technology for transport and localization of micro- and nanomaterials towards targets. 1,2 The inherent advantages of the approach include: (1) multifunctionality. Magnetic particles can be coated with biological molecules to modify surface chemistry and physical properties and further multifunctional capabilities can be prepared by combining with other materials such as DNA and cells.3,4 (2) Targetability. Magnetic particles can be precisely delivered to a target region with local maximum magnetic fields by magnetic forces.5 (3) Controllability. Magnetic particles can be manipulated in numerous ways with the aid of controllable magnetic forces through designing magnetic fields.6 (4) Noncontact. Magnetic particles can be interacted with magnetic fields and magnetic forces wirelessly without direct contact with the magnets. These advantages enable the approach to be initially developed in magnetic drug and gene delivery7,8 as well as magnetic separation9,10 in macroscale applications. The application of the technology in microfluidic systems has attracted growing interest due to the multiple advantages of the microscale effect, such as large surface-to-volume ratio and comparatively fast reaction times. Moreover, magnetic fields become increasingly controlled by the flexible arrangement of external or internal magnets in a microfluidic environment, Wuhan National High Magnetic Field Center, State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan, Hubei, 430074, PR China. E-mail: [email protected]

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and thus, they can effectively enhance the capability of manipulating magnetic particles. Therefore, the magnetic manipulation technology with microfluidics has developed quickly in biological and chemical applications over the last years, and the progress in these areas has been reviewed in a number of excellent papers.11–14 Meanwhile, several reviews are beginning to pay attention to previously often ignored issues of the magnet system design15 and the interactions between magnetism and microfluidics.16,17 In this review, we intend to present a more comprehensive overview of existing magnet systems and the mechanisms of particle manipulation. We start with a discussion on the physical principles of two types of magnetic forces and the magnetic torque acting on the magnetic particles under magnetic fields. Then we summarize the existing magnet systems proposed in the microfluidic applications into three categories based on their spatial relationships with microfluidic devices: external, internal, and hybrid magnet systems. Thereafter we discuss the dynamic behavior of magnetic particles under uniform magnetic fields and gradient magnetic fields generated by these magnet systems for typical microfluidic applications, such as magnetic separation, pumping, mixing and transport. Finally, based on the reviewed results, we offer some suggestions for future developments in the technology of magnetic manipulation for microfluidic applications.

2 Fundamentals of magnetism 2.1 Magnetization   When a magnetic particle is located in a magnetic field of H a , the magnetic particle can be magnetized with a magnetic

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moment aligned to the field direction:   M p   Ha

(1)

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where χ is the magnetic susceptibility, and magnetization  M p refers to the magnetic moment per unit volume. It should be noted that some confusion exists in calculating the magnetization in free space. Two different expressions of magnetic susceptibility are usually used to obtain the magne 3  20,21 Ha . tization:  H a (ref. 18 and 19) and This is  3 mainly because the concept of magnetic susceptibility χ is rather vague. Actually, two types of magnetic susceptibility should be distinguished: intrinsic magnetic susceptibility χp and measured magnetic susceptibility χm. The magnetic susceptibility χ mentioned in eqn (1) is equal to χm and should be defined as the ratio of the magnetization to the applied magnetic field, while the χp is the ratio of the magnetization to the local magnetic field inside the magnetic particle. The intrinsic susceptibility of the material is the common definition of magnetic particles which can be expressed as χp = μp/ μ0 − 1, where μp is the relative permeability of the material and μ0 is the permeability in vacuum ( μ0 = 4π × 10−7 N A−2). In fact, when a magnetic particle is magnetized, the local  magnetic field inside the particle H in can be seen as a superposition of the applied field and the demagnetization field:    H in  H d  H a

(2)

  where H d is proportional to M p but in the opposite direction. For a spherical particle in free space, the demagnetizing 23 field can be described as:  1  Hd   M p 3

(3)

 Then the relation between the magnetization M p and the  applied magnetic field H a can be expressed as:   3 p  M p  m Ha  Ha p  3

(4)

Thus it should distinguish the used magnetic susceptibility  before calculating the magnetization M p . Further, when the magnetic particle is placed in a medium of susceptibility χf, the   relation between M p and H a should be expressed as:24  Mp 

3 p   f  1

  p   f   3   f  1   

 Ha

(5)

 An equivalent bipolar magnetic moment M p is usually obtained to calculate the magnetic force:24  mp  Vp

3  p  f 

  p   f   3   f  1   

 Ha

(6)

In the above equations, the magnetization is assumed to be linear with the applied magnetic field. Actually, the effect of external magnetic field on the magnetic susceptibility χp or χm should be considered, especially in the case of high magnetic fields. When the applied magnetic field is very low, the magnetization curve is nearly linear in Fig. 1(a) and the magnetic susceptibility can be regarded as a constant. But with the increase of the magnetic field, the magnetization and magnetic field are nonlinearly related. Two simple equations can be taken to approximately reflect the nonlinear characteristics of the curve:22

m  Ha  

  Ha  Ms tanh  0  Ha  Ms 

m  Ha  

0 Ms M s   0 Ha

(7)

(8)

Fig. 1 (a) The actual magnetization curve for a type of magnetic nanoparticles of 100 nm measured with SQUID-VSM (Quantum Design). (b) The relationship between M and H for different functions of x(Ha).

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where Ms is the value of saturation magnetization. The two equations are obtained based on the following two fundamental requirements:  m  H a  H a 0

H a

 0

(9)

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χm(Ha)Ha|Ha→∞ = Ms

(10)

It should be noted that the two equations, eqn (7) and (8), can be appropriately chosen based on the actual magnetization curves of magnetic particles. For example, for the magnetization curve in Fig. 1(a), eqn (8) is a better approximation for both in the cases of low field and high field. 2.2 Magnetic forces To understand how the magnetic particles can be manipulated and controlled under magnetic fields, magnetic forces acting on magnetic particles should be analyzed. In essence, the motion of a magnetic particle under magnetic forces is typically induced by two types of energy: the interaction energy between the particles and the magnetic field E H and the interaction energy between particles EM ij , which are expressed as follows:25   E H   m B

EijM 

0 mi m j 4rij 3

(11)

        ni  n j  3 ni  tij n j  tij









(12)

 where m is the equivalent dipolar magnetic moment of each  particle, rij is the magnitude of the vector rij drawn from par  ticles i to j, ni and tij denote the unit vectors given by      ni  mi /mi and tij  rij /rij . Here the particles are treated as magnetic dipoles. According to eqn (11), the magnetic force generated by the interaction of the magnetized particle and magnetic field can be written as:   Fmp    E H    m  B          m B  B  m  m  B  B  m



 















(13)

Since there are no currents induced in the particles, both the third and fourth terms in eqn (13) vanish based on the Ampere law. In addition, the particles have been assumed to have a constant equivalent dipole moment and the second term can be ignored. Then the following expression for the magnetic force can be obtained:    Fmp  m   B





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(14)

When magnetic particles are suspended in a fluid of per  meability μf, the relationship between B and H a is   B  f H a . Then according to eqn (6) and (14), the magnetic force acting on the magnetic particles is:  Fmp  f Vp

3  p  f 

  p   f   3  f 



H  1  

a

   Ha



(15)

According to eqn (15), the particles will be actuated under an attractive force in the case of χp > χf. Inversely, in the case of χp < χf, a repulsive force will be generated. For the common water-based solutions of χf = 0, the magnetic force equation can be reduced to     3 p  0M s Fmp  0Vp H a   H a  0Vp H a   H a (16) 3 p  1 M s  0 H a









From this equation, it can be seen that the magnetic force is related to the physical parameters of magnetic particles (volume and magnetization) and magnetic field (field strength and gradient). Note that for a uniform magnetic field, the magnetic particles will experience no force. According to eqn (12), the magnetic force generated by the interactions between magnetized particles can be written as:    m m Fpp    EijH     0 i 3 j  4rij

      ni n j  3 ni  tij n j  tij 







 

(17)



Considering two neighboring magnetic particles with the same volume in Fig. 2(a), eqn (17) can be replaced by   1  3 cos 2    mm Fpp    E12H    0 1 2    4 r123  

(18)

In a 2D cylindrical coordinate system, the two components of magnetic force can be further expressed as  1  3 cos 2     2 r123  mm   30 m1m2 (1  3 cos  ) Fr   0 1 2  4 4 4r12 r12  1  3 cos 2     r123  mm 1    30 m1m2 (2 cos sin  ) F   0 1 2 4 r12 4r12 4 

(19)

Based on the above equation, the interaction force versus the angle θ and the arrows of the interaction force are shown in Fig. 2(b)–(c). Assuming that the position of the particle m1 remains fixed, the force Fr along the linking line of the two particles is negative when the angle θ is less than 54.73°, which means that there is a magnetic attraction force between the particles. The force Fθ is positive which means the particle m2 will move in a counterclockwise direction, as shown in Fig. 2(c). These are the reasons why the particle

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Fig. 2 The interaction forces of magnetic particles in the two-dipole system. (a) The physical model, (b) the relationship between the interaction forces and the angle θ and (c) the arrows of the interaction forces. The angle θ means the angle between the linking line of the two particles and the direction of magnetic field.

aggregation phenomenon will exist under an applied magnetic field. As shown in Fig. 3, the aggregation behavior of magnetic particles under different magnetic field directions was investigated by use of Monte Carlo algorithms. The distribution of 200 blue particles in a square area shows the initial distribution of particles in the absence of an external magnetic field. After a large uniform magnetic field is applied, the particles (red particles) are redistributed and clustered to form chainlike clusters along the applied magnetic field direction, as shown in Fig. 3(a)–(c). Systematic studies based on the Monte Carlo method have been reported by Satoh's group to analyze the aggregation behavior of magnetic particles under an external static magnetic field.26–28 According to the above analysis, two types of magnetic force acting on the particles would appear when an external  magnetic field is applied. The magnetic force Fmp in eqn (16) should require a gradient magnetic field and can transport the magnetic particles towards a region with maximum mag netic field. The magnetic force Fpp in eqn (17) can be generated as long as magnetic particles are magnetized under a magnetic field and will lead to the aggregation of magnetic particles. Thus the dynamic behavior of movement and

aggregation of magnetic particles could both appear in a gradient magnetic field, while only the latter would appear in a uniform magnetic field. In addition, it should be noted that another interesting motion behavior of rotation or oscillation    will also be induced by the magnetic torque   0 m  H a when an alternating magnetic field is applied, and the behavior can also be used to manipulate the motion of magnetic particles that will be analyzed later.

3 Magnet systems in microfluidics According to the magnetic force equations, eqn (16) and (17),    and the magnetic torque equation   0 m  H a , the dynamic behavior of magnetic particles is directly related to the characteristics of magnetic fields including the direction, strength, and gradient. Thus designing the magnet system (permanent magnet or electromagnet) to generate the required magnetic fields is a key issue to manipulate magnetic particles. Typically, there are mainly three types of magnet system proposed in microfluidic systems: (1) macro-sized external magnet system; (2) integrated internal magnet (micro-sized magnet) system; (3) hybrid magnet system of external magnets and integrated magnets.

Fig. 3 Aggregation behavior of magnetic particles under magnetic field with different directions. (a) The horizontal direction, (b) 45 degrees from the horizontal direction and (c) the vertical direction.

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3.1 Macro-sized external magnet system Macro-sized external magnets have been widely used for delivering drug/gene in vitro and in small animal models, and progress in this area has been reviewed in our previous work.6 Permanent magnets and iron-cored electromagnets are usually taken as external magnets because of their two distinguishing features: (1) permanent magnets can generate a high magnetic field with a small volume and they are a kind of wireless devices; (2) electromagnets have an ability to control the strength of the magnetic field through the flowing currents. Due to advantages of easy fabrication and no heat on-chip, these magnets have been used in microfluidic systems to generate magnetic forces for manipulating magnetic particles.16 Recently a superconducting magnet of 13 T with microfluidic technology has also been proposed to generate a high gradient magnetic field for the separation of two particles via diamagnetic repulsion.29 Compared with the two conventional gradient magnets, the superconducting magnet can generate a higher gradient magnetic field due to a large current flowing in the magnet. However, the superconducting magnet setup is much more complex and expensive which prohibit its widespread use for some time. Since the macro-sized external magnet system can easily generate a wide range of gradient magnetic fields or uniform magnetic fields, two approaches can be taken for magnetic manipulation: (1) External electromagnets with ferromagnetic poles30,31 or permanent magnets32–34 are placed next to a microchannel to directly generate a gradient field. There are two typical applications of continuous flow separation and ferrofluidic pumping: The basic principle of continuous flow magnetic separation methods is to control the flow direction of magnetic particles by manipulating the magnetic force against the hydrodynamic force. 35,36 As shown in Fig. 4(a), when an

Fig. 4 Principle of continuous flow magnetic separation according to Pamme et al.36 (a) Two outlets. (b) Multiple outlets. Different types of magnetic particles can be sorted and separated by a different deflection path under the action of magnetic force. (Reproduced from ref. 36 with permission from the Royal Society of Chemistry).

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external gradient magnetic field is applied, magnetic particles are attracted away from the direction of laminar flow under the magnetic force and then flow into the outlet closer to the magnet, while nonmagnetic particles will move along the initial flow direction.37,38 Multiple outlets in Fig. 4(b) can be used to separate multiple types of magnetic particles39,40 or magnetically labelled cells,41,42 whose deflected angles from the direction of initial flow depend on the external magnetic field, the flow rate and the magnetic properties of particles. In addition, the microfluidic system can be used to manipulate nonmagnetic particles if they are dispersed in magnetic ferrofluids, which was previously introduced by Yellen et al.43 This point can be explained by use of eqn (15), which shows that a magnetic force can be generated, as long as the magnetic susceptibilities of particles and fluids ( χp and χf) are not equal. Based on this, Mao's group has systematically studied the motion behavior of nonmagnetic microparticles in a suspension of magnetic nanoparticles inside a microfluidic channel coupled with external permanent magnets.44–46 Following a similar idea, Xuan's group has demonstrated the effectiveness of sorting of 5 μm and 15 μm diamagnetic particles suspended in a dilute ferrofluid.47 Further, they proposed an enhanced separation of magnetic and diamagnetic particles using an inverted T-shaped microchannel by replacing the water solution with a dilute ferrofluid.48 The enhancement is mainly due to the fact that attraction and repulsion magnetic forces can be generated for magnetic and diamagnetic particles, respectively. The basic principle of ferrofluidic pumping is to actuate ferrofluid plugs through channels using the magnetic force generated by a gradient magnetic field. Based on the wireless behavior of permanent magnets, alternating or rotating micropumps through the mechanical motion of external permanent magnets have been proposed.49–51 For example, Hatch et al.49 proposed a closed-loop ferrofluidic micropump based on two plugs of ferrofluid. One plug was generated and trapped between the channel inlet and outlet by a stationary permanent magnet and can play the role of a closed valve. The other plug was generated and driven by a rotating permanent magnet along the pumping loop, which can be moved to pull and push the fluid through the circular channel for pumping. Another type of micropump can be realized without mechanical moving parts through the controllable gradient magnetic field. By controlling the time and working states of a series of electromagnets, dynamic magnetic forces can be generated to actuate the motion of the ferrofluid.52–54 As an example, in ref. 54, three magnetic bead plugs are formed by external electromagnets, taken as two valves and one plunger to pump the nonmagnetic fluid. As shown in Fig. 5(a), electromagnets M1 and M2 can be used to close (M1 and M2 ON) or open the valve (M1 on and M2 OFF). Three working states of the plunger can be controlled by changing the switch status of electromagnets M3 and M4: left (M2 and M3 ON), right (M2 and M4 ON), and open (M2 ON). The forming mechanism of different plug configurations is that the magnetic force distribution is related to the

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Fig. 5 Principle of a ferrofluidic pump based on magnetic manipulation technology according to Ando et al.54 (a) Magnetic manipulation strategy for operating the valve and plunger. (b) Magnetic actuation sequence with a timing signal for pumping. (Redrawn from ref. 54, © 2009 IEEE).

geometry of external magnets, and the similar behavior of particles under permanent magnets has been qualitatively analyzed by Gassner et al.55 and simulated by Cao et al.56 Then a ferrofluidic pump adopting an externally electromagnetic actuation can be realized to obtain a maximum flow rate of 0.9 ± 0.1 ml min−1 using the consistent translation strategies shown in Fig. 5(b). More details of other ferrohydrodynamic micropumps were reviewed by Nguyen et al.17 Compared with other magnetic actuation approaches, this approach is the simplest way to manipulate magnetic particles. However, the approach has poor control accuracy and limits applicability in microfluidic systems with a high flow velocity due to the generated magnetic forces being not large enough. The relatively large distance between the magnet and microchannel results in a marked drop in the magnetic field strength and gradient. Actually, some studies have been shown to increase the magnetic force by optimizing the magnetization orientation of permanent magnets57 or the geometric parameters of the magnetic tip.58,59 These methods could be used to design external magnets with a better performance for microfluidic applications. (2) External electromagnets or strong permanent magnets are used to generate a uniform magnetic field (or low gradient field) to magnetize the ferromagnetic materials integrated in the microfluidic devices, which can induce strong localized gradient magnetic fields near these materials. The

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basic idea of the approach is known as the high gradient magnetic separation (HGMS) principle that has been widely used for applications such as wastewater treatment and food processing. Based on the approach, Deng et al.60 developed a magnetic filtration system consisting of cylindrical nickel posts with a 7 μm height and a 15 μm diameter in a microfluidic channel. When an external magnetic field generated by one or two permanent magnet system is applied, magnetic particles of 4.5 μm can be trapped around these posts with an efficiency of 95% in a flowing stream at the speed of ~4.4 mm s−1. Microfluidic magnetic separators with the same principle were developed by others for trapping magnetic particles in a fixed position against a fluid flow.61–63 The method can also be used for continuous magnetic separation with magnetic strips or wires.64–67 For example, Han et al.64 designed continuous single-stage and three-stage cascade microseparators by incorporating ferromagnetic nickel wires along the microchannel. By applying a magnetic flux of 0.2 T generated by an external permanent magnet, red and white blood cells were effectively separated in continuous flow at the speed of ~0.1 mm s−1. Another interesting research based on the method was reported by Yu et al.68 for controlling the magnetic field distribution on a micrometer scale. It has been demonstrated that controllable distribution of magnetic particles can be generated by designing the geometric

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parameters of nickel posts and the direction of the external magnetic field, which could be useful for trapping magnetic particles in multiple locations with scattered patterns. Compared with the first approach, although the approach has to be realized with the aid of microfabrication technology, it can obtain more concentrated and strong magnetic forces and thus also plays an important role in microfluidic applications for magnetic separation and trapping,69 especially in the applications of high-throughput70 and nanoparticle trapping.71 In addition to the motion behavior of magnetic particles under gradient magnetic forces described above, magnetic particles with a relatively high concentration will tend to form aggregates under the dipolar particle–particle interactions, which was analyzed in section 2.2. Further, the motion arising in dispersion can be completely controlled by an alternating external magnetic field even without magnetic field gradients under the action of the magnetic torque, which also plays an important role in microfluidic applications. In the last decade, the dynamic behavior of these structures under a rotating external uniform magnetic field has been numerically and experimentally investigated.72–75 Recently, based on these results, rotating magnetic fields and oscillating magnetic fields have been designed and used for particle manipulation in microfluidic applications. Weddemann et al.76 proposed a method to control the flow of magnetic bead agglomerates by changing the orientation of the microfluidic device and magnetic field. On this basis, they applied an external rotating magnetic field of 690 Oe generated by a magnetic stirrer to enhance fluid mixing and separation of magnetic particles in a microchannel (Fig. 6(a)).77 As shown in Fig. 6(b), when there is no external magnetic field applied, the uniformly distributed particles in a T-junction microchannel will flow out of both

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the two diverging outlets. When a rotating uniform magnetic field with an appropriate frequency is applied, magnetic microchains are formed and can be guided to the upper or the lower outlet at the separation junction by controlling the direction of field rotation. The rotating magnetic field can also be used to increase the mixing efficiency due to chaotic advection by rotating magnetic agglomerates at the interface of two fluids in Fig. 6(b). Furthermore, the effects of rotation frequency and magnetic field strength on the separation efficiency were also investigated.78 To achieve more variable control of the chain movement, Gao et al.79 designed and fabricated an octopolar electromagnetic system as shown in Fig. 7(a). Four types of magnetic field have been generated by the device in the experiments of Gao et al.:80,81 (1) an alternating vertical and horizontal uniform magnetic field by applying currents to coils 5 and 8 sequentially, (2) a uniform rotating magnetic field by applying currents to coils 5–8 with values of I5 = Imax sin(2πft) and I8 = Imax sin(2πft + π/2), where Imax is the current magnitude and f is the alternating frequency, (3) an upward gradient magnetic field by applying currents through coils 1 and 3 simultaneously and (4) a horizontal gradient magnetic field by applying currents to coils 5 and 7 or coils 6 and 8 simultaneously. The alternating magnetic field in the case of (1) has been used to disaggregate clusters of magnetic particles80 based on the fact that magnetic repulsion forces between the clustered particles will appear when the angle between the linking line of the clusters and the external magnetic field is 90°, which was explained in Fig. 2. The disaggregation technology can ensure that the magnetic particles are uniformly distributed in an external magnetic field. The gradient magnetic fields in cases (3) and (4) can be used to manipulate the motion of the formed particle chains in a fluid cell, as shown in Fig. 7(b). Thus more chains can be concentrated at the interface of fluids,81 which could induce better chaotic mixing under a rotating magnetic field. Different from the above studies, Li et al.82 investigated the dynamic motion behavior and potential applications of microchains of magnetic particles subjected to an external oscillating field. As shown in Fig. 7(c), the experimental setup for the oscillating field is similar to that of coils 5–8 in Fig. 7(a) but with different types of current supplied to the coils. A DC current was supplied to one pair of coils to generate   a static magnetic field H x  H x x and an AC current to the   other pair to generate a sinusoidal field H y  H y sin  2ft  y with an alternating frequency f. Then the resulting combined     magnetic field H  H x x  H y sin(2ft ) y will oscillate around

Fig. 6 Dynamic behavior of magnetic particle chains in a microchannel.77 (a) Microfluidic device with a T-junction channel and a separation junction (two outlets) for magnetic mixing and separation. (b) Operation principle of magnetic particle chains for separation. (c) Rotation of magnetic particle chains at the interface of two fluids for mixing. (Reproduced with permission from ref. 77. Copyright 2012, AIP Publishing LLC).

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the x axis. A similar oscillating field source has been previously presented by Dreyfus et al.83 to propel a red blood cell attaching a linear chain of magnetic particles with a beating pattern. By using the device, Li et al.82,84 experimentally investigated the motion behavior of magnetic particle chains in the two cases: (1) the phase angle between the chains and the external field in the oscillating process is less than 90°; and (2)

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Fig. 7 External electromagnetic setup for generating alternating magnetic fields. (a) Schematic of an octopolar electromagnetic system for generation of gradient magnetic fields and rotating uniform magnetic fields.81 (b) Manipulation of magnetic particle chains in a fluid cell:81 (1) generation of magnetic particle chains by a static uniform magnetic field. (2) Location of magnetic particle chains in the fluid cell by a static gradient magnetic field. (3) Mixing of two fluids by a rotating magnetic field. (c) Schematic of a quadrupole electromagnetic system for generation of an oscillating magnetic field.82 (Reproduced from ref. 81 and 82 with permission from Springer).

the phase angle exceeds 90°. In the case of (1), oscillating chains can be formed around the x axis following the external AC/DC combined magnetic field under the action of the magnetic torque and inducing hydrodynamic drag. In the case of (2), unlike the roughly synchronous oscillation phenomenon in the case of (1), the oscillating trajectory of chains has been shifted and the oscillating shaft has been changed from the x axis to the y axis due to the magnetic torque acting on the chains becoming negative. It's an interesting phenomenon that has been further investigated to effectively control the steering orientation of micro-swimmers consisting of magnetic particle chains.85 According to the above studies, it can be seen that the dynamic behavior of magnetic chains under an external alternating magnetic field could provide a new strategy to effectively manipulate the magnetic particles in microfluidic systems. Using a similar idea, it has been demonstrated that magnetic cilia microstructures can be effectively actuated by a rotating magnetic field, which can be used to enhance mixing in microfluidic systems.86–88

3.2 Micro-sized integrated magnet system With the development of miniaturization of techniques and instrumentation, integrating microfabricated magnets into microfluidic systems has served an important role in manipulating magnetic particles. Since magnetic fields in microfluidic systems generated by micro-sized permanent magnets can't be removed, micro-electromagnets consisting of single

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or multiple layers of conducting wires are usually used as internal magnetic sources. Early work done by Ahn et al.89 proposed a microfluidic system integrating two meander type micro-electromagnets with magnetic cores on the sides of a microchannel and demonstrated that the generated magnetic force can effectively separate magnetic particles with median diameters of 0.8–1.3 μm under a flow velocity of approximately 1 mm s−1. Later, several types of the micro-electromagnets have been proposed and designed by Ramadan et al. with consideration of the effects of their geometrical and structural parameters on the magnetic field and gradient.90–93 Similar to the external gradient magnetic sources, a micro-electromagnet system can also be used for trapping and separation of particles,94,95 and progress has been reviewed by Basore et al.15 Since micro-electromagnets can provide a way to control magnetic fields at small scales, they can be used for the transport of magnetic particles and micromixing of fluids. Compared with the magnetic separation technology, the tasks of magnetic particle transport are more challenging due to the fact that the transport process can be regarded as a multiple contiguous process of the former. The basic transport principle is to generate a moving maximum magnetic field by programming the currents flowing in series of microelectromagnets,53 similar with the principle of micropumps based on external magnetic sources. With the aid of microfabrication technology, Lee et al.96 reported a microelectromagnet matrix system consisting of 7 × 7 wires to microscopically manipulate and trap magnetic particles with

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Fig. 8 Schematic of integrated electromagnet systems for magnetic particle transport on microscopic length scales. (a) Microelectromagnet matrix consisting of two layers of current-carrying conductors. (Redrawn with permission from ref. 96. Copyright 2001, AIP Publishing LLC). (b) A pair of current-carrying conductors with saw-tooth borders. (Redrawn from ref. 54, © 2004 IEEE). (c) Arrays of microcoils. (Redrawn with permission from ref. 101. Copyright 2006, AIP Publishing LLC).

a diameter of 1–2 μm. By controlling the current in each wire, the system can generate static or dynamic maximum magnetic field patterns to trap, continuously move and join separated magnetic particles suspended in a fluid (Fig. 8(a)). Similar work exists on the on-chip manipulation of biological cells or magnetotactic bacteria.97,98 Another microfluidic transport system combined with two integrated tapered conductors was proposed by Wirix-Speetjens et al.99,100 Maximum magnetic fields can be generated in the corners of the current-carrying tapered conductor and magnetic forces mainly orient perpendicular to the bevel and bottom edges as shown in Fig. 8(b). Thus the magnetic particles can be easily trapped and transported in a wavelike manner by passing a DC current through the two conductors alternatingly. A more straightforward method for moving magnetic particles by use of microcoils was presented by Ramadan et al.101 By individually supplying currents in an array of microcoils in Fig. 8(c), magnetic particles can be moved between the centers of these coils. Based on this method, magnetic particles can be transported over a long distance in one step with a relatively small current due to multiple turns of microcoils but at the expense of location accuracy. Another interesting use of micro-electromagnets is for microfluidic mixing. It is well known that the mixing efficiency of the two solutions in microfluidic systems is very low due to the diffusion behavior becoming dominant while the effect of convection is limited under low Reynolds number conditions. Based on the magnetic manipulation

technique, additional agitation and chaotic advection, pioneered by Rida et al.102 and Suzuki et al.,103 have been added in the fluid flow to enhance the mixing behavior in microfluidic systems. Rida et al.102 fabricated a special electromagnet that consists of an external electromagnet and two soft magnetic tips integrated in the microfluidic channel, which is regarded as one type of micro-electromagnet here. By using the device, a static gradient magnetic field was firstly generated in the microchannel to form a plug of magnetic particles resisting the fluid flow. Then a sinusoidally varying gradient magnetic field was applied with an appropriate frequency; the plug will be shifted up or down periodically in a loose way under the alternating magnetic force. During this process, a vortex-like fluid motion could be induced similar to mechanical agitation in the microchannel and then the mixing efficiency can be improved significantly. Suzuki et al.103 developed a micro-electromagnet system with integrated conductors at the bottom of the microchannel. When a time-dependent magnetic force is generated by these conductors, chaotic advection can be induced in the microchannel to enhance mixing. The key issue of chaotic mixing is to create stretching and folding by applying an oscillatory force to attract the particles and then push them back (Fig. 9(a)). However, only an attractive magnetic force could be generated in the flow channel by an integrated coil and thus particles would be retained in the sides of the channel (Fig. 9(b)). To realize the oscillatory mode of motion in Fig. 9(a),

Fig. 9 Chaotic behavior of magnetic fluids under magnetic forces for microfluidic mixing.103 (a) Principle of creating stretching and folding by the use of attractive and repulsive forces. (b) Transport behavior of magnetic particles under an attractive force generated by a single current-carrying conductor. (c) Arrays of conductors for producing chaotic mixing with a time-dependent control signal. (Reproduced from ref. 103, © 2004 IEEE).

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a row of integrated conductors was used in the work of Suzuki et al.103 Since the magnetic particles are attracted towards the region between the two parallel conductors with opposite currents, take the paths of ① and ② as examples, the magnetic nanoparticles will be transported along the direction of path ① when currents are applied to conductors 3 and 4 in Fig. 9(c). The trajectory of path ② can be obtained when currents flow in conductors 2 and 3. Then stretching and folding can take place by changing the currents in different pairs of conductors through switching on/off currents periodically, yielding a favorable situation for mixing. Several micromixing systems based on the two similar principles were later presented by others.104–106 Compared with mixers driven by an external electromagnet,107,108 the length of mixing channels can be significantly reduced while maintaining a high efficiency. There are two major challenging issues in microfluidic applications of on-chip magnets. One is the inevitable Joule heating effect due to the relatively high current density for producing strong magnetic force. Typically, three conventional ways can be used to reduce the heat problem: (1) by optimizing geometrical parameters of micro-electromagnets including consideration of a ferromagnetic core to obtain the maximum magnetic force per unit of heating power;109–111 (2) by applying an external uniform magnetic field to enhance the magnetic field generated by the micro-electromagnets as well as the magnetic force per unit of heating power;112 and (3) by using a large substrate with a high thermal conductivity (such as copper113 and silicon103) to share the generated heat. Recently, several microfluidic cooling systems based on the principle of heat transfer have been proposed for magnetic manipulation of particles and cells by use of cooling channels114 or a thermoelectric cooler.115,116 Compared with the conventional ways, the approach with the aid of cooling systems could be more efficient when larger currents are required due to the fact that the generated Joule heat can be dissipated timely by a coolant or a heat exchanger. Furthermore, a precise temperature in microfluidic environments can be controlled by measuring and monitoring the temperature in time using thermoelectric devices and the appropriate circuitry, which will be useful for developing on-chip magnetic manipulation techniques in cell biological applications. The other challenging issue is the integration of microfabricated magnets into microfluidic devices. Embedding conventional permanent magnets into microfluidic systems is a simple and low-cost construction without complex microfabrication process, but at the expense of control accuracy and flexibility, and is limited to magnets with a size of at least about 1 mm (taken as macro-sized external magnets in section 3.1). Actually, multiple fabrication steps and complex technologies such as electron beam evaporation and electrodeposition are usually used for integrating micromagnets (micro-electromagnets or thin film magnetic materials) into microfluidic systems. To meet the needs of low-cost and simple fabrication, several methods have been reported recently. For example, Derec et al.113 proposed a novel approach to fabricate a microchannel and micro-electromagnet system for

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magnetic separation at the same time based on printed circuit board (PCB) technology. Rahbar et al.88 developed a simple fabrication technique for integration of artificial cilia directly inside the microfluidic system, which is based on a new micromolding and sacrificial polyethylene glycol (PEG) fabrication process. It is encouraging to note that the magnetic nanocomposite polymers (M-CPs) have been employed for microfluidic applications, which may offer solutions to difficult microfabrication and integration of magnetic materials into microfluidic devices. More details of the applications and fabrication process of M-CPs as well as advantages have been reviewed by Gray et al.117

3.3 Hybrid magnet system In the previous sections, external and internal magnet systems have both demonstrated the feasibility for the manipulation of magnetic particles in microchannels and used widely in microfluidic applications of magnetic separation and trapping. Actually, there are strong complementarities in the properties of the generated magnetic fields between the two types of magnet system, which is based on the fact that micro-electromagnets can produce a high magnetic field gradient with a low magnetic field, while a relatively high magnetic field can be generated easily by external permanent magnets or electromagnets. Thus combining micro-electromagnets and external magnets into a hybrid magnet system should be beneficial for microfluidic applications. There are mainly two evident features of the hybrid magnet system: (1) an external uniform magnetic field can be used to make up for the low magnetic field and thus can further increase the magnetic actuation force. (2) The magnetic field and field gradient can be dominated and controlled by micro-electromagnets and external magnets, respectively, and thus more types of magnetic force distribution can be obtained. The second feature is very interesting and important for manipulating magnetic particles in microfluidic systems. Take the micro-electromagnetic ring for example; it has been reported that the magnetic particles can be trapped into and repelled out of the center of the ring by changing the currents in the micro-electromagnet with a uniform external magnetic field,118,119 which neither an external magnet system nor an internal magnet systems can do. Similar with the internal gradient magnetic sources, the hybrid magnet system can be used for the microfluidic transport of magnetic particles. Deng et al.120 proposed a hybrid magnet system consisting of two serpentine wires and an external uniform magnetic field to transfer 4.5 μm microbeads with a step size of 100 μm. When there is no external magnetic field, the maximum magnetic field will be generated in each corner of the wire with opposite directions in neighboring corners. Such a situation is not effective for transport of magnetic beads due to an uncertain trap location having a lack of regularity. By applying an external magnetic field, the magnetic field distribution can be changed and the maximum magnetic field will appear at an interval of one corner. Then magnetic particles can follow those field

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Fig. 10 Schematic of hybrid magnet systems for magnetic particle transport on microscopic length scales. (a) A pair of current-carrying conductors in a serpentine shape for generating gradient field and an external uniform magnetic field for controlling the distribution of the maximum field. (Redrawn with permission from ref. 120. Copyright 2001, AIP Publishing LLC). (b) Two parallel arrays of planar microcoils with partial overlapping for generating an alternating gradient magnetic field and a relatively large external uniform magnetic field for enhancing the magnetic force.112 (Redrawn with permission from ref. 112. Copyright 2003, AIP Publishing LLC). (c) Two perpendicular pairs of planar microcoils for location and actuation of ferrofluid droplets by the combination of a uniform magnetic field.121 (Redrawn with permission from ref. 121. Copyright 2006, AIP Publishing LLC).

maxima and moved in a wavelike manner by sequential activation of currents flowing in the upper and lower wires (Fig. 10(a)). Later, Rida et al.112 reported a magnetic transport system on a larger scale by use of two arrays of planar coils and a uniform magnetic field generated by two permanent magnets with a soft magnetic steel sheet. The external magnetic field was used to enhance the magnetic force and generate a removable maximum magnetic field to attract and move magnetic particles by the combination of the spatial overlap coils in a specific sequence in Fig. 10(b). It should be noted that the particles could be moved towards the left or the right due to the repulsive force generated by the neighboring coil before the particles move into a new center. Thus an oscillatory field has also been considered to transport all magnetic microbeads in a given direction.

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Following a similar principle, a simple concept for manipulating ferrofluid droplets was reported by Nguyen et al.121 As shown in Fig. 10(c), the front pair of planar coils with the same current signs is used to trap a ferrofluid droplet in the central region of a virtual channel. The back pair of planar coils with opposite current signs is taken to generate a gradient magnetic field along the x-axis to drive the droplet. The relatively large external uniform magnetic field is used to enhance the magnetic force and keep the magnetic moment of the ferrofluid droplet in one direction. Thus the straight reciprocating motion of the ferrofluid droplet can be realized by just changing the current direction of the back coils. Further, more details about the mechanism of magnetic manipulation and kinetic characteristics of the droplet during movement were also investigated numerically and experimentally by his research group.122,123

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external magnetic field along the negative y-axis, the magnetic nanoparticles can be concentrated in the regions near the corners of the two microcoils as shown in Fig. 11(c). The motion behavior has been used as an approach for a bidirectional actuation of the ferrofluid by Assadsangabi et al.126 Furthermore they have realized a micropatterned controllable inductor based on the similar actuation principle.127 The external uniform magnetic field in the existing hybrid systems is usually generated by permanent magnets, which are invariable in both the direction and intensity of the field. Actually, based on the above results, it can be supposed that more different movement trajectories of magnetic particles can be obtained through adjusting the external magnetic field parameters. Thus further developments to work with the hybrid system should consider the use of controllable external magnetic fields, which could be generated and controlled in two/three dimensions by typical two/three orthogonal Helmholtz coil pairs128 or other coil pairs with iron cores similar to coils 5–8 in Fig. 7(a). Fig. 11 Distributions of magnetic nanoparticles in a microchannel under a hybrid magnet system with different external magnetic fields.124 (a) No external magnetic field. (b) Applying an external magnetic field of 50 mT along the x-axis. (c) Applying an external magnetic field of 50 mT along the negative y-axis. (Reproduced with permission from ref. 124. Copyright 2013, the Japan Society of Applied Physics).

Based on the above microfluidic transport systems, it can be seen that controlling the repulsive and attractive magnetic forces generated by the hybrid system is important for effective manipulation of magnetic particles. For example, the field gradient between the centers of the two actuation coils in Fig. 10(c) was designed to have the same sign to ensure that the two magnetic forces do not occur simultaneously. Thus the ferrofluid droplet can be driven in just one prescribed direction. Actually, the magnetic force distribution generated by the hybrid magnet system is also directly related to the external uniform magnetic field besides the internal gradient magnetic field. In our previous work, the influence of an external magnetic field on the concentration distribution of magnetic nanoparticles as well as the magnetic force based on a hybrid system have been numerically analyzed.124 As shown in Fig. 11(a), when there is no external magnetic field, the magnetic particles are attracted towards the middle of the two microcoils carrying currents in opposite directions under the magnetic force. When an external magnetic field is applied, the magnetic force distribution in the microchannel was changed. With the aid of a field along the x-axis as shown in Fig. 11(b), a repulsive force and an attractive force can be generated in the upper regions of the microcoils, respectively, transporting the magnetic particles from left to right and producing one low concentration region and one high concentration region. A similar motion behavior under a hybrid gradient magnetic field has previously been used to separate magnetic particles from a flow stream into just one outlet at a Y-shaped junction.125 Further, in the case of an

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4 Conclusion and outlook In this paper, we have reviewed magnet systems combined with microfluidics and the interactions between magnetic particles and magnetic forces in a variety of ways. It could be seen that there have been exciting achievements in microfluidic applications with the technology of magnetic manipulation through considerable research efforts in improving magnet systems and particle transport mechanisms in solution. To further promote the development of magnetism in microfluidics, some comments and suggestions are put forward based on the above-reviewed results: (1) There have been many approaches for manipulating the motion of magnetic particles for different microfluidic applications based on the three types of magnet system. However, they were not widely promoted due to an interdisciplinary background which has restricted their use with respect to the applications. For example, the approach by use of the HGMS principle discussed in section 3.1 has been mainly used for magnetic trapping and separation, while it can also play an effective role in magnetic mixing. By applying a time-dependent current to the external electromagnets, periodic magnetic forces can be generated around an integrated ferromagnetic wire or needle and used to make the particles or solution oscillate for mixing. Compared with the existing micromixing approaches, this approach may work more effectively due to the relatively large magnetic force and absence of heat induced in microfluidic systems. (2) Two types of magnetic forces, generated by the interaction of particles with magnetic fields and dipolar coupling interaction between particles, have both shown their respective merits for controlling the dynamic behavior of magnetic particles in static. A more effective approach in some specific microfluidic applications can be realized by an intentional combination of the two magnetic forces. For example, a gradient magnetic force has been applied to adjust the position

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of the rotating magnetic particle chains induced under a uniform magnetic field.80 Further the approach can be used to produce an additional movement during rotation of the chains. (3) There is an inevitable Joule heating (temperature) issue induced in microfluidic systems by use of integrated microelectromagnets for generating much larger magnetic forces. Actually, the temperature acts as a double-edged sword in the microfluidic applications such that: (1) the solution viscosity decreases with increasing temperature, thus leading to an increase in the magnetically induced velocity to improve the efficiency of magnetic separation.129 (2) However, an increased temperature in microchannels may damage biological samples during the manipulation process. Thus temperaturecontrollable methods such as adjusting the input flow rate of the coolant114 or current in the electromagnet130 should be developed with a cooling system for solving the issue well. (4) The hybrid magnet system can play an important role in the manipulation of magnetic particles in microfluidic systems. The system has decoupled the parameters of magnetic field strength and gradient, and thus the two components can be separately controlled to produce magnetic forces with various distribution modes. The system has been developed for attractive and repulsive forces by switching the direction of current flow in a single micro-electromagnet,118,119 and the manipulation strategy can be well used for micromixing without multiple micro-electromagnets in the work of Suzuki et al.103 It should be interesting to further consider the interaction between the external and internal magnetic fields to investigate the effects of the external magnetic field direction and the geometry configurations of micro-electromagnets on the dynamic behavior of magnetic particles.

In addition, there are many interesting and challenging issues arising from the magnetic aggregation behavior of particles due to the significant dipole–dipole interactions. For example, an interesting issue is the possibility of separating and sorting magnetic nanoparticles. Current research focuses on the separation of magnetic microparticles in microfluidic applications (Table 1), primarily because the gradient magnetic forces generated by most existing magnet systems are not large enough to manipulate particles on the nanometer scale. Recently, the possibility of low gradient magnetophoretic separation of magnetic nanoparticles with the aid of aggregation behavior has been demonstrated.131–133 The mechanism of separation enhancement is that the aggregation behavior can result in nanoparticles forming aggregates which could be seen as equivalent microparticles. Although the present method may be effective in trapping nanoparticles of a single size, it is hard to cleanly separate each type of nanoparticle from complex mixtures.133 This is mainly due to the fact that the aggregation behavior would occur among magnetic particles with different sizes, which makes it difficult to distinguish different types of nanoparticles. Further in-depth studies should be taken to understand the aggregation behavior in mixtures of nanoparticles with different sizes and concentrations under gradient magnetic fields,134 which will help in designing appropriate system parameters, such as nanoparticle diameters and magnetic field strength, to separate multiple types of nanoparticles from complex mixtures. Another interesting issue is avoiding the aggregation of magnetic microparticles for microfluidic applications, which is the inverse of the above discussion. Actually, the aggregation behavior will give rise to some problems in the continuous magnetic separation process. Apart from the separation

Table 1 A selected series of references which have given the detailed system parameters, such as the properties of magnetic particles and magnetic forces

Magnet system (MS) Magnet geometry External MS

Integrated MS

Permanent magnets (8 mm high, 2 mm long and thick) Nickel wire arrays with external magnetic field Micrometric iron beads with an external magnetic field Assembly of permanent magnets (3 mm length, 1 mm diameter) Meander coil Square parallel coils with/without magnetic pillars Circular spiral coil with/without magnetic pillars Micro-coil arrays

Application

Magnetic particle

Magnetic trapping

Diameter: 1 μm, magnetic susceptibility: 1

~100 pN, 0.33 mm s

55

Magnetic manipulation Magnetic trapping

Diameter: 1.05 μm, magnetic susceptibility: 1.52 Diameter: 30 nm (10 wt.% of magnetite) Diameter: 1 μm, magnetic susceptibility: 1.377 Diameter: 2 μm, magnetic susceptibility: 0.245

~250 pN to 1 nN,a 12.5 mm s−1b ~0.2 pN,a 4.6 mm s−1b

68

~50 pN,a 10 mm s−1b

135

Sample purification Magnetic separation and transport

a

Array of planar coils and an external field

a

Ref. −1b

a

~20 pN ~30/700 pNa

71

91

~175/2000 pNa

Magnetic manipulation Copper conductor in an integrated Magnetic separation microcircuit

Hybrid MS

Key parameters

Magnetic transport

Diameter: 2.8 μm, magnetic susceptibility: 0.17 Diameter: 5 μm (10 wt.% of magnetite), magnetic susceptibility: 0.2 Diameter: 1 μm, magnetic susceptibility: 0.94

1–10 pN,a 1.33 mm s−1b

94

14 pN,a 0.56 mm s−1b

113

~0.5 pN,a 10 mm s−1c

112

Calculated magnetic force. b Fluid velocity in the experiment. c Particle transport velocity.

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difficulty of multiple types of particles (as mentioned above), non-target particles (impurities) will physically remain in the aggregated particles, resulting in a relatively low separation purity. Further, the aggregated microparticles could cause the problem of adhesion to microchannel walls. Thus, for magnetic microparticles, avoiding the aggregation behavior in the separation process should be a good way to solve these problems since each individual microparticle can be manipulated in the existing microfluidic system without the help of the aggregation behavior. Most of the existing studies on the magnetic separation of microparticles are usually carried out in the case of low particle concentrations to minimize the influence of the aggregation behavior, while high magnetic particle concentrations may be used in practical applications and thus the problem still remains. It could be interesting to introduce an alternating magnetic field instead of a static way for regulating the magnetic dipole–dipole interactions among microparticles,80,135 which could inhibit the aggregation behavior and realize the magnetic separation of microparticles in a dispersed way. In conclusion, we would like to emphasize the importance of magnet design and manipulation mechanisms of particle motion in microfluidic applications as well as the interweaving and evolution of different approaches. We hope more researchers with an interdisciplinary background can be involved in the area and believe that a wider breakthrough of magnetic manipulation technology for new microfluidic developments will exist. Table 1 lists several references with the detailed parameters of the particle and magnetic force to provide some design data in microfluidic applications.

Acknowledgements The authors gratefully acknowledge financial support from the National Natural Science Foundation of China (51077064) and the Program for New Century Excellent Talents in University (NCET-13-0225).

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