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Microfluid Nanofluid DOI 10.1007/s10404-011-0903-5

REVIEW PAPER

Micro-magnetofluidics: interactions between and fluid flow on the microscale

Nam-Trung Nguyen

Received: 15 September 2011 / Accepted: 30 October 2011 Springer-Verlag 2011

Abstract Micro-magnetofluidics refers to the and Keywords Micro-magnetofluidics Magnetism technology that combines magnetism with microfluidics to Microfluidics Magnetic bead Ferro fluid gain new functionalities. Magnetism has been used for actuation, manipulation and detection in microfluidics. In turn, microfluidic phenomena can be used for making tun- 1 Introduction able magnetic devices. This paper presents a systematic review on the interactions between magnetism and fluid flow Magnetofluidics traditionally refers to a class of devices that on the microscale. The review rather focuses on physical and utilize a magnetic fluid for sensing and actuating functions. engineering aspects of micro-magnetofluidics, than on the These devices were used as sensor for applications such as biological applications which have been addressed in a hearing aid and accelerometer. However, the term of number of previous excellent reviews. The field of micro- ‘‘magnetofluidics’’ is used here for the broader research field magnetofluidics can be categorized according to the type of involving magnetism and fluid flows. Figure 1 shows the the working fluids and the associated microscale phenomena basic relationships between the four principal fields of of established research fields such as magnetohydrodynam- with the most applications: fluidics, electrics, , ics, ferrohydrodynamics, magnetorheology and magneto- and magnetism. The links between these fields cover most phoresis. Furthermore, similar to microfluidics the field can modern technologies, especially micro/nanotechnologies. also be categorized as continuous and digital micro-mag- However, efforts on the exploration of magnetofluidics in netofluidics. Starting with the analysis of possible magnetic microscale and its applications have been scattered. Many in microscale and the impact of miniaturization on possibly interesting phenomena have been neglected due to these forces, the paper revisits the use of magnetism for the lack of a systematic approach. Compared to an electric controlling fluidic functions such as pumping, mixing, field, a magnetic field has various advantages in microfluidic magnetowetting as well as magnetic manipulation of parti- applications. Magnetic manipulation can utilize external cles. Based on the observations made with the state of the art that are not in direct contact with the fluid. Non- of the field micro-magnetofluidics, the paper presents some magnetic molecules and cells can be attached to magnetic perspectives on the possible future development of this field. beads, so that they can be sorted and detected by an external While the use of magnetism in microfluidics is relatively magnetic field. In contrast to electric concepts, magnetic established, possible new phenomena and applications can manipulation and detection are not affected by other be explored by utilizing flow of magnetic and electrically parameters such as surface charges, pH and concentra- conducting fluids. tion. In most cases, magnetic manipulation does not induce heating and does not require expensive external systems as compared to optical concepts. N.-T. Nguyen (&) A number of excellent reviews on applications of School of Mechanical and Aerospace Engineering, magnetism in microfluidics exist in the literature. However, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore the scopes of these reviews are limited to phenomena with e-mail: [email protected] existing biological applications. Gijs (2004) reviewed the 123 Microfluid Nanofluid

aspects of micro-magnetofluidics, than on the biological Electrokinetics applications which have been addressed in the above- Fluidics Electrowetting mentioned excellent reviews. The field of micro-mag-

s netofluidics can be categorized according to the type of the

c

i d

i working fluids, and the microscale phenomena of estab- u

Magnetofluidics l

o t

p lished research fields such as magnetohydrodynamics O Magnetism Electrics (MHD), ferrohydrodynamics (FHD), magnetorheology (MR) and magnetophoresis (MP). Furthermore, the field

Magneto optics can also be categorized as continuous and digital micro- magnetofluidics as in traditional microfluidics. Figure 2 shows an overview of micro-magnetofluidics and its sub- Optics Optoelectronics fields. In general, the field can be categorized according to Photonics the properties of the fluids or to the ways the fluids are Fig. 1 The basic domains of physics and their interfaces handled. The majority of magnetofluidic phenomena are based on electrically conducting fluids and magnetic fluids. The mutual interaction of magnetic field and the flow of use of magnetic beads for analytical applications. Later, Gijs electrically conducting fluids is covered by MHD, which is et al. (2010) followed up with a more comprehensive and well established and studied in the past hundred years updated review on applications of magnetic particles for (Davidson 2011). The fluids need to be electrically con- biological analysis and catalysis. Pamme (2006) extended ducting and non-magnetic, thus are limited to liquid , the scope in her review and covered a wider range of appli- plasmas and strong . The traditional applica- cations of magnetism in microfluidics: pumping, mixing, tions of MHD are , astrophysics, plasmaphysic manipulation of partiles and magnetic detection. Pamme’s and metallurgy. review was the first attempt to look at the field from a broader Magnetic fluid consists of a carrier fluid and a suspen- perspective and to consider both ways of the interactions sion of magnetic particles. Depending on the size of the between magnetism and microfluidics. Since Pamme’s magnetic particles,the magnetic fluid behaves differently review was only based on reported works, many potentially leading to three main areas of FHD, MR and MP. If the interesting phenomena were neglected. Weston et al. (2010) magnetic particles are smaller than about 10 nm, the discussed the use of different types of magnetic forces for thermal dominates over the magnetic energy fluid . Weston’s review was based on the discussion of induced by an external magnetic field. Thus, the particles possible magnetic forces followed by their applications. can disperse well in the carrier fluid. The whole fluid Fisher and Ghosh reviewed the use of magnetism for pro- behaves as a paramagnetic liquid and is called ferrofluid. If pulsion of swimming particles (Fischer 2011). This minire- the magnetic particles is large enough, ranging from 10 nm view offers a new perspective on ‘‘smart’’magnetic particles. to 10 lm, they interact and react to the external magnetic Magnetic micro- and nano-structures with unique shapes field changing the of the fluid. The fluid is then other than the conventional sphere can be controlled with an called magnetorheological fluid. For magnetic particles on external magnetic field. Weddemann et al. (2010) reviewed the order of several microns or larger, the magnetic parti- the implementation of magnetic components in total analysis cles need to be considered individually as discrete entities, systems for biomedical applications. The scope of this leading to the field of magnetophoresis. review was limited to the detection and manipulation of According to the properties of the fluid flow, the research magnetic beads. Similarly, the review of Suwa and Watarai field can be categorized as continuous-flow and digital only focuses on the manipulation and detection of micro- MMF. In continuous-flow MMF, fluids are supplied or particles (Suwa 2011). Ganguly and Puri reviewed micro- manipulated in a continuous manner, where the fluids exist in fluidic transport of ferrofluid and magnetic particles in a single phase as in the case of MHD pumps and MHD mixers MEMS, Bio-MEMS devices (Ganguly 2010). Friedman and or in multiple phases such as emulsion. In digital MMF, Yellen discussed the physical fundamentals of magnetic fluids are manipulated as individual droplets or marbles, separation, manipulation and assembly using relatively which are droplets with a protective coating of hydrophobic simple but useful scaling analysis of the magnetic and particles. Magnetic particles inside a droplet allow its con- its counter parts (Friedman 2005). trol and manipulation using a magnetic field. In this paper, micro-magnetofluidics (MMF) is under- Following fundamentals of magnetic forces in micro- stood as the science and technology that combines mag- scale, dimensionless numbers and their scaling laws are netism with microfluidics to gain new functionalities. The first discussed. Important phenomena are subsequently present review rather focuses on physical and engineering discussed according to the type of the fluid. 123 Microfluid Nanofluid

- droplet-based - MHD micropumps - instabilities - droplets - MHD micromixers - MR fluid plug - magneto wetting - charged droplets Single-phase Multi-phase - droplets with magnetic beads - magnetic marbles

Continous-flow micro magnetofluidics Digital micro magnetofluidics

Micro magnetofluidics

Electrically conducting fluids Magnetic fluids

Magnetohydrodynamics Small magnetic particles Medium magnetic particles Large magnetic particles (MHD) d<10 nm 10 nm1 m

DC-MHD AC-MHD -MHD Ferrohydrodynamics Magnetorheology Magnetophoresis (FHD) (MR) (MP)

Fig. 2 Micro-magnetofluidics, its subfields and representative applications. The line widths correspond to the number of references reviewed in this paper 2 Fundamentals of micro-magnetofludics ferromagnetic , can randomly flip direction under the influence of temperature. In the 2.1 Magnetic properties, field and forces absence of an external magnetic field, their average mag- netization is zero, this state is called superparamagnetic.In Magnetic force in microscale is generally well understood. the presence of an external magnetic field, the nanoparti- All existing theories and models assume the magnetic cles are magnetized and becomes ferromagnetic. Balancing material or the fluid as a bulk continuum and the force the magnetic energy and the thermal energy, a critical caused by a magnetic field gradient as a body force. A diameter for a ferromagnetic particle to be super para- magnetic field is induced by free Jf and magnetic can be estimated. Table 1 lists the critical bound electric current Jb. The set of equations diameters of ferromagnetic particles, below which the describing the magnetic field is: material is superparamagnetic as well as the critical , beyond which the material loses its net rH ¼ Jf ð1Þ magnetization. rM ¼ Jb ð2Þ A magnetic field in a liquid medium can induce the following magnetic forces: magnetohydrodynamic force, rB ¼ l0ðJf þ JbÞ¼l0J ð3Þ magnetic gradient force, magnetization gradient force B 0 4 r ¼ ð Þ and magnetic interfacial force. While the first three -7 where B, H, M and l0 = 4p 9 10 are the flux density forces are body forces, the last one is seen as an in (T), magnetic field strength in A/m, the local effective surface force and can take advantage of the magnetization in A/m and the permeability of vacuum in scaling law in microscale. N/A2. The relationship between the flux density, the field The Lorentz equation describes the force acting on a strength and the local magnetization results from Eqs. 1–3: charged species with charge q moving with a v in an electric field E and a magnetic field B: B ¼ l0ðH þ MÞ¼l0ð1 þ vÞH ð5Þ where v is the susceptibility of the material. Materials with fLorentz ¼ qðÞE þ v B ð6Þ negative susceptibility (v \ 0) are called diamagnetic. In the absence of an electric field, the sum of qv over a unit Paramagnetic materials have a positive susceptibility volume represents the current flux J and the magnetic body (v [ 0). Ferromagnetic materials such as , , force acting on the unit volume is: and their compound with rare earth elements have large positive susceptibility (v 0). In small fB ¼ J B ð7Þ

123 Microfluid Nanofluid

Table 1 Critical diameters of ferromagnetic particles conductivity rel and l is described by the Material Diameter (nm) Curie temperature (C) magnetic (Davidson 2011): Advection of magnetic ul Co 70 1,130 Re ¼ ¼ ð13Þ m of k Fe 14 770 Ni 55 358 where k = 1/(lrel) is the diffusivity of the magnetic field, u

Fe3O4 128 585 is the velocity of the fluid and l is the characteristic length scale. In a system with a large , the field line is bent toward the flow direction. In micro- In the absence of both electric field and electric current, the magnetofluidics, a typical length scale of l = 100 lm, force density acting on a magnetic fluid is calculated based velocity of u = 100 lm/s and magnetic field diffusivity of 2 on the magnetic energy density em ¼M B: The k = 1m/s, the typical magnetic Reynolds number is 8 magnetic force can then be derived as: OðRemÞ¼10 : For comparison, the magnetic Reynolds number of a sun spot, of the earth core flow are OðRemÞ¼ f ¼rem ¼rM B 8 2 10 and OðRemÞ¼10 ; respectively. Typical magnetic ¼ðM rÞB þðB rÞM Reynolds number of macroscale lab experiments and þ M rB þ B rM ð8Þ industrial metallurgy ranges from 10-3 to 10-1. The low magnetic Reynolds number in microscale indicates that the Since no electric current exists, the law of (Eqs. 1– flow of an electrically conducting fluid will not significantly 3) to r 9 B = 0 and r 9 M = 0, and the magnetic alter the magnetic field. Compared to other microfluidic force density acting on a magnetic fluid is: phenomena with the same flow condition and dimension, the f ¼ðM rÞB þðB rÞM: ð9Þ diffusivity of magnetic field OðkÞ¼1m2=s is several orders In a nonuniform magnetic field, the force acting on a of magnitude higher than the kinematic viscosity (momen- 6 2 homogenous magnetic fluid is called the Kelvin body force tum diffusivity) OðmÞ¼10 m =s and diffusion coefficient 9 2 (Weston et al. 2010): (species diffusivity) OðDÞ¼10 m =s: In contrast to momentum and specie diffusion, diffusive transport of a frB ¼ðM rÞB: ð10Þ magnetic field dominates over in microscale. In an inhomogeneous magnetic fluid with a gradient rM a Another dimensionless number used in traditional MHD is the Hartmann number (Davidson 2011): uniform magnetic field B, the force acting on the magnetic rffiffiffiffiffiffi fluid is: r Ha ¼ ¼ Bl el ð14Þ Friction force g frM ¼ðB rÞM: ð11Þ The gradient of is caused by a gradient where g is the dynamic viscosity of the fluid. Since Ha of , or concentration gradient of l, Hartman number decreases with miniaturization, magnetic nanoparticles as well as paramagnetic . indicating that Lorentz force does not scale favorably in In a two-phase system, the mismatch in magnetization microscale. The ratio between Lorentz force and inertial

M1 and M2 between the two fluids 1 and 2 leads to the force is called the interaction parameter (Davidson 2011): Kelvin body force which can be expressed as the gradient 2 Lorentz force relB l of surface stress (the ) and has the N ¼ ¼ ð15Þ Inertial force qu form (Friedman 2005): where q is the density of the fluid. The interaction F ¼ Vf s s parameter does not depend on the length scale. However, ¼ V½ðM1 M2ÞrB this number is proportional to the square of magnetic flux ¼ð½m1 m2ÞrB ð12Þ indicating the fast response of MHD flow when a strong magnetic field is applied. where m and m are the magnetic moments of fluid 1 1 2 Magnetic Bond number represents the ratio between enclosed in the volume V and the corresponding displaced magnetic force and force (Ganguly 2010): fluid 2. magnetic force Bom ¼ 2.2 Dimensionless numbers and scaling laws surface( tension force 2 l0vmlH ðbelow saturationÞ ¼ r In traditional MHD, the interaction between the magnetic l /M lH 0 sat (above ) ð16Þ field and the flow field of a fluid with an electrical r

123 Microfluid Nanofluid where r is the surface or interfacial tension, / is the number is large if the diameter of the particle is small. A volume fraction of the magnetic particles in the fluid and large particle reduces Sd leading to the dominance of Msat is the bulk saturation magnetization of the magnetic interaction. The magnetic particles are then able to self- material. Magnetic Bond number represents the magnetic assemble forming supraparticle structure (SPS) and leading body force and scales unfavorably in microscale as in the to magnetorheological behavior. case of Hartman number. The magnetic Laplace number The magnetophoretic stability number: represents the ratio between magnetic force and friction Em 1 MBd force: Smp ¼ ¼ ð21Þ Ef 18 gu 2 2 magnetic force l0H ql decreases with decreasing particle diameter. Thus, small Lam ¼ ¼ : ð17Þ friction force g2 magnetic particles cannot be separated by magnetic force To apply the scaling law to magnetic particles suspended in due to the dominant friction force. a fluid, the diameter d of the magnetic particle is taken as the characteristic length. The ratio between the magnetic p 3 3 Electrically conducting fluids energy Em ¼ mB ¼ 6d MB with M the magnetization of the particle and other types of energy such as: MHD for pumping and mixing of electrically conducting • thermal energy Eth = kBT with kB the Boltzman fluids in microfluidics was investigated and implemented constant and T the temperature, early. Qian and Bau gave a comprehensive review on 3 • gravitational potential energy Eg ¼ Dqghpd =6 with MHD-based microfluidics (Qian 2009). In addition to g the gravitational acceleration and h the relative height Maxwell’s equation and continuity equation, the flow of a to a surface, conducting fluid in a magnetic field is governed by Navier– 2 3 • potential energy E ¼ l0pM d with d Stokes equation with the additional term of Lorentz force: d 72ðd=dþ1Þ3 Du the distance between two neighboring particles and q ¼rp þ gr2u þ J B ð22Þ 2 Dt • frictional energy Ef = 3pgd u to a number of magnetofluidic dimensionless Solving the above equation for a two-dimensional parallel numbers, which are called here stability numbers S to plate model leads to the velocity distribution of the MHD estimate the relative stability of the magnetic particles. The flow (Davidson 2011):  thermal stability number also called the Langevin coshðÞHay=h u ¼ u 1 ð23Þ parameter: 0 coshðHaÞ 3 Em p MBd Sth ¼ ¼ ð18Þ For a small Hartman number, the velocity distribution Eth 6 kBT 2 approaches that of pressure-driven flow u = u0[1 - (y/h) ]. is proportional to d3. Thus miniaturization leads to For a large Hartmann number, the velocity distribution diminishing influence of magnetic energy. If the particles is pflattensffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi with a boundary layer called Hartman layer d ¼ small enough, thermal energy dominates leading to the qm=rB2: In most microfluidic applications, the conduct- superparamagnetic property mentioned above. ing fluids are solutions with low conductivity The sedimentation stability number: corresponding to a low Hartman number. Therefore, a Em MB velocity profile similar to that of pressure-driven flow can Ss ¼ ¼ ð19Þ Eg Dqgh be expected for MHD flow in microchannels. Liquid metals and plasma are not relevant for microfluidics. The two main does not scale with miniaturization because both gravita- challenges posed by electrolyte solutions are the low con- tional and magnetic forces are body forces. Since the two ductivity and the associated with the use of forces are comparable, magnetic force can replace buoy- in direct contact with the solution. However, the ancy force in microgravity condition. This feature has been ions generated by reduction/oxidation reactions at the used for free convective cooling in space flight. could lead to interesting flow phenomena that can The dipole stability number:  be utilized for mixing and pumping. E B d 3 Jiang and Lee (2000) reported a MHD micropump made S m d ¼ ¼ 12 þ 1 ð20Þ in a straight microchannel (Fig. 3a). The pump Ed l0M d worked with a maximum flux density of 0.44 T generated has two length parameters, the particle diameter d and the by a permanent and a from 10 to 60 V. distance between the particles d. The dipole stability Zhong et al. (2002) implemented the MHD concept in an

123 Microfluid Nanofluid

Flow annular microchannel (Fig. 3b) for pumping , sal- + ine solution and deionized . Due to the high con- ductivity of mercury, operation at relatively high Hartmann + number and high magnetic Reynolds number is possible even in the microscale. A serious problem of the above -- B DC-MHD micropump is the generation of hydrolysis bubbles at the electrodes. To avoid the problem of bubbles B trapped in the flow channel, Homsey proposed a design (a) (b) -- with electrodes placing outside the flow channel. The electric field is applied through a small gap connecting the Fig. 3 Basic configurations of MHD micropumps: a straight channel; reservoirs with electrodes and the flow channel. To b annular channel increase the flow rate, Homsy et al. (2007) used a strong magnet of 7 Tesla. A linear relationship between the flow correlates with the Reynolds number. Large Hartman rate and the applied voltage was found. Nguyen and number and corresponding high Reynolds number can be Kassegne (2008) reported a similar bubble-trapping design achieved with highly conducting fluid such as mercury or allowing operation with relatively high voltage and flow abundant supply of ions as in the case of RedOx-MHD rate. Recently, Kang and Choi (2011) proposed a DC-MHD pump. The high Reynolds numbers in these cases are with planar electrodes. However, the pumping effect was consistent with the unstable and turbulent flows observed in not as strong as that with conventional electrodes on the the experiments. Effective MHD pumping schemes are side wall. located at the lower right corner of Ha–Re parameter space. Bubble generation can be avoided if both AC magnetic The data in Fig. 4a show that the circular loop is a good field and AC electric field are used. The AC signals are design because the the entire closed-loop microchannel synchronized so that the flow direction remains unchanged works as a pump against a zero back pressure. Further- (Lemoff and Lee 2000). Since the field strength of an more, gas bubbles will absorb all the energy induced by the is much lower than a permanent magnet of Lorentz force. Thus, micropumps with AC-MHD and the same size, only a relatively small flow rate can be designs that can avoid bubble formation also belong to achieved with an AC-MHD micropump. The same concept those of better performance. The higher flow with high of AC-MHD was implemented in a microfluidic network, Hartman number agrees with the correlation shown in where each branch is driven by a MHD pump (Lemoff and Fig. 4b. The small magnetic Reynolds numbers of the Lee 2003). Bubbles can also be avoided by keeping the reported confirm the conclusion from scaling law that voltage bellow the standard potential of water the flowing conducting liquid in micro-magnetofluidics of 1.23 V. Leventis and Gao (2001) utilized reduction/ will not have any effect on the magnetic field. For mod- oxidation (RedOx) reaction at the electrodes to supply the eling purposes, it is safe to assume that the magnetic field is ions. High ion flux generated by Faradaic charging can be not affected by the flow of the conducting fluid. The achieved at low voltage without damaging the electrodes. magnetic field and the flow field can be decoupled and The Faradaic charging process occurs at the interface solved separately. between the electrode and the solution. A chemical species gains or loses leading to a flux of ions to maintain the neutral charge condition. An annular design based on 4 Magnetic fluids the AC-MHD concept was reported by West et al. (2003). The closed-loop design and Taylor dispersion promote fast Magnetic fluids are referred here to liquids with suspended mixing in this AC-MHD pump. Eijkel et al. (2003) magnetic particles. The particles can be as small as free reported another AC-MHD pump with annular design. The ions of a paramagnetic aqueous solution. Dissolved para- pump and electrode are formed by a 30-lm-thick magnetic ions such as Mn2?,Cu2? and rare earth ions can layer deposited on glass. significantly change the magnetic susceptibility of an Figure 4 shows the typical Hartman numbers of the aqueous solution. Larger magnetic nanoparticles can be above MHD pumps versus the magnetic Reynolds numbers stabilized in a solution with the help of a surfactant and the as well as the Reynolds numbers Re = qul/g. The solid dominant thermal energy. Since the magnetic particles are lines are the power-fitting functions. The parameters for well suspended in the carrier fluid, the entire magnetic fluid calculating the Hartman number and magnetic number are is treated as a continuum and are discussed under the taken from the respective papers. If the information is not section on ferrohydrodynamics (FHD). For larger particles, available, data of 1M NaCl solution is assumed. Since the dipole interaction is important leading to magnetoviscous Lorentz force is the driving force, the Hartman number phenomena. In this case, the magnetic fluid can still be 123 Microfluid Nanofluid treated as a continuum and will be discussed under the (2004) the magnetocaloric effect. The additional body force section on magnetorheology (MR). For very large magnetic experienced by the fluid from (11) has the magnetocaloric particles, the particles should be treated as discrete entities form (Love et al. 2004):  in a carrier fluid. The manipulation of magnetic particles in 1 oM diamagnetic carrier fluid and diamagnetic particles in fmc ¼ B rT: ð25Þ 2 oT magnetic carrier fluid are discussed under the section on magnetophoresis (MP). Love et al. used ferrofluid based on Mn0.5Zn0.5Fe2O4 that has a low Currie temperature of 150C. Li et al. (2008) and 4.1 Ferrohydrodynamics Lian et al. (2009) used a similar Mn–Zn based fluid to realize a cooling loop using magnetocaloric pumping. The Navier–Stokes equation formulated with an additional The magnetic field was provided by a NdFeB permanent term of magnetic gradient force reads (Rosenswei 1997) magnet. This pumping concept was implemented in a heat exchanger for cooling applications (Xuan 2011). Pal et al. Du q ¼rp þ gr2u þðM rÞB: ð24Þ (2011) used an electromagnet to provide a homogenous Dt magnetic field in the flow channel (Fig. 5a). The above equation reveals that either a gradient of the In a two-phase system, ferrofluid forms a droplet or a magnetic field or of the magnetization field of the ferrofluid is plug which works as a piston to drive the other immiscible needed to move the fluid against a pressure gradient. Mao phase. Hatch et al. (2001) used ferrofluid plugs as both and Koser (2006) reported numerical and experimental valve and piston to realize a micropump, (Fig. 5b). Two results of single-phase ferrofluid using a traveling magnetic external permanent magnets were used. A stationary field. The pumping frequency is on the order of 1 kHz. Since magnet to hold a ferrofluid plug in place working as a both Brownian and Neel relaxation times (Rosenswei 1997) valve. A second magnet moves in a loop working as a of the magnetic nanoparticles correspond to a much higher piston to pump another immiscible phase such as water in frequency, this relatively low frequency may probably be the microchannel. Ahn et al. (2004) used a rotating exter- caused by the formation of larger particle chains (Mao et al. nal magnet to drive the ferrofluid plug. Sun et al. (2007, 2011). The pump can only achieve a pressure head of few 2008, 2009) used the same concept to drive liquid in a Pascals at an extremely high driving current of 10 A. closed circular microchannel loop (Fig. 5c). A single per- Furthermore, the high current induces heating, which in turn manent magnet can be used for pumping sample liquid in affect the susceptibility and the magnetization of the multiple concentric microchannel loops. Hartshorne et al. ferrofluid. The magnetization degrades with increasing (1996) reported a design with three ferrofluid plugs, two temperature. Beyond the critical Currie temperature working as valves and one as the piston. Synchronizing the (Table 1), the particles lose their net magnetization. A of the pistons and the two valves allow pumping of temperature gradient leads to a gradient of magnetization and both air and water. The pump cycle of 30 minutes makes a gradient of magnetic body force that can drive the ferrofluid the pump not practical for most applications. Ando et al. in a microchannel. This phenomena was called by Love et al. (2009a) used a permanent magnet to keep a ferrofluid plug

2 2 (a)10 (b) 10 Zhong 2002 Zhong 2002 (mercury) (mercury) 1 1 10 10

Leventis 2001 0 0 Leventis 2001 10 (RedOx) 10 (RedOx)

0.4

0.6 m Homsy 2007 Homsy 2007 -1 -1 10 10 Ha ~ Re Kang 2011 Ha ~ Re Kang 2011

Jang 2000 -2 -2 10 Homsy 2005 10 Jang 2000 Homsy 2005 Hartman number Ha Eijkel 2003 Lemoff 2003 Eijkel 2003 Lemoff 2000 Hartman number Ha Lemoff 2003 Lemoff 2000 -3 Zhong 2002 (saline) -3 10 10 Zhong 2002 (saline) Nguyen 2008 Nguyen 2008 Zhong 2002 (water) West 2003 Zhong 2002 West 2003 -4 -4 (water) 10 10 -4 -2 0 2 4 -20 -15 -10 -5 0 10 10 10 10 10 10 10 10 10 10 Reynolds number Re Magnetic Reynolds number Rem

Fig. 4 Hartman numbers of reviewed MHD micropumps versus Reynolds number (a) and magnetic Reynolds number (b) 123 Microfluid Nanofluid

permanent maximum flow rate the pump can achieve. The strength of Electromagnet S magnet 1 N the magnetic field represented by the magnetic Bond number does not affect the Reynolds number. In contrast, the mechanical pumps using a ferrofluid plug as an actuator Ferrofluid have a wide range of Reynolds number indicating that the Ferrofluid Heater N permanent N pump performance depends on other parameters such as S magnet 2 S pumping frequency and the viscosity of pumped liquid. (a) (b) (c) permanent magnet The stroke volume of these pumps does not depend on the Electromagnets magnetic field strength because the ferrofluid is already working in a saturated state. Another observation from Fig. 6b is that the magnetic Bond number are relatively N N N N high. That means magnetic body force dominates over S S S Ferrofluid S Ferrofluid interfacial tension. Using a ferrofluid plug as an actuator permanent permanent magnet magnet requires this condition because magnetic force should (d) (e) Electromagnet Check valves overcome both surface tension and friction to move the plug. In the case of the pump reported by Ando et al. (2009a, b) the magnetic force should be large enough to

N S deform the liquid interface, thus a large magnetic Bond number is needed. permanent (f) magnet (g) Ferrofluid A micropump with an actuating ferrofluid plug is con- sidered as a multiphase system. Recently, the formation, Fig. 5 Concepts of ferrohydrodynamic micropumps: a magnetocalo- manipulation and application of ferrofluid droplets in an ric pump (Pal et al. 2011); b annular pump with two ferrofluid plugs (Hatch et al. 2001); c annular pump with one ferrofluid plug (Sun immiscible fluid have attracted great interests from both et al. 2007); d peristaltic pump (Ando et al. 2009a); e pump with microfluidics and magnetic fluid communities. In the three ferrofluid valves (Ando et al. 2009b); f pump with check valves macroscale, the magnetic Bond number is large due to the and ferrofluid piston (Yamahata et al. 2005); g stepper ferrohydro- dominant magnetic force. For instance, a normal magnetic dynamic pump (Nguyen 2009) field applied to the free surface of a ferrofluid leads to the formation of free-standing spikes called Rosensweig in a glass capillary at a fixed location (Fig. 5d). Actuating instability (Cowley 1967). Research on multiphase systems coils around the capillary causes a peristaltic motion of the involving ferrofluid was mainly focused on the instability plug driving the immiscible phase. The team used the same pattern of a ferrofluid droplet under different conditions of concept to control three separate ferrofluid plugs in a glass magnetic field (Rhodes et al. 2005; Chen et al. 2007). capillary. Synchronizing the actuation of the three plugs In microscale, the smaller magnetic Bond number leads to pumping of the nonmagnetic immiscible fluid makes droplets more stable against the magnetic force. (Ando et al. 2009b) (Fig. 5e). Yamahata et al. (2005) used The formation of ferrofluid droplets can be realized with a ferrofluid as the piston to drive a check valve micro-pump common methods of droplet-based microfludics such as (Fig. 5f). The reciprocating motion of the ferrofluid plug is shear- and pressure-driven formation at a T-junction or a induced by an external permanent magnet. Nguyen et al. flow-focusing junction. Since ferrofluid is a special class of used multiple solenoid magnets around a loop and a fer- nanofluid, even without an applied magnetic field, the rofluid plug to realize a stepper ferrohydrodynamic droplet formation of ferrofluid is affected by the nanopar- micropump (Nguyen 2009) ( Fig. 5g). ticles and their surfactant. Nanoparticles at the fluid inter- Figure 6a depicts the magnetic Bond number of the face reduce the interfacial tension leading to the formation above ferrohydrodynamic pumps versus the corresponding of smaller droplets as compared to those of the pure carrier Reynolds number. The filled circles represent the single- fluid under the same condition (Murshed et al. 2009). Chen phase magnetocaloric pumps, where the ferrofluid itself is et al. (2009) only used the magnetic body force to form pumped. The white circles represent multi-phase pumps ferrofluid droplets through an orifice. Tan et al. (2010) where the ferrofluid plug works as an actuator for a con- combined pressure-driven flow with the magnetic force to ventional mechanical pump. We can clearly observe control the droplet formation process at a microfludic the difference in behavior of these two pump types in the T-junction. The magnetic field gradient was generated by Bom–Re space. Since the magnetocaloric concept relies on an external permanent magnet. The direction of the the temperature dependence of the ferrofluid, the limited induced magnetic force is controlled by the relative posi- range of driving temperature gradient leads to a narrow tion between the the T-junction and the magnet. Both range of the Reynolds number, which represents the direction and magnitude of the magnetic force can be used 123 Microfluid Nanofluid

4 3 Fig. 6 Bond numbers versus (a)10 (b) 10 Reynolds number of a reviewed Nguyen 2010 Love 2004 (oil) Love 2004 (water) FHD micropumps (the filled Lian 2009 Li 2009 2 circles and the open circle m

m 10 1.6 represent the single-phase and Hatch 2001 Chen 2007 3 multi-phase FHD micropumps, 10 m 4x102 Ahn 2004 1 Bo ~ Re respectively); b reviewed 10 droplet-based systems (for a Liu 2011 Ando 2009b Ando 2009a Tan 2010 sessile droplet, the diameter and Hartshorne 2004 Sun 2007 0 properties of the ferrofluid is 10 Probst 2011 taken for calculating the 10 2 Reynolds number. For the Pal 2011 -1 droplet formation process, the 10

Magnetic Bond number Bo Reynolds number is calculated Magnetic Bondnumber Bo Yamata 2005 Nguyen 2007 based on the properties of 1 -2 carrier fluid and the hydraulic 10 10 -4 -2 0 2 -3 -2 -1 0 1 diameter of the microchannel) 10 10 10 10 10 10 10 10 10 Reynolds number Re Reynolds number Re

to tune the size of the formed ferrofluid droplets. In a solenoid electromagnets with a maximum field of 200 mT uniform magnetic field, the magnetic body force disappears for controlling the movement of the ferrofluid droplet. Due due to the missing field gradient. However, the mismatched to the strong decay and the larger distance between the magnetic susceptibilities of the ferrofluid and the immis- magnet and the droplet, the actual magnitude of the actu- cible phases lead to a surface force (12) that can be used for ating magnetic field is only few mT. With digital image controlling the formation process of ferrofluid droplets (Liu acquisition and processing, a closed-loop control of the et al. 2011). Under a uniform magnetic field in flow droplet path can be achieved with an average error of about direction, the stretching of the fluid interface at the flow- 1/3 of the droplet diameter. focusing junction leads to the formation of larger ferrofluid A sessile magnetic droplet on a planar surface represents droplets (Liu et al. 2011). In a T-junction, the uniform a convenient platform for digital microfluidics. Chen and magnetic field has the opposite effect, the formed droplet Cheng (2008) investigated Rosensweig instability of a becomes smaller (Tan 2011). The size of the droplet in a sessile ferrofluid droplet in a uniform field and a large ferrofluid emulsion can be adjusted by flow rates, flow rates magnetic Bond number. Nguyen et al. (2010) utilized a ratio, pressures and temperature (Nguyen et al. 2007). A smaller nonuniform magnetic field to deform the sessile ferrofluid emulsion system can have interesting behavior ferrofluid droplet and observed an decreasing apparent similar to a magnetorheological fluid when exposed to a contact angle with increasing magnetic field. This phe- magnetic field (Liu et al. 1995). Figure 6b shows the nomenon was termed as magnetowetting, which later was characteristic magnetic Bond number and Reynolds num- confirmed by Berim and Ruckenstein using density func- ber of the above examples on formation of ferrofluid tional theory of simple fluids (Berim 2011). Based on this droplets. While a large magnetic Bond number is needed model, the contact angle increases with increasing uniform for forming droplets with magnetic force only, the mag- magnetic field approaching an asymptotic value, Fig. 7a. In netic Bond number increases with increasing Reynolds a nonuniform field, the contact angle first increases with number for the combination of hydrodynamic and mag- increasing magnetic field and then decreases almost line- netic forces. arly with the increasing field strength, Fig. 7b. A sessile A stand-alone magnetic droplet can be manipulated with droplet can be manipulated by moving the external magnet. an external magnetic field. Nguyen et al. (2006) use planar Since the magnetic force needs to overcome the capillary microcoils to control the one-dimensional movement of a force and friction force, the motion of the droplet depends ferrofluid droplet suspended in silicone oil. The magnetic on its size, the field strength and the motion speed. An force is large enough to overcome the friction force and the operation space for a moving sessile droplet was derived deformation of the droplet (Nguyen et al. 2006; Beyzavi with these three parameters (Nguyen et al. 2010). Magnetic 2009). The concept was later extended to two-dimensional beads with size ranging from one to tens of micrometers manipulation using four planar microcoils (Beyzavi 2010). are not homogenously distributed in the droplet, and can be The microcoils can only produce a magnetic field on the easily clustered or extracted from the liquid under a strong order of 1 mT. Thus an external permanent magnet was magnetic field. needed to magnetize the nanoparticles in the ferrofluid The different behaviors of contact angles in a uniform droplet. Probst at al. (2011) used four stronger external and nonuniform field may potentially lead to a new

123 Microfluid Nanofluid

’> ’< 4.2 Magnetorheology

’ ’ A magnetorheological fluid (MR fluid) consists of larger N magnetic particles on the order of 100 nm to 10 lm. The S permanent particles are too large to keep them suspended by Brownian (a) B (b) magnet motion. Under a magnetic field, magnetic particles align under dipole interaction and form chains and structures Diamagnetic droplet ’< permanent called supraparticle structures (SPS). These chains restrict magnet ’ the fluid flow perpendicular to the magnetic field,

N increasing the apparent viscosity of the fluid. If the field is Magnetic nanotubes (c) S strong enough, the MR fluid behaves as a viscoelastic solid. hydrophobic A ferrofluid emulsion system also shows a similar behav- v particles ior, which can be explained theoretically (Liu et al. 1995). v v Despite the interesting properties of magnetorheological permanent N permanent N S magnet S magnet fluids, not many applications were reported in the litera- (d) (e) ture. The magnetically controllable viscosity of MR fluid Fig. 7 Magnetowetting phenomena: a in an uniform magnetic field; can be used for separation of large molecules in micro- b in a nonuniform magnetic field; c with magnetically controllable channels. The change in viscosity helps to solve the surface; d sliding motion of a sessile ferrofluid droplet; e rolling problem of filling microchannels with highly viscous gel motion of a ferrofluid marble matrix. The separation channel is first filled with the less viscous fluid in the absence of a magnetic field. Once the fluid is in place, the magnetic field is turned on and changes manipulation concept based on magnetowetting. The non- it into a solid separation matrix. Doyle et al. (2002) utilized uniform magnetic field can be generated with an array of the SPS assembled in a microchannel as the separation microcoil. Together with an overlapping uniform field, matrix for deoxyribonucleic acid (DNA). Only a relatively switching the coils and the local nonuniform field could small magnetic field of around 10 mT is required to turn the move a sessile ferrofluid droplet around. Another approach magnetic liquid into the matrix. The spacing of the matrix for magnetowetting is using magnetically controllable can be tuned with particle size and concentration. surface. Zhou et al. (2011) created a nanostructured surface MR has similar properties as electrorheological (ER) made of tiny polymeric tubes with embedded superpara- fluids whose viscosity is changed under an applied electric magnetic Fe3O4 nanoparticles. The tubes respond to an field (Zhang et al. 2009). Similar to MR fluids, dipole external magnetic field leading to the change of the contact interactions allow the formation of particle columns and angle of the droplet (Fig. 7c). the increase of the viscosity. As reported by Niu et al. (Niu Liquid marbles are formed by self-assembly of hydro- et al. 2009) for ER droplets, MR droplets can be formed phobic particles at the liquid/air interface of a liquid and manipulated by a magnetic field. The manipulation of droplet (Aussillous 2001). Since the hydrophobic particles these ‘‘smart’’ droplets would allow the implementation of prevent the direct contact between the liquid and a surface, more complex microfluidic functions such as logic gates a liquid marble represents a perfect nonwetting system with (Wang et al. 2010). a contact angle close to 180. Ferrofluid can be used to form a magnetic marble (Bormashenko et al. 2008). While 4.3 Magnetophoresis a sessile ferrofluid droplet dragged by a moving permanent magnet slides on a smooth surface (Fig. 7d), a ferrofluid In a magnetic field gradient, a magnetic bead driven by the marble roles under the same condition (Fig. 7e). A mag- gradient force moves along the gradient. The phenomenon netic marble can also be formed with an diamagnetic fluid is called magnetophoresis. Formulating Eq. 12 for a mag- and hydrophobic magnetic particles. Zhao et al. (2010) netic particle, the force acting on a particle in a carrier fluid synthesized highly hydrophobic Fe3O4 nanoparticles for with mismatching susceptibilities is (Gijs et al. 2010): making magnetic water marbles. The marble can be Vðv v Þ manipulated with an external permanent magnet. Since the F ¼ p f ðB rÞB ð26Þ m l coating particles can be manipulated, this type of marble 0 allows the hydrophobic coating to open and to close where V is the volume of the particle. Since the magnetic reversibly leading to controllable merging of two marbles. force is acting based on the mismatch of susceptibilities, Marble with magnetic coating also rolls after a moving both manipulating a magnetic particle in a diamagnetic permanent magnet (Xue et al. 2010). fluid and a diamagnetic particle in a magnetic fluid are 123 Microfluid Nanofluid possible. The term (Br)B is called the magnetic force the solution, the magnetophoretic force is zero and the field. Magnetic field of microcoils are on the order of few particle stays focused at this location. Since the concept is mT, two orders of magnitude smaller than that of a similar to isoelectrophoresis, this technique was called by permanent magnet. As results, magnetophoretic velocity Kang et al. (2008) isomagnetophoresis (Fig. 8f). Krishnan induced by a coil is about four orders of magnitude smaller et al. (2009) combines magnetophoresis with dielectro- than that generated by a permanent magnet. Since both the phoresis to separate magnetic beads. magnetic field and the field gradient contribute to the Besides ferromagnetic structures, current conducting strength of the magnetic force, overlapping an external electro magnet in form of microcoils (Song et al. 2009)or uniform magnetic field with a local nonuniform magnetic micro-stripes (Kong et al. 2011; Derec et al. 2010) field of a microcoil would result in a strong local magentic (Fig. 8g) also have been used for magnetophoretic sepa- force. Balancing the magnetic force and the friction force ration. The field strength and field gradient will be of a spherical particles Ff = 3pgdu, the magnetophoretic improved if the field lines of a microcoil are trapped by a velocity can be estimated as (Gij 2004): ferromagnetic core. Choi et al. (2001) reported the inte- 2 gration of an electromagnet based on a planar microcoil d ðvp vf ÞðB rÞB 1 u ¼ ¼ fðB rÞB ð27Þ and a permalloy yoke. The same group reported the fab- 18l g l 0 0 rication of a more complex integrated solenoid electro- 2 where f = d (vp - vf)/18g is called the magnetophoretic magnet with NiFe core (Rong et al. 2006). mobility. For the same magnetic force field, the magne- Magnetophoretic effect also applies to diamagnetic tophoretic velocity scales with the square of the particle particles in a paramagnetic solution. Watarai and Namba size. The smaller the particle, the slower is the velocity. (Watarai 2001) observed magnetophoretic migration of

Since the magnetophoretic velocity is also proportional to polystyrene particles in (II) cloride (MnCl2) the magnetic gradient, the small size in microfludics and solution. the design of sharp magnetic poles (Afshar et al. 2011) can Magnetophoretic transport of particles is more chal- help to increase magnetophoretic velocity. lenging than magnetophoretic separation, because in the The dependence of magnetophoretic velocity on the size latter case the particles are transported by the fluid flow. and magnetic susceptibility allows the separation of dia- Without a flow, the magnetic force is the sole driving force magnetic and magnetic particles (Pamme 2004) as well as for the magnetic beads. In general, the same concepts used of magnetic particles with different sizes (Pamme et al. for magnetic droplets can be used for magnetic particles. 2006) (Fig. 8a). Han and Frazier (2006) utilized a ferro- Magnetic particles are dragged by a moving external per- magnetic wire made of electroplated NiFe in a manent magnet (Fig. 5a) or by an array of electromagnets microchannel to generate a magnetic field gradient and (Joung et al. 2000) (Fig. 5g). Lee et al. (2004) realized an consequently a magnetic force field (Fig. 8b). The field electromagnetic trap by two pairs of stripes with opposing was strong enough to separate paramagnetic red blood cells currents (Fig. 8h). Wirix-Speetjens et al. (1944) used saw- and diamagnetic white blood cells. With multiple stages, tooth current conductor to trap and transport particles the sorting efficiency of this concept was improved sig- (Fig. 8i). Plouffe et al. (2011) used a simple current con- nificantly (Jung et al. 2010) (Fig. 8c). The difference in ductor parallel to the flow channel to separate and trap magnetophoretic results in trajectories with dif- magnetic particles. Deng et al. used micro-stripes to locally ferent angles. Adams et al. (2008) utilized this phenome- trap the particles. Sequential activation of neighboring non and the effect of magnetic force field around a traps allows the transport of magnetic particles (Deng et al. ferromagnetic wire to sperate cells tagged to magnetic 2001) (Fig. 8j). beads with different susceptibilities and sizes (Fig. 8d). More control over magnetophoresis can be achieved, if Kang and Park (1784) utilized the sharp poles of the saw- the particle is designed to have a more complex shape than tooth ferromagnetic structure to generate the magnetic field the usual sphere. In this case, the particles can be consid- gradient (Fig. 8e). The corresponding magnetic force field ered as self-propelling devices or micro/nanobots. Kline was used to trap iron-contaminated nanotubes. et al. (2005) fabricated a 1.5 lm 9 400nm nanorod by Smistrup et al. (2005) used integrated permalloy structures alternate of , nickel and gold. While on both sides of the flow channel to separate magnetic bubbles generated by catalytic reaction of H2O2 at beads. Kang et al. (2008) further improved the sensitivity the platinum end provide propulsion, the nickel stripes of magnetophoretic separation by using a gradient of sus- allows remote magnetic control. Burdick et al. (2008) ceptibility generated by diffusive mixing of demonstrated that such as magnetically controllable paramagnetic diethylenetriamine-pentaacetic acid (Gd- nanobot can be attached to a cargo (polystyrene bead DTPA). At a location along the concentration gradient, coated with iron ) and move in a microchannel where the susceptibility of the particle matches with that of network. 123 Microfluid Nanofluid

Fig. 8 Manipulation concepts magnetic field magnetic bead based on magnetophoresis: a S permanent gradient free-flow magnetophoresis N magnet B A

(Pamme 2004); b sorting with r

e

f magnetic gradient induced by a f

u ferromagnetic structure (Han b 2006); c multi-stage sorting with magnetic gradient induced A ferromagnetic sample trajectory A-A by a ferromagnetic structure (a) (b) material (Jung et al. 2010); d sorting with ferromagnetic stripes S (Adams et al. 2008); e trapping N with magnetic gradient induced by sharp poles (Kang 1784); f sorting with a gradient of sample susceptibility (Kang et al. 1 2 2008); g sorting with bead output ferromagnetic electromagnetic stripes (Joung ferromagnetic (d) material stripes et al. 2000); h trapping transport (c) with wire loop created by solution A S addressable current conducting B A N lines (Lee et al. 2004); i f trapping and transport with saw- sample tooth conducting wires (Wirix- ferromagnetic susceptibility Speetjens 1944); j trapping and sample material gradient transport with meandering A (f) A-A conducting wires (Deng et al. (e) solution B 2001) I I I

I I (g) (h)

I I I

I I (i) (j)

Tierno et al. (2008a, b) assembled two paramagnetic using chiral structures such as helical and screw-shaped beads with different diameters of 2.8 and 1 lm. The beads particles. Zhang et al. (2009) fabricated a structure with a are linked by a 8-nm-long cDNA strand and form a para- softmagnetic head and a helical tail. The structure can magnetic asymmetric doublet. A rotating AC magnetic swim with a speed proportional to the rotational frequency field was generated by two external electromagnets. A third of the magnetic field. Ghost and Fisher (2009) fabricated a electromagnet generates a stationary magnetic field. The screw-shaped structure with a spherical silica head and induced rotation of the doublet results in a translation on silicon oxide tail. Half of the structure is coated by a layer the surface of a glass plate. The direction of the motion can of cobalt which is subsequently magnetized. Garstecki be controlled by the current direction in the electromag- et al. (2009) fabricated magnetic micro-swimmers in nets. Dreyfus et al. (2005) used a similar technique to link PDMS by mixing the prepolymers with magnetic particles up magnetic beads to a flexible chain. The external rotating and curing under a magnetic field. The resulting planar magnet induces a beating motion mimicking flagella of PDMS structures has therefore a permanent magnetic spermatozoa. The speed and direction of the motion can be moment. An external uniform rotating magnetic field controlled by the external magnetic field. Another strategy twisted the structure into helical and allowed it to translate rotational motion into translational motion is to propel in a translational manner. This concept mimics

123 Microfluid Nanofluid

-3 10 (Siegel et al. 2006). Magnetic field can be manipulated with a multiphase system with mismatched magnetic sus- ceptibility. There are examples reviewed in this paper where a gradient or a change in susceptibility can affect the 1.1 Garstecki 2009 -4 Zhang 2009 magnetic field. For instance, ferromagnetic solid structures 10 Re ~ f can trap the field lines and generate a magnetic field gra- dient (Han 2006, Jung et al. 2010). This idea can be

Ghost 2009 extended to magnetic fluid such as ferrofluid. The advan- tage of using magnetic fluid is that the geometry and -5 10 configuration of the is tunable using Reynolds number Re conventional fluidic methods. The example of isomagne- tophoresis (Kang et al. 2008) proves that this idea can Tierno 2008 work, and the use of microfluidics for tunable magnetic Dryfus 2005 -6 functions could be an exciting research area in the future. 10 1 2 3 10 10 10 Faradaic RedOx-reactions at electrodes are interesting Rotational frequency f (Hz) phenomena for supplying ions for MHD flow. With a right electrode design and , MHD flow can be utilized Fig. 9 Typical Reynolds number of magnetic micro-swimmer versus corresponding rotational frequency of the driving magnetic field (the for designing effective micromixers. Coupling an external Reynolds number is calculated based on the length of the structure, its magnetic field into a lab-on-a-chip device not only allows velocity and the properties of the surrounding fluid) magnetic manipulation, but also other microfluidic func- tions such as pumping and mixing. microorganisms that use rotational flagella and cilia to Recent works on the manipulation of contact angle of a swim. Figure 9 summarizes the typical parameters of the sessile droplet using an external magnetic field indicate above magnetic micro-swimmers. If the magnetic torque is another trend in micro-magnetofluidics: magnetowetting. strong enough for the swimmer to follow the rotation of the There are two main strategies for magnetowetting: the magnetic field, the swimming velocity is almost propor- manipulation of force balance at the contact line using tional to the rotational frequency. magnetic liquid, field gradient and magnetic particles and the manipulation of surface wetting properties using magneti- cally responsive surface. Preliminary works show that both 5 Conclusions and perspectives strategies could lead to magnetic control of a sessile droplet and offer an actuation alternative digital microfluidics. The above review presents the state of the art of the field There is still a niche for applications of MR fluids in micro-magnetofluidics. Three basic observations are made microfluidics. Active control of MR fluid droplets would with the above-reviewed works. First, micro-magnetoflui- allow complex manipulation in a microfluidic network. dics is not only about magnetic interactions of flow in Ferrofluid emulsion represents an interesting MR fluid, microchannels, but also about behaviour and flow around which has not been systematically explored. With micro- nano/microscopic objects. Second, most of the current fluidic technology, high-quality monodispersed ferrofluid works focus on the use of magnetism to manipulate fluid emulsion can be created. Fundamental investigations of flow or movement of particles in a fluid. The other pathway ferrofluid emulsions could lead to novel applications in the of the interaction, using fluid flow to manipulate magnetic near future. field, is generally neglected. Third, the general reception of The recent development of magnetic micro-swimmers magnetic force as body force prevents the further investi- points to another exciting topic of micro-magnetofluidics. gation and application of magnetowetting. Due to its wireless nature, magnetic field is an attractive As mentioned above, the small Hartman number in most solution for the actuation of ‘‘smart’’ particles. The induced micro-magnetofluidic applications does not allow a flowing magnetic force can not only be used for propulsion, but conducting fluid to affect the magnetic field passing also for motion control if the particle is driven by other through it. However, the use of liquid metals with high concepts. These magnetic micro-swimmers could have conductivity would allow the increase of Hartman number. potential applications in micro-surgery and drug delivery. Although mercury has been used for MHD actuation, the Another exciting idea is the use of a large number of these availability of other liquid metals and alloys with magnetic micro-swimmers in a droplet to gain macroscopic low melting temperature would allow the use of liquid control over the droplet. Thus, droplet-based micro-mag- metals in microchannels (Siegel et al. 2007). A magnetic netofluidics can work with any liquid suitable for practical field can be generated with a liquid metal electromagnet lab-on-a-chip applications. 123 Microfluid Nanofluid

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