Recent advances in manipulation of micro- and nano-objects with magnetic fields at small scales

Quanliang Caoab, Qi Fanab, Qi Chenab, Chunting Liuab, Xiaotao Han*ab and Liang Li*ab
aWuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, China. E-mail: xthan@mail.hust.edu.cn; Liangli44@mail.hust.edu.cn
bState Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Wuhan, 430074, China

Received 9th May 2019 , Accepted 11th September 2019

First published on 11th September 2019


Manipulation of micro- and nano-objects has been widely studied in the past two decades due to its potential applications in various fields. In this review, we focus primarily on magnetic field-based manipulation techniques, which have shown to be extremely promising for the motion control of such objects at small scales. We start from the fundamental analysis of the magnetic forces and the torques acting on objects subjected to magnetic fields, and then summarize the most recent contributions in magnetic manipulation employed in four typical applications: micro-mixing, trapping, colloidal assembly, and object transport. Moreover, how magnetic fields can be applied to object manipulation and the physical principles underlying these manipulation processes are highlighted.


1. Introduction

The manipulation of micro- and nano-objects has attracted widespread attention in various fields including (but not limited to) chemistry, materials, biology and medicine.1–4 The great progress in this area has benefited from the unique ability of minute objects to operate in small environments and from the multiple distinct advantages of their use in miniaturized regions of interest, such as lower sample/reagent consumption and energy consumption, and shorter time analysis. A key requisite for the existing investigations is to control the motion of micro- or nano-objects at small scales, usually via the use of several types of external fields, such as the electric,5–7 magnetic,8–10 optical11–13 and acoustic fields.14–16 Here, we review the most significant recent advances and the new developments in the field of object manipulation via magnetic fields. The studies in the past few years are highlighted in more detail.

Magnetic field-based manipulation has been an interesting and widely used technology due to the following advantages: (1) magnetic fields can penetrate non-magnetic or weakly magnetic materials that are used for fabricating microfluidic devices (such as glass and polydimethylsiloxane) or biological matter. Therefore, micro- and nano-objects in enclosed environments can be effectively manipulated in a non-contacting manner; (2) magnetic fields can be used to manipulate and identify both magnetic and non-magnetic objects with different physical properties. For instance, non-magnetic objects can be manipulated via the use of magnetic labels,17,18 or a label-free method with the aid of magnetic fluids.19,20 Moreover, particles with different shapes may exhibit different magnetic forces and torques in a magnetic field,21–24 and this results in a difference in the particle motion behavior in microfluidic channels; (3) multiple types of magnetic fields can be generated and well controlled at small scales, and therefore, magnetic manipulation can be achieved in a variety of ways. There exist three main types of magnetic systems: external macro-sized magnets, integrated micro-sized magnets, and hybrid magnet systems with external and integrated magnets.25 Both static and dynamic magnetic fields, such as rotating and oscillating fields, have been used to achieve different manipulation functions, which can be easily realized via electromagnets with coil current control26–28 or via the mechanical motion of permanent magnets.29–31 Moreover, according to their spatial distribution characteristics, these magnetic fields can be further divided into uniform and gradient magnetic fields. Therefore, over the past two decades, researchers have focused their studies on the use of magnetic manipulation in a variety of applications, and the progress in these areas has been reviewed in a number of excellent papers in multiple disciplines.32–39 However, the majority of them focuses on the object manipulation via one single magnetic action, such as a gradient magnetic force/torque, or on object manipulation for a particular application.

In this work, we provide a full picture of the most recent advances in micro- and nano-object manipulation using magnetic fields from the perspective of manipulation methods and mechanisms. Initially, we focus on the use of actuation forces and of torques to describe the manipulation of objects via magnetic interactions between the magnetic field and the objects, and among the objects themselves. Then, four representative applications, micro-mixing, trapping, colloidal assembly and object transport, are analyzed in detail. Finally, we end the review with conclusions and several suggestions for future developments.

2. Fundamentals and principles

Typically, there exist three ways to manipulate micro- and nano-objects placed in a magnetic field: the use of (1) a gradient magnetic force, (2) a magnetic interaction force between objects, and (3) a magnetic torque. Note that the magnetic interaction force is actually one special type of gradient magnetic force. In this case, the field gradient is induced by the surrounding objects and the force disappears if a single object is present in the field. The objects that can be manipulated in these cases can be magnetic liquids, magnetic/non-magnetic particles, and micro/nanorobots or biomolecules and cells. In the following analysis, we focus on the use of particles as an example to describe how magnetic forces and torques act on them when they are subjected to different types of magnetic fields.

2.1 Gradient magnetic force

The magnetic force acting on an isolated particle in a fluid subjected to a gradient magnetic field can be expressed as follows:40
 
Fm = μ0((mpmf)·∇)Ha (1)
where μ0 is the permeability of free space, ∇ represents the Hamilton operator, Ha is the value of the applied magnetic field where the particle is located, mp and mf correspond to the magnetic moment of the particle and to the effective moment of the liquid surrounding the particle, respectively. If the particle is spherical and subjected to a linear magnetization condition, an equivalent point dipole moment, meq, expressed via the low-field measured susceptibility of the particle and of the fluid (χp and χf), can be applied to calculate the force:41
 
image file: c9mh00714h-t1.tif(2)
 
image file: c9mh00714h-t2.tif(3)
Here, Vp corresponds to the particle volume. According to these equations, the following two conclusions can be drawn: (1) a magnetic field gradient is necessary to generate the magnetic force acting on a particle. One way to achieve this goal is to directly produce a gradient magnetic field via the use of magnets, including permanent magnets, electromagnets, and superconducting magnets, as schematically shown in Fig. 1a. Another way is to use the magnetization difference between an auxiliary element and the surrounding media under a uniform magnetic field. These two implementation approaches can be used to achieve this goal, as shown in Fig. 1b and c. In Fig. 1b, an auxiliary element made of high-permeability magnetic materials is used to produce a local strong gradient magnetic field. This is a well-known effective approach to generate high gradient magnetic fields. In Fig. 1c, an auxiliary element made of non-magnetic materials and a magnetic fluid (paramagnetic salt solution or ferrofluid) as the surrounding media are used. A gradient magnetic field is generated around the element, due to the locally distorted field induced by the external uniform magnetic field. (2) Both magnetic and non-magnetic particles can be manipulated via gradient magnetic fields as long as there is a difference in magnetization between the particle and the surrounding liquid. A non-magnetic particle, for example, experiences a nearly-zero net magnetic force in water when a gradient magnetic field is applied. Contrarily, it can be well manipulated once it is suspended into a magnetic fluid. The phenomenon can be used for label-free manipulation of non-magnetic objects, which is known as negative magnetophoresis.34,39 The direction of the magnetic force is determined by the sign of the difference between the magnetization of particles and that of the surrounding fluid. As shown in Fig. 1, the particles are driven toward the location where the magnetic field is higher due to the gradient magnetic force, when mp > mf. Contrarily, when mp < mf, the direction of the magnetic force is reversed, while the other conditions remain unchanged, and the particles move toward the location having a minimum magnetic field. This phenomenon can be well understood via the analysis of the magnetostatic potential energy. For the particles represented in Fig. 1, the potential energy, Ui, can be expressed as
 
image file: c9mh00714h-t3.tif(4)

image file: c9mh00714h-f1.tif
Fig. 1 Magnetic field distribution and schematic of the motion of particles P1 and P2 in a fluid subjected to: (a) field gradient generated via an external magnet; (b and c) field gradient generated via an auxiliary element under an external uniform magnetic field. The magnetic susceptibility of the element is larger than that of fluid in (b) and the reverse in (c).

From this formula, one can notice that the potential energy is negative for particle P1 and positive for particle P2. Therefore, the two particles respectively move towards the regions where the maximum and minimum magnetic fields are located to achieve a higher stability by using the minimum energy.

2.2 Magnetic interaction force between particles

The physics principle of the generation of the field gradient for magnetic interparticle force (magnetic dipole–dipole force) is similar to that shown in Fig. 1b and c, where each particle plays an equivalent role as the auxiliary element. As shown in Fig. 2, a magnetic field gradient can be generated around each particle having a different magnetization than that of the fluid. The force acting on each particle and the particle motion behavior can be understood by analyzing the interaction energy among the particles. For particles Pi and Pj suspended in a fluid, the expression of their interaction energy can be written as follows:42
 
image file: c9mh00714h-t4.tif(5)
where μf is the magnetic permeability of the fluid, rij represents the magnitude of the vector rij drawn from the position where Pi is located to that of Pj, mi and mj are the equivalent dipole moment of particles Pi and Pj, respectively, which can be obtained via eqn (2) assuming that they are linearly magnetizable spherical particles. Three possible cases can be defined depending on the values of the parameters in eqn (5):

image file: c9mh00714h-f2.tif
Fig. 2 Magnetic field distribution and magnetic interaction force among particles in a fluid subjected to an externally applied magnetic field. (a) Identical magnetic particles (particle P1) are suspended in a non-magnetic fluid. (b) Identical nonmagnetic particles (particle P2) are suspended in a magnetic fluid. (c) Magnetic and non-magnetic particles are suspended in a magnetic fluid.

(1) The two magnetic particles are identical (mi = mj) and they are suspended in a non-magnetic fluid (χp > χf = 0). In this case, the magnetic energy between them and their corresponding interaction force can be described via the following equations:25

 
image file: c9mh00714h-t5.tif(6)
 
image file: c9mh00714h-t6.tif(7)
 
image file: c9mh00714h-t7.tif(8)
where m1 corresponds to the absolute value of mi and mj for the two magnetic particles, θ means the angle between the linking line of the two particles and the direction of magnetic field, er represents the coordinate variable along the linking line of the two particles and eθ in a cylindrical coordinate system. The magnetic force component along er has a negative value when 0° ≤ θ < 54.73°, showing that the interparticle interaction is attractive. Inversely, the interparticle interaction is repulsive when 54.73° < θ ≤ 90°. Two examples for the interparticle interaction in this case are illustrated in Fig. 2a.

(2) Two identical non-magnetic particles are suspended into a magnetic fluid (χf > χp = 0). In this case, the magnetic energy and the interaction force between the particles can be calculated via the following equations:

 
image file: c9mh00714h-t8.tif(9)
 
image file: c9mh00714h-t9.tif(10)
 
image file: c9mh00714h-t10.tif(11)
where m2 corresponds to the absolute value of mi and mj for the two non-magnetic particles. When compared to case (1), the direction of the equivalent particle magnetization changes, but the trend of the energy and of the magnetic force as a function of the angle, θ, remains unchanged, showing that the interaction between non-magnetic particles coincides with that of the magnetic ones.

(3) Magnetic and non-magnetic particles are suspended in a magnetic fluid (χp1 > χf > χp2 = 0). In this case, the magnetic energy and the interaction force between the particles can be calculated via the following equations:

 
image file: c9mh00714h-t11.tif(12)
 
image file: c9mh00714h-t12.tif(13)
 
image file: c9mh00714h-t13.tif(14)
 
image file: c9mh00714h-t14.tif(15)
where m1 and m2 represent the absolute value of the equivalent magnetization for the magnetic particle and the non-magnetic particle, respectively. When these expressions are compared with cases (1) and (2), one notices that the trends of the energy and the magnetic force as a function of the angle, θ, are different, due to the opposite magnetization directions of the two particles. The particle interaction is repulsive when 0° ≤ θ < 54.73° and attractive when 54.73° < θ ≤ 90°. For instance, when the magnetic particle and the non-magnetic particle are aligned along the direction of the magnetic field, they are subjected to repulsive forces (Fig. 2c), whereas in all the other cases, they are attracted to each other (Fig. 2a and b).

2.3 Magnetic torque

The magnetic torque acting on an isolated particle in a fluid subjected to a magnetic field can be expressed as follows:43
 
Tm = μ0(mpmf) × Ha (16)
where Tm is the magnetic torque. A magnetic torque for both magnetic and non-magnetic particles can be induced as long as the equivalent magnetic moment (mpmf) of the particle is not zero. Moreover, the generation of a magnetic torque is independent of the presence of a magnetic field gradient.

In this review, the most common case with magnetic particles suspended in a non-magnetic fluid is presented in the following analysis. The magnetic torque acting on a magnetic particle is non-zero when the particle magnetization is not aligned with the applied magnetic field. Magnetic torques can be used to manipulate objects which present either geometric anisotropy, such as ellipsoid-shaped and rod-shaped structures,44,45 or magnetic anisotropy, such as magnetic particles with pinned magnetic moments and Janus particles.46,47 The generation mechanism of a magnetic torque in particles with a geometric anisotropy is related to the demagnetizing field. Furthermore, the demagnetization factor is associated with the particle shape, resulting in an anisotropic magnetization.48 Generally, the magnetic torque tends to deflect the long dimension of the particles toward the direction of the magnetic field. Magnetic spherical particles with self-assembled chain structures are included in the anisotropic case. According to eqn (16), once the direction of the magnetic dipole moment of the particle is collinear to the applied field line, the particle stops moving under the action of a static magnetic field. Therefore, if the particles are manipulated continuously via a magnetic torque, dynamic magnetic fields, such as rotating and oscillating magnetic fields, are typically required in the applications.

3. Magnetic mixing

Microfluidic systems have attracted significant attention over the past two decades, and have become more and more popular in chemistry, biology, medicine, and other related fields.49–51 However, in practical applications, rapid and efficient mixing of fluids or suspended objects under micro-environmental conditions is a challenge due to the low rate of diffusive transport at low Reynolds numbers. Therefore, micro-mixing enhancement technologies are typically required for most microfluidic systems, particularly for applications such as in chemical reactors, biological analysis, chemical synthesis and polymerization.52,53 In general, the mixing performance can be enhanced by using either passive techniques via the design of channel geometries to improve either the chaotic advection effect or the contact area between the fluids,54–56 or active techniques via the introduction of external driving fields to disturb the fluid flow.57–59 Among these variety of methods, the mixing techniques based on magnetic fields and magnetic particles triggered considerable attention. These methods can be categorized into two main classes: mixing via magnetophoresis and mixing via magnetic stirring. Each method is analyzed in the following sections.

3.1 Mixing via magnetophoresis

Magnetophoresis is a simple way to improve mixing efficiency via the use of gradient magnetic forces. According to the principle of force generation, this type of mixing method can be further divided into two categories:

(1) Magnetic forces generated via a magnetic field gradient in an externally applied non-uniform magnetic field. In this case, permanent magnets and magnetic fluids containing magnetic nanoparticles are commonly used in the experimental studies. During the mixing process, additional flows can be induced by the motion of the magnetic fluids under the action of magnetic volume forces or via the motion of magnetic particles, which results in an improvement of the mixing performance.60–64 For example, Nouri et al.61 numerically and experimentally investigated the mixing performance of deionized water and a Fe3O4 ferrofluid in a Y-shaped microchannel by placing a permanent magnet next to the side of the water solution in the microchannel. The results show that the mixing efficiency can be improved from 8% to around 90%, when an external magnetic field is applied. Moreover, the mixing length can also be reduced. Azimi et al.62 experimentally investigated the liquid–liquid mass transfer between two immiscible fluids in the presence of magnetically excited nanoparticles with a permanent magnet. They observed that the lateral motion of the magnetic nanoparticles and the particle aggregation along the magnetic field lines improve the mixing efficiency. In addition, this work shows that placing the permanent magnet next to the channel side, instead of underneath the channel, increases the performances of this technique. Hejazian et al.63 investigated the dynamic behavior of nonmagnetic particles and a fluorescein dye suspended in a ferrofluid-based microchannel with a circular chamber. An external non-uniform magnetic field generated via a permanent magnet was applied to the system. The results show that an additional secondary flow induced by the magnetic force acting on the magnetic nanoparticles in the ferrofluid induces the mixing of the core with the upper sheath flow. In addition to permanent magnets, other non-uniform magnetic sources such as external electromagnets,65,66 integrated micro-electromagnets67,68 and integrated magnetic elements69 have been employed to improve the mixing of the ferrofluid and water. For instance, Liu et al.69 numerically investigated the mixing performance of a magnetic micromixer system using a two-dimensional model. In such a system, they integrated several soft-magnetic elements and an external magnetic bias field to generate a local high gradient field. A magnetic volume force was induced on the ferrofluid via the gradient field to improve the mixing performance of the system. The results show that the mixing efficiency can be improved from about 10% to 97.5% when a low bias field of 50 mT is applied. Compared to the mixing methods via external permanent magnets, the micro-mixers based on the integrated micro-electromagnets and magnetic elements have a more compact structure and a higher integration. However, the fabrication processes of these micro-mixers are much more complex, and therefore the current studies in this area are mainly based on simulation analysis. It is worth mentioning that a hybrid magnet system consisting of external uniform-field magnets and integrated micro-electromagnets could be used to increase the flexibility of the mixing system. In this case, the magnetic force acting on the ferrofluids can be controlled by adjusting either the internal gradient magnetic field or the external uniform magnetic field.68,70 Investigating the mixing behavior of fluids in different modes of magnetic force is an interesting task, and the results help producing effective mixing under different flow conditions.

(2) Magnetic force generated via a magnetic susceptibility gradient between fluids in a uniform magnetic field. As discussed in Section 2.1 and shown in Fig. 1, when a solid element has a magnetic permeability different from that of the surrounding liquid, a gradient magnetic field is generated around the element. Similar phenomena also occur in the presence of a magnetic susceptibility gradient between two liquids, which are in contact. According to the two-dimensional simulation results shown in Fig. 3, the mismatch between the magnetic susceptibilities of the fluids causes a magnetic field distortion in the surroundings of these fluids in both cases with different magnetic field directions. This results in the appearance of a field gradient and a magnetic force acting on the magnetic liquid. Note that the direction of the magnetic force changes with the magnetic field direction. The instability induced by the magnetic force at the liquid–liquid interface has been numerically and experimentally investigated, and it is known as magnetic micro-convection71,72 or magnetic spreading.73–75 The induced instability behavior at the fluid interface has recently been used to enhance the mixing process in microfluidics.76–78 For example, Zhu and Nguyen76 experimentally demonstrated that a mixing efficiency of about 90% can be achieved between a water-based ferrofluid and a mixture (DI water and glycerol) via the use of a circular chamber with three streams (Fig. 4a). In this system, a low magnetic field with a flux density of 10 mT is applied, and the relative positional relationship between the magnetic field direction and the cross section of the microchannel is similar to that in Fig. 3a. Kitenbergs et al.77 investigated the mixing behavior of the two fluids (water-based magnetic fluid and distilled water) in a Hele–Shaw cell in the presence of a uniform magnetic field (Fig. 4b). In their work, a magnetic field with the same field direction shown in Fig. 3b is applied. It is found that the mixing efficiency is four times higher than that with pure diffusion, when a relatively low magnetic field (13.3 mT) is applied for 0.4 s.


image file: c9mh00714h-f3.tif
Fig. 3 Magnetic field and force distribution in the presence of a magnetic susceptibility gradient between fluids. (a) Magnetic flux density and field contour diagram in the cross section of a microchannel with three streams under an applied magnetic field of 10 mT along the horizontal direction, and arrow plots (logarithmic scale) of the magnetic force in the ferrofluid region. (b) Magnetic flux density and field contour diagram in the cross section of the microchannel under an applied magnetic field of 10 mT along the vertical direction, and arrow plots of the magnetic force in the ferrofluid region. In the simulations, a ferrofluid with a relative magnetic permeability of 1.5 was defined as the core stream and diamagnetic fluids with a relative magnetic susceptibility of 1 were defined as the cladding streams. Each stream has a width of 80 μm and height of 60 μm.

image file: c9mh00714h-f4.tif
Fig. 4 Microfluidic mixing via different magnetic manipulation methods. (a) Microfluidic mixing in a circular chamber under a uniform magnetic field: schematic of the electromagnet and microfluidic channel. Reproduced with permission from ref. 76, Copyright 2012, Royal Society of Chemistry. (b) Microfluidic mixing in a Hele–Shaw cell under a uniform magnetic field: schematic of the experimental setup (b-i); snapshots of the magnetic micro-convection development under different magnetic fields (b-ii). Reproduced with permission from ref. 77, Copyright 2015, Elsevier. (c) Microfluidic mixing using scattered rotating magnetic beads as micro-stirrers: the principle behind bead rotation and the image of the bead distribution in the experiments. Reproduced with permission from ref. 84, Copyright 2016, Elsevier. (d) Microfluidic mixing using rotating magnetic particle chains as micro-stirrers: schematic of the octopolar electromagnetic system (d-i); particle motion under different magnetic fields (d-ii); snapshots of the mixing behavior of a fluid under the action of rotating particle chains (d-iii). Reproduced with permission from ref. 89, Copyright 2013, Springer Nature. (e) Microfluidic mixing in microdroplets using rotating nanometer-size stir bars as micro-stirrers: schematic of the stirring system (e-i); fluorescent microscope images captured in the microdroplets before and after stirring (e-ii). Reproduced with permission from ref. 92, Copyright 2018, John Wiley and Sons. (f) Microfluidic mixing using flexible and deformable micropillar arrays: schematic to achieve controllable mixing (f-i); micropillar arrangements (f-ii); snapshots of the mixing behavior of a fluid in the presence and absence of a magnetic field (f-iii). Reproduced with permission from ref. 96, Copyright 2015, Royal Society of Chemistry.

In general, compared to the mixing processes using an external gradient magnetic field, the case using a magnetic susceptibility gradient has a low requirement on magnetic field conditions, whereas it usually requires a high concentration of ferrofluid to ensure sufficient magnetic force, and the generated magnetic force has an upper value due to the saturation characteristics of magnetic nanoparticles. Note that the magnetic force acting on the magnetic fluids may be generated via the combination of the magnetic field gradient and the mismatch in magnetic susceptibility of the fluids (if it is present) in a non-uniform magnetic field. Such a system was investigated by Hejazian et al.64 However, the simultaneous influence of these two factors on the motion behavior of particles or fluids for different magnetic fields and structural parameters of the microchannel have been rarely investigated. Since the magnetic field distribution along the cross section of a microchannel cannot be well reflected by its two-dimensional model, three-dimensional models of this mixing process are required to accurately analyze these cases.

3.2 Mixing by magnetic stirring

Magnetic stirring is also a widely used mixing technique in microfluidics: micro-stirrers are driven by external magnetic fields to stir the fluid to enhance the mixing performance of the system. Compared to the magnetophoresis-based micro-mixing method, this method is characterized by the fact that no magnetic fluid is required, and therefore there is no need to consider the potential impacts of magnetic fluids on subsequent analysis in actual applications. However, dynamic magnetic fields are typically required and numerical models for simulating the mixing behavior of fluids in this case are much more complex. According to the structure of the micro-stirrers, the mixing strategy can be further divided into three categories:

(1) Scattered magnetic beads used as micro-stirrers.79–85 In this case, the enhancement of the mixing performance relies on the motion of single or multiple magnetic beads under the dynamic gradient magnetic fields generated via electromagnets or moving permanent magnets. Tan et al.79 developed a micro-stirring system in submilliliter microbioreactors with different configurations (circular, diamond, and triangular). In such systems, a 1 mm-diameter magnetic bead (permanent magnet) was electromagnetically actuated via a controllable on/off sequence to disturb the fluids in the chamber and to accelerate the mixing process. Goovaerts et al.81 analyzed the consistent mixing performance of a micromixer using active and passive mixing strategies. Several steel balls (1 mm-diameter) were located in a row of chambers (one ball per chamber) and used as active stirring elements. The movement of the balls was induced by a rotating magnetic field. The experimental results show that a good mixing performance can always be achieved for a wide range of flow rates by using the active stirring method. Moreover, the mixing length can also be shortened. Owen et al.84 proposed a mixing method based on the rotation of 2.8 μm-diameter magnetic beads (Dynabeads M-280) around soft magnetic circular elements integrated in a microchannel (Fig. 4c). An external rotating magnetic field was applied to capture the magnetic beads and hold them towards magnetic elements. Moreover, the magnetic field was used to alter the magnetization direction of the magnetic elements to induce the rotation of the magnetic beads. The results show that a good mixing performance of the two streams can be achieved in a short mixing region (270 μm) when the ratio between the flow rate and the bead velocity is lower than 0.1.

(2) Magnetic agglomerates used as micro-stirrers.86–92 Non-spherical agglomerates, such as magnetic chains and clusters consisting of multiple spherical particles, can be generated under the effect of the magnetic dipole–dipole forces between particles. The dynamic motion of these non-spherical agglomerates under a magnetic torque can be applied to induce a chaotic flow to enhance the mixing performances of the system. Gao et al.89 developed a multifunctional octopolar electromagnetic system to manipulate magnetic particles, which has been used to enhance the fluid mixing in a microfluidic cell (Fig. 4d-i). Different types of magnetic fields, including uniform static magnetic fields, gradient magnetic fields and uniform rotating magnetic fields can be generated to form chains of magnetic particles, to prevent the sedimentation of particle chains, and to rotate the particle chains, respectively (Fig. 4d-ii). The mixing performances of rigid chain rotations and break-reform chain rotations have been experimentally investigated (Fig. 4d-iii). The results show that the periodic chain break-up and re-formation could be more beneficial to chaotic mixing in the whole region. Chang et al.91 experimentally investigated the mixing performance of two fluids in a T-shaped microchannel by using a magnetic stirring system. In the mixing process, magnetic agglomerates consisting of magnetic nanoparticles were formed under the effect of the magnetic interaction among the particles. These agglomerates could rotate synchronously with an external uniform magnetic field of ∼6.6 mT generated by two rotating permanent magnets. The results show that the mixing performance can be improved up to 90% with this stirring system. This value is twice larger than the case with only passive diffusion. Chong et al.92 synthesized nano-sized stir bars consisting of magnetic nanoparticles to perform rapid mixing in a droplet, as shown in Fig. 4e-i. These nanoscale bars remained suspended without sedimentation during the stirring process and this has been shown to be beneficial for its complete mixing. Visualization experiments were carried out with the aid of additional fluorescent particles, showing that several vortexes can be generated and controlled via the rotating magnetic field, as shown in Fig. 4e-ii. The results show that this rapid mixing inside such an ultra-small fluid volume can be realized under a weak magnetic field of about 11.6 mT.

(3) Deformable magnetic micropillars used as micro-stirrers.93–99 Elastically deformable micropillars with embedded magnetic particles can be flexibly actuated via external magnetic fields to induce flow disturbances. This results in an enhancement of the microfluidic mixing. Chen's group proposed several micromixing strategies based on different structures of the micropillar (micropillar arrays parallel to the flow direction, V-shaped pattern of micropillars) and a variety of actuation modes (rotating model, oscillating model, symmetric and asymmetric figure-of-eight modes) with the aid of a controllable electromagnetic system.93–95 The results show that the actuation method with a symmetric figure-of-eight mode is more efficient at enhancing the mixing performances when compared to the rotating and oscillating modes. In addition, the mixing performance can be further improved using the asymmetric figure-of-eight mode when a flow behavior along the out-of-plane direction is induced via the in-plane asymmetric motion.93,94 It has also been pointed out that a V-shaped pattern of micropillars is more efficient than conventional micropillar structures with a line-by-line configuration since such a configuration can generate a vortical zone between the micropillar rows, which facilitates micromixing.95 Zhou et al.96 proposed a controllable micromixing system with micropillar arrays based on a simple magnetic actuation mode. The setup is shown in Fig. 4f-i. In the absence of a magnetic field, the symmetrical micropillar arrays have only a small influence on the flow field and on the mixing performance, due to their small size. In the presence of the gradient magnetic field generated by a permanent magnet, the free parts of the micropillars with embedded magnetic nanoparticles deform towards the directions of the magnetic source due to the induced magnetic force. This leads to a modification in the symmetry of the system, as shown in Fig. 4f-ii, which disturbs the fluid flow for enhanced mixing. Moreover, since the status (on–off) of the magnetic field in the microchannel can be switched by controlling the position of the permanent magnet with the aid of an automatic manipulator, the fluid field inside the microchannel and the mixing behavior of fluids can be regulated (Fig. 4f-iii). Yu et al.97 demonstrated that a single micropillar with embedded magnetic nanoparticles can also be used to enhance the mixing performance of two fluids. Such a system provides mixing efficiency of up to 95% for small Reynolds numbers (∼0.016), which is achieved with a sufficiently high frequency (∼160 Hz).

4. Magnetic trapping

With the rapid development of lab-on-chip technologies, the ability to trap objects (e.g., micro/nano particles and cells) from the surrounding media in microfluidics has attracted considerable attention in both industry and scientific fields. Trapping and preconcentrating objects in a specific region can be used for separation and purification, and allow for subsequent detection and characterization with an enhanced sensitivity.100,101 Moreover, by means of fine-scale trapping technologies, single-particle or single-cell analysis can be achieved, which enables researchers to reveal and better understand the heterogeneity among individual objects in both temporal and spatial dimensions.102–104 Not surprisingly, various methods have been employed to improve trapping, and this section provides an overview of the most common manipulation methods using magnetic fields for trapping both magnetic and nonmagnetic objects.

For magnetic objects or non-magnetic objects attached magnetic particles, gradient magnetic fields are typically applied to move these objects towards a magnetic source and retain them at the location of the magnetic field maximum. The trapping principle is similar to the positive magnetophoresis. In this respect, magnetic field sources are required to provide sufficiently strong magnetic forces to dominate the motion behavior of magnetic objects. A simple choice is to use external permanent magnets, which do not pose the problem of energy consumption. It is important to underline that using this method the aggregation of particles could appear in the trapping process due to the relatively large coverage area of the magnetic field, and this phenomenon may affect the subsequent analysis of the sample or introduce impurities. In order to solve these issues, some investigations have been carried out to modulate the in-channel magnetic field and the channel structures.105–108 For instance, Ramadan et al.105 developed a dynamic trapping–releasing system for the purification of magnetic beads using periodically rotational permanent magnets. As schematically shown in Fig. 5a, the magnetic beads can be trapped when the magnetization direction of the nearby magnet is directed along the y-direction. The beads can instead be released when the magnet is rotated 90° since the generated magnetic field gradient in the microchannel decreases. The experimental results have shown that the sample purity can be effectively improved via the dynamic trapping process when compared to the use of a conventional static trapping process. Huang et al.108 developed a microfluidic device, which integrates a permanent magnet for on-chip immunomagnetic-labeled cell trapping. By introducing an additional array of microwells between the microchannel and the magnet, single-cell trapping is achieved without aggregation. When compared to external permanent magnets, micro-sized magnetic field sources are more widely used in object trapping in microsystems. Stronger magnetic forces can be generated to enhance the trapping ability since the magnetic field gradients increase as the distance between the magnetic source and the object decreases. Furthermore, the presence of a more concentrated field in a local region enables a finer capture process. Several different micro-sized magnetic field sources have been previously reported. The first type is the use of integrated magnetic materials, including soft or hard magnetic elements107,109–114 and magnetic domains.115–117 In the aspect of magnetic elements, Malic et al.111 developed a microfluidic chip with an array of integrated cylindrical pillars made from a soft nickel-coated polymer for the manipulation of magnetic objects (magnetic nanoparticles and bacteria conjugated to magnetic nanoparticles). As schematically shown in Fig. 5b, these objects can be trapped towards the cylindrical pillars when an external magnetic field is applied due to the high gradient magnetic field generated around the pillars. Meanwhile, they can be easily released away from the pillars in the absence of the magnetic field due to the low remanence of the nickel shell. Fratzl et al.114 developed a hard-magnetic micro-magnet array via the thermomagnetic patterning technique to trap 50 nm diameter nanoparticles in a droplet, as schematically shown in Fig. 5c. They have shown that the convective flow induced by the magnetophoretic behavior of such nanoparticles under gradient magnetic field accelerates the trapping process. A similar phenomenon has been previously reported as an important mechanism to accelerate the nanoparticle sedimentation in low gradient magnetic separation processes via a macro-fluidic system.118,119 In actual applications, the magnetic composite-polymer approach could be a good choice for the production of both soft and hard magnetic elements in microfluidics, due to its simple fabrication process and ease of integration within the microdevices.112,113,120 When compared to soft magnetic elements, hard magnetic elements have a residual magnetism, and thus they can generate gradient magnetic fields to trap without the use of additional external magnetic fields, although it is more difficult to release the objects. Similar to hard magnetic elements, magnetic domains can also independently produce local stray fields after magnetic processing. For example, Vautrin et al.117 developed snake-shaped magnetic nanowires with domain walls to trap 500 nm-diameter magnetic beads. In such a system, the local gradient magnetic fields are generated by the domain walls at the wire corners and they are activated by an external magnetic field. The switching process between the capture and the release states can be achieved with the aid of externally applied excitation magnetic fields pointing in different directions. Micro-electromagnets are another type of micro-sized magnetic field sources widely employed to trap objects.121–125 For instance, Silverio et al.123 developed an integrated microfluidic system consisting of planar circular microcoils to magnetically trap 300–500 nm superparamagnetic nanoparticles. They employed a closed loop cooling system to reduce the Joule heating generated by the current-carrying conductors. Riedmüller et al.125 reported that a single superparamagnetic bead with a diameter of 2.8 μm can be reliably trapped in the region close to the micro-ring center by using a current-carrying micro-ring in combination with a homogeneous magnetic field pointing perpendicularly to the ring plane. Since micro-electromagnets have the characteristics of high magnetic field gradient and low magnetic field strength, the gradient and strength of the total field can be respectively dominated by micro-electromagnets and an additional external uniform magnetic field.25 Then the trapping position of the objects in a microsystem can be well controlled by using hybrid magnetic fields consisting of internal and external fields.121,126–128 For example, Basore et al.126 developed a controllable trapping system to gate microelectrodes in the center of a single microcoil and produce an ON/OFF glucose sensor, as schematically shown in Fig. 5d-i. The manipulation mechanism of such a system lies in that the magnetic particles can be trapped or released from the coil center by adjusting the current direction with the aid of an external magnetic field, as shown in Fig. 5d-ii. Han et al.128 showed that 100 nm-magnetic nanoparticles can be captured around two parallel microwires by using a hybrid magnet system consisting of the microwires and external permanent magnets. Both the external magnetic field direction and the configuration of current flow in the microwires have a great impact on the focusing regions of the magnetic particles (Fig. 5e). Moreover, tunable magnetic trapping by using micro-sized magnetic field sources can be applied to transport particles at the microscale. This method is described in the following sections of this review.


image file: c9mh00714h-f5.tif
Fig. 5 Micro-trapping with different magnetic manipulation methods. (a) Schematic diagram of a trapping-and-releasing system based on a rotating magnet array. Reproduced with permission from ref. 105, Copyright 2011, Royal Society of Chemistry. (b) Schematic representation of the capture and the release of particles in a microfluidic chip with nickel-coated micro-pillars in the presence and absence of an external magnetic field. Reproduced with permission from ref. 111, Copyright 2015, Royal Society of Chemistry. (c) Schematic design of a trapping system with an integrated hard-magnetic micro-magnet array. Reproduced with permission from ref. 114, Copyright 2018, Royal Society of Chemistry. (d) A controllable microtrapping system with a single coil and an external magnetic field: schematic representation of ON/OFF glucose detection (d-i); snapshots of the particle distribution around the microcoil under different current directions (d-ii). Reproduced with permission from ref. 126, Copyright 2012, Royal Society of Chemistry. (e) Microscopic images of the distribution of magnetic nanoparticles around two microwires when the wire current flows in different directions and a magnetic field is applied externally. Reproduced with permission from ref. 128, Copyright 2016, IEEE. (f) Micro-trapping system of non-magnetic colloids based on the magnetofluidic tweezing method: schematic diagram of the trapping system with an electromagnet and a coaxial “micro-pen” consisting of a weak magnetic core and a low-coercivity ferromagnetic supermalloy cladding (f-i); magnetic field distribution around the tip of the micro-pen (f-ii); images of the trapping, lifting, moving, and releasing of a micro-bead using such a trapping system (f-iii). Reproduced with permission from ref. 136, Copyright 2016, John Wiley and Sons.

Non-magnetic objects can be trapped under the action of gradient magnetic fields via negative magnetophoresis. This technique is based on the use of magnetic fluids. In this case, non-magnetic objects are attracted towards the region with a local field minimum, which has been schematically explained in Fig. 1. This method can be implemented in the following three ways: (1) the trapping of non-magnetic objects can be achieved by using gradient magnetic fields generated by embedded permanent magnets.129–133 Xuan's group has systematically investigated the trapping behavior of diamagnetic particles or cells with different configurations of permanent magnets. Their experiments included the study of two attracting magnets placed on the top and bottom of a microfluidic chip,130 two attracting magnets placed on the left and right sides of a microchannel,131 and a single permanent magnet placed behind the T-junction of a microchannel.132 The non-magnetic particles tend to be trapped in a region away from the surface of the magnet, where the magnetic field strength is low. (2) Trapping of non-magnetic objects via localized gradient magnetic fields induced by a non-magnetic element in a ferrofluid. As mentioned in Section 2 and shown in Fig. 1, local gradient magnetic fields can be generated around an element once there is a difference in magnetization between the element and its surrounding medium. Therefore, non-magnetic elements exposed to magnetic fluids can also be employed as gradient magnetic sources when an external magnetic field is present. This method has been recently developed for trapping bacteria in both stationary and flowing fluids by Ramanujan's group.134,135 (3) Trapping of non-magnetic objects can also be achieved by using localized gradient magnetic fields generated by magnetofluidic tweezers. As shown in Fig. 5f-i, Grzybowski's group developed a novel magnetic tweezer with a special tip consisting of an inner non-magnetic core and an outer shell of soft-ferromagnetic supermalloy.136 Non-magnetic particles can be trapped towards the tip surface of a magnet when this tweezer design is employed. As shown in Fig. 5f-ii, two typical magnetic field distribution regions can be formed below the tip of the tweezer when the external electromagnet is switched on: the non-magnetic particles in region I are subjected to a radial magnetic force, which points toward the central axis of the tip, and an axial magnetic force directed toward the tip surface, which enables 3D trapping. It has been demonstrated that non-magnetic particles (≈1–50 μm in size) could be lifted up and released. Taking the manipulation of 50 μm particles as an example, the experimental results are shown in Fig. 5f-iii. The magnetic tweezer technique has also been applied to trap live cells in a bio-compatible magnetic fluid containing magnetic nanoparticles.137 Among the above three trapping methods, the first one is the simplest to implement, and it is mainly suitable for occasions where the trapping accuracy is not too high. The third method can be used to achieve the trapping of a single non-magnetic object in a micro-scale region, while the fabrication process of the device is complex. The second method is at an intermediate level in terms of the ease of implementation and trapping accuracy.

In general, the methods for trapping magnetic and non-magnetic objects are similar in principle and they are all mainly based on the use of gradient magnetic forces. The difference is that magnetic and non-magnetic objects are trapped in the maximum and minimum magnetic field regions, respectively. From this perspective, the magnetic trapping systems for these two types of objects have certain similarities: the magnetic tweezing technique used to trap magnetic objects138,139 and the use of integrated magnetic elements to trap and assemble non-magnetic objects have also been reported.140,141

5. Magnetic assembly

Colloidal self-assembly is the process of automatically arranging individual components into ordered structures. This process is of practical and fundamental interest for the bottom-up fabrication of functional materials and technological applications in various fields.142–146 For instance, the colloidal self-assembly can be used in coating applications to produce polymer latex binders with diverse and controllable particle morphologies to improve coating performance;144 the colloidal self-assembly combined with bionics could provide an effective way to realize functional micro/nano-machines for biomedical applications in practice.145 To produce controllable self-assembly structures in a short amount of time, magnetic field guided colloidal self-assembly processes have attracted considerable attention due to their advantages for object manipulation as mentioned in the Introduction. Similar to other self-assembly methods, magnetic assemblies can be categorized into two groups, depending on whether the final assembled structure reaches its equilibrium state: static self-assembly (SSA) and dynamic self-assembly (DSA). Herein, we focus on the assembly behavior of micro- and nanoparticles in the microscale region.

5.1 Static self-assembly

The SSA involves particle systems that are in the equilibrium state without dissipating energies. The SSA structures induced by a magnetic field can be divided into two categories according to the type of magnetic action: magnetic interparticle interaction and the gradient magnetic force.

(1) Magnetic interparticle interaction. In the various SSA processes, which may occur in the presence of magnetic fields, chain-like structures of aggregates induced by the magnetic dipole–dipole interaction are the most widely investigated in both theoretical and experimental studies. The interaction processes and the formation of such chains are typically studied by analyzing either their interaction forces or their energies.147–150 If one considers a simple case with two magnetic particles in a uniform magnetic field, it is well known that these two particles always tend to align along the direction of the applied field independently for their different initial configurations. The magnetic force between the two particles in the aggregation process may be either attractive or repulsive depending on the angle between the direction of the applied field and the line connecting the two centers of the particles.151 The critical angles for 3D spherical paramagnetic particles and 2D circular particles are about 54.7° and 45°, respectively. This feature makes it possible to alter the pattern of the particle aggregates via a dynamic adjustment of the magnetic field directions. This process has been demonstrated to be effective for the dis-assembly of magnetic particle chains.152–155 For the cases where multiple magnetic particles are present, the induced particle aggregates may still exhibit chain-like structures, whereas the final chain characteristics are determined by various multi-factors, such as the magnetic field strength and the particle parameters. In this area, Faraudo's group has conducted a praiseworthy work on the prediction of the assembly behavior of superparamagnetic particles in the presence of uniform magnetic fields.156,157 In their work, a parameter N* image file: c9mh00714h-t15.tif which is related to the volume fraction of particles ϕ0 and to the magnetic coupling parameter Γ = μ0ms2/2πd3kBT has been proposed to predict the particle aggregation behavior. It has been pointed out that magnetic self-assembly of superparamagnetic particles does not occur when N* < 1 due to the weak magnetic interactions or the too large particle spacing. Meanwhile, an approximate critical value (Nc* = 10–14) was provided to predict whether magnetic ribbons (with structures wider than one particle) could be generated. Specifically, one-chain configuration with mean particle number of N* is dominated for the cases of 1 < N* < Nc*, while magnetic ribbons consisting of two or more parallel chains could appear for the cases of N* > Nc*. Similar work and results to predict the ribbon formation of magnetic particles were also carried out by Darras et al.158 and Messina and Stanković.159 These studies showed that the two-chain assembly is more stable than the one-chain case when the total number of particles is above a critical value (27–30), and the ribbons with multilayer chains could appear upon a further increase in the particle number. Note that there is still much work to be done in this area since the existing models and the predictions are mainly focused on the relatively simple cases of static uniform magnetic fields and quiescent (no flow) conditions. In addition to dynamic magnetic fields and flow fields, many other factors, such as the magnetic field gradients160,161 and the electrostatic interactions,162,163 may have an impact on the magnetic assembly processes, and should be further investigated for a better prediction of the particle assembly process.

Similar to magnetic particles, non-magnetic particles can also assemble into chain structures along the magnetic field direction with the aid of magnetic fluids.164–166 Magnetic interaction forces between non-magnetic particles can be induced via the magnetization difference between these particles and surrounding magnetic fluids. This can be easily understood by using eqn (10). A larger variety of particle assemblies can be produced when both magnetic and non-magnetic particles are suspended in magnetic fluids due to the dissimilar magnetic interactions among these different types of particles. In the case of a mixture of particles, particles with a magnetization larger than that of the magnetic fluid exhibit a paramagnetic response parallel to the magnetic field direction, whereas particles with a lower magnetization exhibit a diamagnetic response antiparallel to the field direction. Moreover, the magnetic interactions between different types of particles could differ from the cases where a single type of particle is present. A simple example is shown in Fig. 2c, where the magnetic and non-magnetic particles tend to attract each other and self-assemble in a structure, which is perpendicular to the magnetic field. Based on this basic assembly phenomenon, a great variety of SSA structures have been generated in the presence of static uniform magnetic fields. These structures differ in the type and size of the particles, their number ratio and the magnetic field strength. For instance, Liu et al.167 demonstrated that the magneto-induced stress perpendicular to the direction of an externally applied magnetic field can be enhanced by increasing the number of diamagnetic particles close to that of superparamagnetic particles, since the structures, which assemble along both the longitudinal and the transverse directions, are induced by the two types of particles. Erb et al.168 produced four types of assembly structures (‘rings’, ‘poles’, ‘two tone’, and ‘flowers’) consisting of magnetic and non-magnetic particles suspended in a ferrofluid in the presence of a uniform magnetic field. In their system, the ferrofluid concentration and the size ratio between the particles are two key parameters to control the assembly configurations. The assembly structures of ‘two tone’ and ‘flowers’ are shown in Fig. 6a. Successively, with a similar assembly method, Khalil et al.169 demonstrated that over 20 different assembly structures, including a series of rings, chains, and tiles can be formed in a two-particle system, as shown in Fig. 6b. This result is based on the calculation of the potential energies of these different structures. In their work, two types of particles (magnetic and non-magnetic particles) with a similar size were used and the assembly structures were tuned by controlling the ferrofluid concentration and the relative particle number. Furthermore, Yang et al.170 investigated the tunable assembly of a mixture of particles in a ferrofluid for a 2- and 3-particle system characterized by particles of different sizes. For the 2-particle system, it has been found that several assembly structures, which cannot be observed when particles of similar size are used, can be formed, as shown in Fig. 6c. Moreover, they demonstrated that the strength of the applied magnetic field leads to a structure transition in a 3-particle system (Fig. 6d), which cannot be observed in the 2-particle system.


image file: c9mh00714h-f6.tif
Fig. 6 Magnetic assembly of diamagnetic and paramagnetic spherical particles in a magnetized ferrofluid achieved by using magnetic particle interactions. (a) Schematic and observed images of the assembled patterns of a three-component particle mixture: two-tone structures consisting of 0.21 μm (red) non-magnetic particles, 2.7 μm paramagnetic core particles and 1 μm (green) non-magnetic particles (a-i); flowers consisting of 1.0 μm (red) non-magnetic particles, 2.7 μm paramagnetic core particles, and 9.9 μm (green) non-magnetic particles (a-ii). Reproduced with permission from ref. 168, Copyright 2009, Springer Nature. (b) Simulation results for the assembled structures of a two-component particle mixture with particles of the same size (1 μm paramagnetic and non-magnetic particles) as a function of the ferrofluid and the relative particle concentrations. Reproduced with permission from ref. 169, Copyright 2012, Springer Nature. (c) Simulation results for the assembled structures of a two-component particle mixture consisting of different particle sizes (2.7 μm paramagnetic and 4.8 μm non-magnetic particles) as a function of the ferrofluid and the relative particle concentrations. Reproduced with permission from ref. 170, Copyright 2013, American Chemical Society. (d) Field strength tuned structure transition of the assembled structures of a three-component particle mixture (4.8 μm nonmagnetic particles, 1 μm nonmagnetic particles, and 2.7 μm magnetic particles). Reproduced with permission from ref. 170, Copyright 2013, American Chemical Society.

(2) Gradient magnetic force. Gradient magnetic fields can also be applied to assemble SSA structures by attracting the magnetic materials to the region with the highest magnetic field or by attracting the diamagnetic materials to the region where the lowest magnetic field is present. The assembly principle is similar to the trapping principle mentioned in Section 4. The patterns of the particle assembly mainly depend on the magnetic field distribution, and therefore different methods for producing gradient magnetic fields have been reported. A relatively easy method to produce local gradient magnetic fields is to introduce micro/nano magnetic elements in the presence of externally applied uniform magnetic fields.140,141,171–173 For example, Demirörs et al.140 developed a magnetic field micro-gradient system for the assembly of a large number of both magnetic and non-magnetic particles in a paramagnetic fluid. In such a system, the field gradients were produced by nickel micro-grids, which were placed on a permanent magnet. As shown in Fig. 7a-i, local high magnetic fields appear in the nickel regions, whereas local low magnetic fields appear in the void regions between two consecutive nickel grids. The magnetic and non-magnetic particles are then respectively attracted toward the nickel regions and the void regions in the presence of magnetic forces, as schematically shown in Fig. 7a-ii. To verify these results, several visualization experiments involving magnetic, non-magnetic, and mixed particles were carried out with different configurations of the nickel arrays. The results are presented in Fig. 7a-iii–iv. As previously shown in Fig. 1, the local gradient magnetic fields can be generated around an element once there is a difference in the magnetization between the element and its surrounding medium. Therefore, non-magnetic elements exposed to magnetic fluids can be used as gradient magnetic sources via the introduction of an external uniform magnetic field. Based on this strategy, He et al.174 obtained localized assemblies of non-magnetic particles suspended in a ferrofluid. The position of the assemblies was defined by the non-magnetic patterns. As shown in Fig. 7b-i, the mismatch of the magnetic susceptibilities between the non-magnetic patterns and the surrounding ferrofluid can distort the magnetic field around these patterns, leading to the existence of local low magnetic fields above the pattern surface. The non-magnetic particles are then attracted onto the top surface of the patterns, as schematically shown in Fig. 7b-ii. The SEM images in Fig. 7b-iii and b-iv show the structures of the non-magnetic patterns before and after the assembly process of the non-magnetic particles, respectively. The gradient magnetic fields produced when non-magnetic elements are present may be relatively small, when compared to the other methods, since the magnetization of the magnetic fluid is limited. However, the non-magnetic templates can be conveniently fabricated with simpler procedures and lower costs.


image file: c9mh00714h-f7.tif
Fig. 7 Magnetic assembly of particles achieved by using gradient magnetic forces. (a) Assembled patterns of nonmagnetic and paramagnetic particles in a magnetized ferrofluid in the presence of magnetic templates: magnetic field distribution above the templates, showing that the maximum values of the fields appear on the upper surface of the templates and the minimum values of the fields appear in the region between the templates (a-i); lateral magnetic forces acting on the magnetic (red) and non-magnetic particles (blue) (a-ii); assembled patterns of 2.85 μm magnetic particles (a-iii); 1.2 μm non-magnetic particles (a-iv); particle mixtures of 1.5 μm magnetic and 2.5 μm non-magnetic particles (a-v). Reproduced with permission from ref. 140, Copyright 2013, Springer Nature. (b) Assembled patterns of non-magnetic particles in a magnetized ferrofluid achieved by using non-magnetic templates: magnetic field distribution around the templates (b-i); assembly scheme of non-magnetic particles on the template surface (b-ii); SEM image of non-magnetic templates (b-iii), and SEM image of non-magnetic templates with assembled particles. Reproduced with permission from ref. 174, Copyright 2012, American Chemical Society. (c) Schematic of selective magnetization-based assembly system: principle of the selective magnetization method (c-i); fabrication process of magnetic microstructures with the shape of a defined pattern of magnetic nanoparticles (c-ii). Reproduced with permission from ref. 178, Copyright 2015, American Chemical Society. (d) Assembled patterns of paramagnetic microspheres above a magnetic substrate: schematics showing the distribution of particles without and with an external magnetic field Hz perpendicular to the substrate (d-i); magnetic potentials on the substrate surface without the external magnetic field and with Hz = 1800 A m−1 (d-ii); assembled patterns of 2.8 μm paramagnetic particles above the substrate (d-iii) for different conditions (left to right: no field and an area fraction of 0.09; Hz = 1800 A m−1 and an area fraction of 0.19; Hz = 1800 A m−1 and an area fraction of 0.41). Reproduced with permission from ref. 179, Copyright 2014, American Chemical Society.

Another technique to produce gradient magnetic fields during an assembly process is by using magnetic recording media,175–177 in which magnetized Co nanograins generate enormous field gradients around them (MT/m level). Therefore, this method shows an obvious advantage: magnetic nanoparticles can be controlled and assembled in the nanosize range. In particular, Ye et al.177 demonstrated that multiple types of 2D nanoparticle patterns can be assembled by using perpendicular magnetic recording media. Such results could not be achieved in the longitudinal case. In addition to the above methods, several interesting techniques have also been adopted to alter the original gradient magnetic fields of magnetic substrates by introducing additional fields to control the assembly patterns. For instance, Velez et al.178 developed a selective magnetization technique to regulate the local distribution of the gradient magnetic fields in a magnetic substrate (a Hi8MP video cassette tape) via the introduction of additional soft magnetic structures (Ni masks), as shown in Fig. 7c-i. In this setup, the magnetization direction of the magnetic structures is opposite to that of the magnetic substrate. Following this method, different configurations of assembled magnetic nanoparticles can be obtained by designing different shapes of the magnetic patterns. The fabrication process at the basis of this technique is schematically shown in Fig. 7c-ii. Tierno179 investigated the assembly behavior of the particles, which are located above a magnetic substrate (ferrite garnet film) with and without an externally applied magnetic field perpendicular to the substrate (Fig. 7d-i). They demonstrated that the distribution of the minimal magnetic energy in the magnetic garnet film (a lattice of cylindrical magnetic domains) can be adjusted via an externally applied magnetic field, as shown in Fig. 7d-ii. Therefore, the triangular pattern of the microparticle assembly in the absence of an external field can be varied via the additional field. The final assembled patterns are honeycomb or kagome-like lattices, which depend on the particle concentration, as shown in Fig. 7d-iii.

5.2 Dynamic self-assembly

The DSA processes induced by the presence of magnetic fields are required to consume a continuous magnetic energy, which can be applied for out-of-equilibrium assemblies of particles. In these cases, time-dependent magnetic fields have typically been adopted to form complex structural assemblies by adjusting the magnetic field parameters (such as the field amplitude, the field direction, and the frequency). Among them, the precessing and the oscillating magnetic fields have been widely investigated and the research results are highlighted in this section.
(1) Precessing magnetic fields. Precessing magnetic fields including static and rotating components can be described as H = H0(sin[thin space (1/6-em)]θ[thin space (1/6-em)]cos[thin space (1/6-em)]ωt, sin[thin space (1/6-em)]θ[thin space (1/6-em)]sin[thin space (1/6-em)]ωt, cos[thin space (1/6-em)]θ) in mathematics. As shown in Fig. 8a, H0 is the amplitude of the total magnetic field, θ is the precession angle, and ω is the angular frequency of the rotating-field component. A special type of precessing magnetic field is the rotating magnetic field generated by the condition θ = 90°. In this case, the paramagnetic particles tend to form chains due to the magnetic interactions among them. Moreover, the rotation of the assembled chains follows the field vector of the rotating magnetic field under the action of a magnetic torque when the angular frequency is relatively small. The synchronous rotation can be broken due to the increasing phase lag between the chain direction and the magnetic field orientation when the angular frequency exceeds a critical limit,180,181 as schematically shown in Fig. 8b. More generally, in addition to the angular frequency, the asynchronous rotation behavior is related to multiple factors, such as the magnetic field strength, the fluid viscosity, and the chain length. During these asynchronous rotation processes, the particle chains can break into small pieces and then eventually transform into cluster-like assemblies, such as two-dimensional microwheels and multi-particle aggregates with an approximately circular cross-section, which have been applied for microrobot propulsion.182,183
image file: c9mh00714h-f8.tif
Fig. 8 Assembly behavior of particles under precessing magnetic fields. (a) Coordinate diagram of a typical precessing magnetic field. (b) Schematic of the magnetic field-induced assembly of magnetic particles under a special type of precessing magnetic field (rotating magnetic field). Reproduced with permission from ref. 180, Copyright 2013, Royal Society of Chemistry. (c) Assembly behavior and distribution of paramagnetic particles around a permalloy disk: simulations and experimental results of the particle distribution (c-i); assembled patterns of the particles at the center of the disk upon the variation of the precession angles (c-ii). Reproduced with permission from ref. 184, Copyright 2013, Springer Nature. (d) Assembly behavior of magnetic droplets containing magnetic microparticles: schematic presentation of the reversible assembly of the microparaticles in a droplet (d-i); assembled patterns of the droplets with different droplet numbers (d-ii); reversible assembly of the magnetic droplets with and without the magnetic field (d-iii); tunable pattern of the droplets achieved by adjusting the precession angle (d-iv). Reproduced with permission from ref. 185, Copyright 2018, American Chemical Society. (e) Images of the assembled structures of Janus microparticles (∼100 μm diameter) generated by increasing the precession angles (from left to right): single-chain case (e-i); double-chain case (e-ii); close-packed case (e-iii). Reproduced with permission from ref. 186, Copyright 2016, American Institute of Physics. (f) Assembled structures of Janus microparticles (∼3 μm diameter): observed images and simulations of the generated microtubes parallel to the precession axis (f-i); image of the generated hexagonal sheet perpendicular to the precession axis (f-ii). Reproduced with permission from ref. 187, Copyright 2012, Springer Nature. (g) Dynamic phase diagram and assembled patterns of the superparamagnetic spheres (∼1 μm diameter) by varying the precession angles and the frequencies. Reproduced with permission from ref. 188, Copyright 2016, American Chemical Society.

Similar to the interaction behavior of several particles in a static magnetic field, the interaction forces between the paramagnetic particles under the effect of precessing magnetic field differ with the precession angle. This characteristic can be used to tune such assemblies in a precessing magnetic field. As shown in Fig. 8c, Chen et al.184 investigated the assembly behavior of paramagnetic microspheres with a radius of 4 μm around a permalloy disk in a precessing magnetic field. In their setup, the gradient magnetic force generated by the particle–disk interaction was used to confine the particles and the precession angle was used to adjust the arrangement of the particles. The results show that the mean center-to-center separation between the particles decreases to a certain value upon the increase of the precession angle. Moreover, the critical angle for the transition from a discrete-particle pattern to a compact-cluster pattern occurs at θ ≈ 54.7° in the simulations and θ ≈ 60° in the experiments. As shown in Fig. 8d, Wang et al.185 investigated the assembly behavior of droplets containing magnetic microparticles at an air–liquid interface in a precessing magnetic field. During the assembly process, the magnetic particles in the droplets form a chain and this state can be restored to a discrete state when the magnetic field is removed, as shown in Fig. 8d-i. It has been demonstrated that various ordered patterns consisting of a different number of droplets can be formed (Fig. 8d-ii). Moreover, these patterns become compact under the action of a capillary attraction between the droplets when the magnetic field is removed, as schematically shown in Fig. 8d-iii. In addition, the results show that the center distance between the droplets in a pattern can be tuned by adjusting the precession angle (Fig. 8d-iv). The expansion and shrinking of such an ordered pattern is determined via both the hydrodynamic repulsion and the magnetic interactions among the droplets. More complex assemblies can be obtained in the presence of a precessing magnetic field for different particles (concentration, size, and type) and magnetic field characteristics (field strength, precession angle, rotating frequency, and mode).186–189 For instance, Yan et al.187 investigated the assembly behavior of magnetic Janus particles consisting of 3 μm spherical silica particles coated with thin nickel films (18 nm or 21 nm) in a precessing magnetic field. In their experiments, both the particle rotations and oscillations were controlled via the variation of the precession angles as well as their frequencies. The experimental results have shown that assemblies including microtubes, zigzag chains, and planar hexagonal sheets were observed, as shown in Fig. 8f. Moreover, these structural transitions were mainly dependent on the precession angles. Mohorič et al.188 found that various assembly structures of massive particles can be generated in the simulations by adjusting the precession angles and the rotational frequencies. As shown in Fig. 8g, ribbon-like assembly structures and planar membranes are dominant when low precession angles (<30°) and high precession angles (>80°) are used, respectively. Multiple types of structures including ribbons, vertical membranes, vortex phase, planar membranes, and magnetic foam were found by varying the precession angles between 30° and 80° and the field frequency.

(2) Oscillating magnetic field. This section focuses on the analysis of the DSA processes under a uni-axial oscillating magnetic field. Such a field can be described as H = H0[thin space (1/6-em)]sin[thin space (1/6-em)]ωt in mathematics, where H0 and ω represents the magnitude and the angular frequency of the field, respectively. A series of systematic numerical and experimental studies on the DSA of ferromagnetic microspheres at the fluid interface have been carried out by the Snezhko and Aranson groups.190–194 These experiments showed that the processes which trigger the formation of the assemblies are mostly determined by the combination effects of the dynamic magnetic interactions among the ferromagnetic particles, the self-induced interface deformation, and the surrounding hydrodynamic flows. For instance, Snezhko and Aranson190 demonstrated that aster-like shape of ferromagnetic particles can be formed at the interface between two immiscible liquids in the presence of an oscillating magnetic field perpendicular to the interface. Moreover, the size of such assembled aster-like structures can be reduced by increasing the oscillation frequency of the external field. In addition, different assembly patterns including “arrays”, “linear hybrids”, and “linear trains” can be realized (Fig. 9a), depending on the particle concentration, frequency, and amplitude of the magnetic field. Kokot et al.193 demonstrated that an oscillating magnetic field parallel to a liquid–air interface can also be applied to adjust the DSA process of the ferromagnetic microparticles at the interface. Several assembly patterns, including pulsating clusters, long wires, and spinners (short chains), can be formed and tuned by adjusting the magnetic field. A series of interesting observations show that the assembly patterns always tend to be long single-particle-thick wires (Fig. 9b) when the magnetic field frequency is higher than 150 Hz. This cannot occur in the static assembly processes, since magnetic ribbons consisting of two or more parallel chains could be more stable than a long single-particle-thick chain when the number of assembled particles is too large, as mentioned in Section 5.1.
image file: c9mh00714h-f9.tif
Fig. 9 Assembly behavior of particles in the presence of uni-axial oscillating magnetic fields. (a) Assembled patterns of nickel spherical microparticles (∼90 μm diameter) formed at a liquid–liquid interface in the presence of oscillating magnetic fields perpendicular to the interface: “arrays”, “linear hybrids”, and “linear trains” (from left to right). Reproduced with permission from ref. 190, Copyright 2011, Springer Nature. (b) Assembled patterns of nickel spherical microparticles (∼90 μm diameter) formed at the air–liquid interface in the presence of oscillating magnetic fields parallel to the interface: schematic representation of the assembly system (b-i); consecutive formation of a long single-particle-thick chain at 36 Oe and 240 Hz (b-ii). Reproduced with permission from ref. 193, Copyright 2015, Springer Nature. (c) Assembled patterns of spherical particles with shifted dipole (∼5 μm diameter) in the presence of oscillating magnetic fields perpendicular to the particle plane. Reproduced with permission from ref. 195, Copyright 2016, Springer Nature. (d) Assembled chains of particles under an oscillating magnetic field oriented along the y direction:185 assembled chain of ferromagnetic ellipsoids (d-i); assembled chains (d-ii) of ferromagnetic ellipsoids (aligned along the x direction) and paramagnetic particles (aligned along the y direction). Reproduced with permission from ref. 196, Copyright 2016, Royal Society of Chemistry. (e) Morphology of the assembled ring consisting of several ferromagnetic ellipsoids in the presence of an oscillating magnetic field perpendicular to the ring (Hz, ring expansion) and an oscillating magnetic field in the ring plane (Hx, ring compression). Reproduced with permission from ref. 197, Copyright 2016, American Physical Society.

In addition to these studies, uni-axial oscillating magnetic fields have also been applied for tuning the assembly processes of other types of particles. Steinbach et al.195 investigated the interaction behavior of particles with a radially off-centered net magnetic moment in the presence of an oscillating magnetic field perpendicular to the particle surface. Due to the anisotropy of the magnetostatic interactions, the relative orientation between the particles and the assemblies varies with the field strength. As shown in Fig. 9c, a staggered chain can be transformed into linear chains when the oscillating out-of-plane field increases. The dis-assembly phenomenon of such particle chain occurs instead in the presence of a high field. Martinez-Pedrero et al.196 investigated the dynamics of ferromagnetic ellipsoids with a permanent magnetic moment perpendicular to their long axis under static and oscillating magnetic fields. Their results indicate that the assembled particle chains can be oriented perpendicularly to the oscillating magnetic field, whereas the chains were formed along the field direction when isotropic particles or static fields were used in the experiments (Fig. 9d). The special assembly behavior of these ferromagnetic ellipsoids is mainly due to the altered magnetic energy distribution caused by the nonsynchronous response between the particles and the high-frequency magnetic fields. Based on a similar mechanism, Martinez-Pedrero et al.197 further demonstrated that uni-axial oscillating fields can be applied to control the morphology of a colloidal ring consisting of ferromagnetic ellipsoids. As shown in Fig. 9e, an oscillating field perpendicular to the ring plane (Hz) and an oscillating field in the ring plane (Hx) can be applied to realize the ring expansion and compression, respectively.

6. Magnetic transport

Transport of miniaturized objects is currently a quite active and fascinating research field due to its unique natural advantages in small and complex working environments. The miniaturized objects have been widely used in multiple real-world biological and medical applications, such as drug delivery,3,198,199 surgery,200–202 sensing,201,203,204 and environmental treatment.205–207 In this review, the miniaturized objects are mainly referred to as millimeter- and micrometer-scale microrobots. In practice, how to power and transport these microrobots is the core, and therefore the energy sources and manipulation methods required for controllable motion of microrobots have attracted considerable attention in the past decade.208 Magnetic fields have been popularly used as a powerful strategy since they can be easily generated and controlled. Typically, the basic principle of magnetic transport is to control the motion of the microrobots by using magnetic forces and/or torques in a dynamic manner.209 Time-varying gradients and uniform magnetic fields are usually applied to generate the forces and torques, respectively. Since electromagnets can be easily and simultaneously controlled via electric currents, they are more flexible when compared to permanent magnets, and have been widely used in magnetic transport systems to generate dynamic magnetic fields. According to the basic principle of magnetic manipulation, both magnetic and non-magnetic objects can be efficiently transported, although, at the current stage, the investigations on the transport of magnetic objects are dominant.

6.1 Magnetic transport based on dynamic gradient magnetic fields

Different types of electromagnetic sources have been used to generate the required dynamic gradient magnetic fields to transport micro-objects. They can be categorized into three main groups.

In the first group, the electromagnetic system is mainly composed of pairs of Helmholtz and Maxwell coils210–213 (or other coils with similar functions such as saddle coils214,215) to generate uniform and uniform-gradient magnetic fields, respectively. The configurations of these types of coil pairs in an electromagnetic drive system are schematically shown in Fig. 10a.215 The current direction of each coil in the coil pair for generating gradient magnetic fields is the opposite, while the current direction is the same for the case of uniform magnetic fields. The actuation mechanism of such systems lies in the application of uniform magnetic fields to rotate the microrobots (permanent magnets) by using magnetic torques. A gradient magnetic field is then applied to propel the magnetized mircorobots. A simple 3-D spatial motion control for these microrobots can be realized via changing the stationary pairs of coils along one axis to a rotational case.216,217 To reduce the system volume and the power consumption, it has also been demonstrated that the number of coil pairs required can be reduced by controlling the coil currents.218–220 The actuation systems which belong to this group are easily modeled and analyzed, whereas the generated magnetic field strength and gradient by these systems are much limited.


image file: c9mh00714h-f10.tif
Fig. 10 Object transport using dynamic gradient magnetic fields. (a) A schematic diagram of the construction of these types of coil pairs in an electromagnetic drive system. Reproduced with permission from ref. 215, Copyright 2017, Springer Nature. (b) Top view of a six-pole magnetic tweezer used for 2D actuation. Reproduced with permission from ref. 223, Copyright 2015, AIP Publishing. (c) Magnetic actuation method using integrated circuits and an external rotating magnetic field to transport magnetic particles and magnetic-nanoparticle-labelled cells: potential energy distributions around the circuits for different magnetic fields and images of the particle trajectory (c-i); effects of the current line on the potential energy distribution and particle trajectory (c-ii). Reproduced with permission from ref. 230, Copyright 2014, Springer Nature. (d) A magnetic actuation method using magnetic domain walls and external dynamic magnetic fields: experimental images showing size-selective directed transport (d-i); magnetostatic potential wells near the domain wall junction for the cases with different magnetic fields (d-ii). Reproduced with permission from ref. 233, Copyright 2017, Springer Nature.

The second group of force-based actuation devices dynamically manipulates magnetic objects by using a magnetic tweezing technique (either “far-field tweezing” or “near-field tweezing”221). An obvious advantage of this method is that magnetic tweezers apply a much higher force to an object, due to the local enhanced magnetic field gradients in the presence of magnetic poles with high magnetic permeability properties. Differently from the single/double-pole magnetic tweezers for particle trapping, multi-magnetic poles are typically required to achieve good maneuverability in the multidimensional movement control of mircorobots. To achieve this goal, 2D actuators with three-pole or quadrupole arrangements222,223 and 3D actuators with six or more magnetic poles224–228 are used. For example, Chen et al.223 fabricated a hexapole magnetic tweezer system with three poles located in the top and bottom planes, as shown in Fig. 10b. Moreover, then they could obtain the 2D actuation of a 2.8 μm diameter magnetic bead using such a three-pole coil. Wang et al.226 fabricated a similar hexapole magnetic tweezer system and achieved the 3D position control of a 5 μm magnetic bead inside a mouse embryo.

The third group of the force-based actuators consists in dynamically trapping via a tunable magnetic field, generated by using integrated micro-magnetic sources.229–234 In this case, an external magnetic field is typically required. Since high-field gradients can be generated via such micro-magnetic sources at the microscale even with low magnetization, the induced magnetic forces are large enough for the actuation of microparticles. For example, Lim et al.230 could transport a 2.8 μm diameter magnetic bead along the magnetic track of a half-disk by using a rotating magnetic field (Fig. 10c-i). The particle motion is induced by the change in the location of the minimum magnetic energy. Furthermore, with the aid of micro current lines, more transport modes could be obtained by using different configurations of the magnetic track system (Fig. 10c-ii). Rapoport et al.233 demonstrated that the motion direction of magnetic beads of 2.8 μm and 5.8 μm diameter across a junction can be controlled by adjusting the bead–domain wall interaction, as shown in Fig. 10d-i. This process can be generated by varying the magnetostatic potential wells around the domain walls via either an external magnetic field or the bead properties (Fig. 10d-ii). The control strategies of the actuation methods belonging to this group are easier to achieve when compared to the previous two groups, since the dynamic positioning points are typically determined by the arrangements of the micro-elements. However, higher requirements for the microfabrication of such microelements are needed.

6.2 Magnetic transport based on dynamic uniform magnetic fields

The transport of objects relying on the use of dynamic uniform magnetic fields is commonly known as the magnetic swimming technique for actuating microrobots. This technique is based on escaping the constraints from the scallop theorem by breaking the time-reversal symmetry of the fluid flow at low Reynolds numbers. In this case, dynamic magnetic torques are widely used, as well as magnetic interaction forces. The torque-based transport is generally considered to be more effective for actuating microrobots with small body sizes compared to the use of gradient magnetic force-based magnetic transport. This is mainly because the maximum velocity of microrobots could scale with their equivalent diameter in the torque-driven cases, while scale with the square of their equivalent diameter in the force-driven cases.235 Several types of dynamic magnetic fields have been adopted as power sources: the rotating and oscillating magnetic fields are the most commonly used.

There exist three strategies based on rotating magnetic fields to achieve nonreciprocal motion: they rely on magnetic helical structures, flexible magnetic structures, and close-to-surface motion, some of which are shown in Fig. 11. Among these methods, magnetic helical structures are commonly used for propulsion, where the induced rotation around their helical axis can be transformed into a translation. These helical structures have two typical configurations: (1) the first one consists of a magnetic head and a helical ribbon tail.236–238 For example, as shown in Fig. 11a-i, Zeeshan et al.236 developed helical magnetic microrobots consisting of a cobalt–nickel head and a poly-pyrrole tail via 3D template-assisted electrodeposition. These microrobots could move in a controlled fashion and could swim in a swarm-like fashion by dynamically adjusting their plane of rotation, as shown in Fig. 11a-ii. (2) The second configuration consists in a helical body with a magnetic coating,239–243 such as the Ni-coated nanoscale helical nanorobots, which can be fabricated via the template electrodeposition approach in Fig. 11b-i.240 Such magnetic helical microrobots show a wobbling motion at low frequencies, due to the natural asymmetry of their helical tail. Their motion behavior can be modified into a corkscrew by increasing their rotation frequency, as represented in the schematic illustration of Fig. 11b-ii. As previously mentioned, rotating magnetic fields can be used to actuate flexible microrobots with either deformable tails or joints.244–247 For instance, Gao et al.244 developed a flexible nanowire robot with a three-segment configuration (Ni–Ag–Au). This system is shown in Fig. 11c. The robot can swim under a precession-type rotating magnetic field, which consists of an in-plane rotating magnetic field and a perpendicular static field (Fig. 11c-i). The swimming direction of the nanowire can be altered by adjusting the length of the robot's head and tail (Fig. 11c-ii). Ye et al.246 fabricated flexible swimming microrobots with several tails (up to six) and compared their swimming behavior. Their results show that the swimming speed of the microrobots can be improved by increasing the number of flexible tails. Rotating magnetic fields can also be applied to actuate microrobots with the aid of a nearby surface, which may or may not be in contact with the robot. Several types of swimmers, such as magnetic colloidal assemblies,248–250 geometric, and magnetic anisotropic robots,251–254 have been reported. They exhibit either a rolling or a tumbling motion. For example, Tasci et al.250 proposed a wheel-shaped magnetic assembly for surface-enabled propulsion based on a special rotating magnetic field. In their setup, an in-plane (xy plane) field is applied to produce a wheel-shaped cluster and to create a driving torque. A variable-phase magnetic field along the z direction was simultaneously added to incline the microwheel relatively to the surface, as shown in Fig. 11d. It has been demonstrated that the rolling velocity and the direction of the wheel-shaped swimmer can be controlled by varying its spin frequency and its angle relatively to the surface. Mair et al.254 fabricated a gold–nickel–gold microrod via sequential electrodeposition (Fig. 11e-i). Its translational motion near a solid surface was generated by using a rotating magnetic field. As shown in Fig. 11e-ii, a tilted angle was introduced between the short axis of the rod and the magnetization direction. This angle is responsible for the generation of the kayaking motion and a considerable translation.


image file: c9mh00714h-f11.tif
Fig. 11 Magnetic swimmers using rotating magnetic fields. (a) Hybrid helical magnetic swimmers consisting of a ferromagnetic alloy head and a helical polymer tail: SEM images of the hybrid swimmers (a-i); experimental images of swarm-like swimming for the three swimmers. Reproduced with permission from ref. 236, Copyright 2014, John Wiley and Sons. (b) Ni-coated helical nanoswimmers: schematic illustration of the tumbling (left) and corkscrew (right) motions of the swimmer (b-i); experimental images of the swimmer trajectory (b-ii). Reproduced with permission from ref. 240, Copyright 2014, Royal Society of Chemistry. (c) Flexible nanowire swimmers: schematic illustration of a precession-type rotating magnetic field (c-i); a reversal motion control (‘forward’ and ‘backward’), which was achieved by changing the component length of the swimmers (c-ii). Reproduced with permission from ref. 244, Copyright 2010, American Chemical Society. (d) Colloidal microwheels near a surface: experimental images (d-i); schematic illustration of a dynamic particle assembly into microwheels under a rotating magnetic field (d-ii); the altered field rotation axis with the aid of a normal field (d-iii); translation of the microwheel composed of 7 particles at three seconds (d-iv). Reproduced with permission from ref. 250, Copyright 2016, Springer Nature. (e) Microrods near a surface: an SEM image of a gold–nickel–gold rod (e-i); schematic illustration of the magnetic setup and rod motion (e-ii). Reproduced with permission from ref. 254, Copyright 2017, Royal Society of Chemistry. (f) Two-dimensional rigid swimmers: schematic illustrations of the swimmer motion (f-i); experimental images of the swimmer trajectory at 1 s intervals under a precession-type rotating magnetic field (f-ii). Reproduced with permission from ref. 257, Copyright 2018, John Wiley and Sons.

In addition to the swimmers described above, the propulsion of rigid non-helical microscale objects (including those with achiral or randomly-shaped geometries) away from a surface via a rotating magnetic field has recently attracted considerable attention,255–262 since neither flexibility nor chirality is required. In terms of achiral geometries, for instance, Cheang et al.256 realized the propulsion of a simple microswimmer consisting of three magnetic beads via a rotating magnetic field. Their results show that the application of a torque is required to generate a component along the two principal axes of rotation perpendicularly to the symmetry planes of the swimmer. Tottori et al.257 demonstrated that rigid achiral ferromagnetic structures can be actuated by using a precession-type rotating magnetic field (Fig. 11f-i). The chirality along their precession axis can be obtained and these structures always swim toward their longer arm, as shown in Fig. 11f-ii. In fact, it has been pointed out that the symmetry (e.g., chirality) of a microobject during a transport process cannot be determined only by its shape; the magnetic effects induced by the external rotating magnetic field should be considered to determine whether the object can be set in motion.258 The motion behavior of microrobots with randomly-shaped geometries is also studied, where the propulsion efficiency evaluation and the structure optimization are the research focus. As reported by Vach et al.,259 the dimensionless speeds of randomly shaped magnetic aggregates are comparable to the ones of helical micropropellers. Moreover, higher speeds can be achieved by optimizing such structures. To guide the structural design and achieve a more efficient propulsion, Mirzae et al.260 developed a particle-based hydrodynamic model and a genetic search algorithm to find these optimal structures. The results show that a chubby skew-symmetric shape may be a good choice for the swimmers. These studies could have important implications in reducing the production costs and the manufacturing complexity of the swimmers in certain applications.

Oscillating magnetic fields can also be applied to actuate magnetic flexible swimmers with either deformable tails or joints, which present a swing motion perpendicular to the traveling direction of the swimmer itself. The dynamic magnetic torques usually play a dominant role. The magnetic actuation via oscillating magnetic fields is more common than the use of rotating magnetic fields in flexible swimmers. An earlier work in this area was reported by Dreyfus et al.,263 showing that a flexible swimmer consisting of DNA-linked particle chains (tail) and a red blood cell (head) can move with a beating pattern under an oscillating magnetic field around one axis. The magnetic field used in the experiment consisted of a static field and a perpendicular sinusoidal field. Following this study, several types of flexible microrobots with relativity simple structures have been reported.264–267 For example, a simple microrobot inspired by sperm-cells consisting of a cobalt–nickel based head and a flexible tail was produced by Khalil et al.265 (Fig. 12a-i). The frequency response of the microrobot motion, which is reported in Fig. 12a-ii, shows the characteristics of such type of flexible swimmers. The swimming speed initially increases with an oscillating field frequency and it decreases upon a further increase of the field frequency above a relatively high value (step-out frequency): the microrobot can oscillate out-of-sync if a magnetic field is applied at high frequencies. Similar phenomena are also observed for the motion of flexible swimmers when rotating magnetic fields are applied, as described above. More recently, the swimming motions of magnetic multilink microrobots under external oscillating magnetic fields have been investigated. As shown in Fig. 12b, three types of magnetic nanoswimmers with 1-, 2-, and 3-link were fabricated by Jang et al.268 Their motion behavior in the presence of an oscillating magnetic field consisting of two orthogonal sinusoidal fields has been analyzed and compared, showing that the multilink design may improve their swimming efficiency. As shown in Fig. 12c, a fish-like deformable multilink nanoswimmer (Au–Ni–Ni–Au with flexible porous Ag hinges) was fabricated by Li et al.269 The swimmer could generate a travelling-wave motion and exhibit a high swimming performance with a maximum speed of ∼6.9 body lengths per second in the presence of an oscillating magnetic field consisting of two opposing electromagnetic fields with an on–off control. Subsequently, Li et al.270 proposed a new multilink nanoswimmer consisting of two magnetic nanowire arms, a gold metallic body, and flexible Ag hinges, as shown in Fig. 12d. The magnetic swimmer exhibits an efficient non-planar freestyle propulsion, due to the cooperative out-of-phase wobbling of the arms and it can reach a maximum speed of ∼12 body lengths per second when an oscillating magnetic field consisting of two sinusoidal electromagnetic fields with a 180° phase-shift is present (Fig. 12d-i).


image file: c9mh00714h-f12.tif
Fig. 12 Magnetic swimmers using oscillating magnetic fields. (a) MagnetoSperm consisting of a magnetic head and a flexible tail: full-length image (a-i); frequency response of the MagnetoSperm (a-ii). Reproduced with permission from ref. 265, Copyright 2014, AIP Publishing. (b) Magnetic multilink nanoswimmers: schematic of a 3-link nanoswimmer with an undulation motion (b-i); SEM images of 1-, 2- and 3-link of swimmers; their corresponding motion trajectory (b-ii). Reproduced with permission from ref. 268, Copyright 2015, American Chemical Society. (c) Fish-like nanoswimmers: schematic of the structure and of the motion of the nanoswimmers (c-i); schematic of the used oscillating magnetic field (c-ii); microscopy images of the swimmers’ trajectory showing their controlled motion (c-iii). Reproduced with permission from ref. 269, Copyright 2016, John Wiley and Sons. (d) Symmetric multilinked two-arm nanoswimmers: schematic of the magnetic setup for the propulsion experiments (d-i), SEM images of a two-arm nanoswimmer and EDX mapping of its components (d-ii), and trajectories of the nanoswimmer over 3 s (d-iii). Reproduced with permission from ref. 270, Copyright 2017, American Chemical Society. (e) Self-assembled microswimmers:252 schematic of the swimmer system with a water–air interface (e-i); a top view of the particle interactions among three particles in a vertical field (e-ii); snapshots of the particle motion over one period, T, of the forcing oscillation (e-iii). Reproduced with permission from ref. 273, Copyright 2015, Springer Nature. (f) Self-assembled nanorod-sphere swimmers: schematic of the transport mechanisms under the magnetic fields with two amplitudes (f-i); trajectories of the swimmer for the two cases with different field amplitudes (f-ii). Reproduced with permission from ref. 276, Copyright 2018, Springer Nature.

Oscillating magnetic fields are also used to actuate magnetic particle-based swimmers.271–276 The underlying swimming mechanisms in these cases are mainly related to the time-dependent magnetic interactions and the resulting surrounding hydrodynamic flow. For instance, Grosjean et al.273 produced the low Reynolds number swimming of three ferromagnetic particles located at a liquid–air interface via a static vertical magnetic field and an oscillating horizontal field, as schematically shown in Fig. 12e-i. When there is no horizontal magnetic field, the three particles form a stable assembly due to the magnetic interaction force (repulsion) and the capillary attraction between the particles, as shown in Fig. 12e-ii. When an oscillating magnetic field is applied horizontally, this equilibrium structure is broken. The assembly can, at this point, change its shape and this generates periodic deformations, a non-reciprocal motion of the assembly, and a hydrodynamic flow around these particles, as shown in Fig. 12e-iii. García-Torres et al.276 developed a simple hybrid microrobot consisting of a paramagnetic microsphere and a ferromagnetic nanorod, which can be actuated by an oscillating magnetic field with bipolar square waves. As shown in Fig. 12f, by adjusting the magnitude of the applied magnetic field, the force state of the microsphere and of the nanorod can be changed. Then the microrobot can move forward or backward under the induced hydrodynamic flow and the nearby-wall effect. Moreover, the propulsion of the microrobot is also related to the oscillation frequency and to the oscillation waveform.

7. Conclusion and outlook

The principles and the typical strategies for micro- and nano-object manipulation at small scales using magnetic fields are summarized in this review together with the most recent progress in the micro-mixing, trapping, colloidal assembly, and transport processes. The gradient magnetic force, the magnetic interaction force between objects and the magnetic torque are the main tools used in magnetic micro-manipulation, which are also employed in other applications, such as magnetic separation,277–280 levitation,281–283 and droplet manipulation.284–286 To further promote the development of the magnetic micro-manipulation technology and its applications, we introduce here some comments and suggestions to the results presented in this review:

(1) From the point of view of manipulation methods, on the one hand, different manipulation applications based on the use of magnetic fields show several technical similarities. For example, the gradient magnetic force works in all the four processes reviewed in this work, and the magnetic micro-trapping methods have been applied to foster particle assembly. Therefore, the reference and integration of multiple methods in different applications could be an effective way to solve the issues. Specifically, when using magnetic fields for object manipulation in an actual application, it is recommended to find a suitable manipulation and implementation method by referring to similar studies in interdisciplinary fields. On the other hand, according to the actual experimental needs, it is recommended to develop hybrid manipulation technologies by combining magnetic fields with other physical fields, such as electric, acoustic, and optical fields, to achieve a higher performance and more challenging functional requirements. Such emerging technology has recently been used in several applications, such as transport of particle aggregates based on combined acoustic and magnetic actuation,183 three-dimensional motion control of an individual magnetic bead based on the combination of magnetophoretic and dielectrophoretic force fields,287 and accelerated enrichment of particles based on temperature and magnetic field gradients.288

(2) Magnets are a key tool to control the motion of micro- and nano-objects via magnetic manipulation. Magnet design and optimization should be investigated in detail since it is critical to improve the ability of manipulating micro- and nano-objects. On the one hand, the high performances of magnetic fields and field gradients constitute a benefit to improve the magnetic torque/force acting on the objects. This means that such systems can meet more demanding requirements, such as the manipulation of smaller objects, larger workspaces, and higher-throughput flow conditions. At present, the research on these aspects has focused on the structural design and optimization of permanent magnet systems,289–291 which can be used as external magnets for object manipulation. For electromagnets, in addition to structural design, an important task, which still needs to be solved, is the heating problem of the coils, which is a critical factor limiting the magnetic field performances. On the other hand, it is encouraged to develop new magnetic configurations to realize the specific magnetic field distributions and unique manipulation functions that conventional magnets cannot achieve. For example, Timonen et al.136 developed a new magnetic tweezer with a special tip structure (“micro-pen”, as shown in Fig. 5f-i), which generates a local minimum magnetic field near the tip surface to trap non-magnetic objects. Such results cannot be obtained by conventional magnetic tweezers. A similar design of magnetic structures has also been previously proposed for manipulating magnetic particles and magnetically loaded cells:292,293 the system consists of an electromagnetic setup with two facing magnetic poles (hollow center) producing a local maximum magnetic field at the center of the two poles. In this fashion, the trapping of magnetic particles is achieved in a tube positioned away from the magnet surface.

(3) In addition to the manipulation methods and magnetic field design, the manufacturing of high-performance and multi-functional magnetic materials is also important to expand and deepen the applications of magnetic manipulation. New developments should be planned toward the production of magnetic responsive composite materials consisting of magnetic matter, such as soft/hard ferromagnetic particles and layers, and polymeric materials.294–296 These materials can be used to produce built-in integrated magnetic elements, deformable magnetic artificial cilia, and soft-bodied magnetic robots, which have become a hot research topic in the field of magnetic micro-scale manipulation. Several relevant breakthroughs have been achieved in the development of soft-bodied magnetic robots by using particle magnetization control with the aid of magnetic fields. For example, Hu et al.297 developed a unique soft robot with a single-wavelength harmonic magnetization, which consists of a silicone elastomer embedded with NdFeB particles and magnetized via a cylindrical-wrapping magnetic process. The soft robot has a high degree of freedom and exhibits different deformation behaviors upon a change in the magnetic field. This feature enables the robot with multiple manipulation functions, such as rolling, walking, crawling, and jumping, via a time-dependent magnetic field. Kim et al.298 developed a magnetic field-assisted 3D printing technology to fabricate soft magnetic composites with programmed ferromagnetic domains. By controlling the structure of the magnetic domains, these materials exhibit a variety of three-dimensional structures upon a change in the magnetic field. This application shows great potential in enabling a flexible and complex driving system for soft objects. It is foreseeable that the main line of future research will be directed toward the functionalization of the internal magnetic properties and of the external response characteristics of magnetic composite materials, as well as the development of large-scale production via simple methods.

(4) From the theoretical point of view, there still appears to be a research gap in the field of computational modeling of such manipulation processes due to their complex physics. Taking the motion behavior of multiple particles under a magnetic field as an example, it is still a challenge to simultaneously model the gradient magnetic force, the magnetic interaction between particles, and the particle–fluid momentum interaction. The two-way particle–fluid method, which is commonly used for the analysis of the magnetic separation and mixing processes,67,69,70,299,300 cannot describe the effect of the particle aggregation behavior induced by the magnetic inter-particle interactions. This limits the quantification process of several experimental phenomena, such as the appearance of counter-rotating circulation of non-magnetic particles suspended in a magnetic fluid during the trapping process, and the accelerated sedimentation behavior of magnetic nanoparticles induced by the particle aggregation in the presence of a relatively high particle concentration under a gradient magnetic field.301,302 Another issue is the accurate three-dimensional simulation of soft objects in a flow subjected to magnetic fields. In this case, various dynamic behaviors could appear, including deformations caused by the magnetic force and torque, translations and rotations (or oscillations), as well as a change in the hydrodynamic behavior. The development of efficient computational tools may enable a deeper understanding of the basic mechanisms behind these magnetic manipulation processes and facilitate the rational design of novel manipulation systems.

This review emphasizes the potential of magnetic manipulation as a means of controlling the motion of both magnetic and non-magnetic objects at small scales. The technologies and the applications of magnetic micro-manipulation are of interest for multiple disciplines, such as electromagnetism, materials science, physics, biology, and fluid mechanics. Therefore, the collaboration between engineers and scientists from different fields would be of great value to foster such interdisciplinary innovations.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We gratefully acknowledge the financial support of the National Natural Science Foundation of China (51877087, 51577083) and the Young Elite Scientists Sponsorship Program by CAST (YESS, 2018QNRC001).

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