Current Opinion in & Interface Science 10 (2005) 141 – 157 www.elsevier.com/locate/cocis

Magnetic and flows

Carlos Rinaldi a,1, Arlex Chaves a,1, Shihab Elborai b,2, Xiaowei (Tony) He b,2, Markus Zahn b,*

a University of Puerto Rico, Department of Chemical Engineering, P.O. Box 9046, Mayaguez, PR 00681-9046, Puerto Rico b Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science and Laboratory for Electromagnetic and Electronic Systems, Cambridge, MA 02139, United States Available online 12 October 2005

Abstract

Major recent advances: Magnetic fluid rheology and flow advances in the past year include: (1) generalization of the relaxation equation by Shliomis and Felderhof and generalization of the governing ferrohydrodynamic equations by Rosensweig and Felderhof; (2) advances in such biomedical applications as drug delivery, hyperthermia, and magnetic imaging; (3) use of the antisymmetric part of the viscous tensor due to spin velocity to lower the effective magnetoviscosity to zero and negative values; (4) and ultrasound velocity profile measurements of spin-up flow showing counter-rotating surface and co-rotating volume flows in a uniform rotating . Recent advances in magnetic fluid rheology and flows are reviewed including extensions of the governing magnetization relaxation and ferrohydrodynamic equations with a that has an antisymmetric part due to spin velocity; derivation of the tensor in a with spin velocity and its relationship to magnetically controlled heating; magnetic force and torque analysis, measurements, resulting flow phenomena, with device and biomedical applications; effective magnetoviscosity analysis and measurements including zero and negative values, not just reduced ; ultrasound velocity profile measurements of spin-up flow showing counter-rotating surface and co-rotating volume flows in a uniform rotating magnetic field; theory and optical measurements of ferrofluid meniscus shape for tangential and perpendicular magnetic fields; new theory and measurements of ferrohydrodynamic flows and instabilities and of thermodiffusion (Soret effect) phenomena. D 2005 Elsevier Ltd. All rights reserved.

Keywords: Magnetic ; ; Ferrohydrodynamics; Magnetization; Magnetic susceptibility; Magnetic forces; Magnetic torques; Magnetoviscosity; Magnetic thermodiffusion; Magnetic Soret effect

1. Introduction to magnetic fluids 5–15 nm and volume fraction up to about 10% [1&&,2&&,3&,4&,5&]. 1.1. Ferrofluid composition keeps the nanoscopic particles from settling under , and a layer, such as oleic Magnetic fluids, also called ferrofluids, are synthesized acid, or a polymer coating surrounds each particle to provide colloidal mixtures of non-magnetic carrier , typically short range steric hindrance and electrostatic repulsion water or , containing single domain permanently magne- between particles preventing particle agglomeration [6&]. tized particles, typically , with diameters of order This coating allows ferrofluids to maintain fluidity even in intense high-gradient magnetic fields [7] unlike magneto- rheological fluids that solidify in strong magnetic fields * Corresponding author. Tel.: +1 617 253 4688; fax: +1 617 258 6774. [2&&,8]. Recent experiments and analysis show that magnetic E-mail addresses: [email protected] (C. Rinaldi), dipole forces in strong magnetic fields cause large nano- [email protected] (A. Chaves), [email protected] (S. Elborai), [email protected] (X. He), [email protected] (M. Zahn). particles to form chains and aggregates that can greatly 1 Tel.: +1 787 832 4040/3585; fax: +1 787 834 3655/+1 787 265 3818. affect macroscopic properties of ferrofluids even for low 2 Tel.: +1 617 253 5019; fax: +1 617 258 6774. concentration [9–12]. Small angle neutron

1359-0294/$ - see front matter D 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.cocis.2005.07.004 142 C. Rinaldi et al. / Current Opinion in Colloid & Interface Science 10 (2005) 141–157 scattering (SANS) distinguishes between magnetic and non- 2. Governing ferrohydrodynamic equations magnetic components of ferrofluids allowing , composition, and magnetization profiles to be precisely 2.1. Magnetization determined [13,14]. Nanoparticle dynamics, composition, and magnetic relaxation affect magnetic fluid rheology 2.1.1. Langevin magnetization equilibrium which can be examined using magnetic field induced Ferrofluid equilibrium magnetization is accurately birefringence [15–19]. described by the Langevin equation for The study and applications of ferrofluids, invented in [1&&,2&&,3&,4&,5&,31&&] the mid-1960s, involve the multidisciplinary sciences of chemistry, , and . Because of the 1 M0 ¼ MS cotha À ; a ¼ l0mH=kT ð1Þ small particle size, ferrofluids involved nanoscience and a nanotechnology from their inception. With modern advan- ¯ ¯ ces in understanding nanoscale systems, current research where in equilibrium M0 and H are collinear; Ms =Nm = focuses on synthesis, characterization, and functionaliza- Md/ is the magnetization when all magnetic tion of with magnetic and surface properties dipoles with magnetic nanoparticle volume Vp and - ¯ tailored for application as micro/nanoelectromechanical ization Md have moment m =MdVp aligned with H; N is sensors, actuators, and micro/nanofluidic devices [20&]; the number of magnetic dipoles per unit volume; and / is and for such biomedical applications as [20&,21&&] nano- the volume fraction of magnetic nanoparticles in the ferrofluid. For the typically used magnetite nanoparticle biosensors, targeted drug-delivery vectors [22], magneto- 5 cytolysis of cancerous tumors, hyperthermia [23], (Md =4.46Â10 A/m or l0Md =0.56 T), a representative volume fraction of / =4% with nanoparticle diameter separations and cell sorting, magnetic resonance imaging À 25 3 [24,25], immunoassays [26], radiolabelled magnetic fluids d =10 nm (Vp =5.25Â10 m ) gives a ferrofluid [27], and X-ray microtomography for three dimensional saturation magnetization of l0Ms =l0Md/ =0.0244 T and å 22 3 analysis of magnetic nanoparticle distribution in biological N =/ /Vp 7.6Â10 magnetic nanoparticles/m . applications, a crucial parameter for therapeutic evaluation At low magnetic fields the magnetization is approx- ¯ [28]. imately linear with H M¯ 0 p 1.2. Applications ¼ v ¼ l m2N=ðÞ¼3kT /l M 2d3 ð2Þ H¯ 0 0 18kT 0 d

Conventional ferrofluid applications use DC magnetic where v0 is the magnetic susceptibility, related to magnetic fields from permanent for use as liquid O-rings in permeability as l =l0(1+v0). For our representative num- rotary and exclusion seals, film bearings, as inertial bers at room temperature we obtain v0 å0.42 and l / dampers in stepper motors and shock absorbers, in l0 å1.42. When the initial magnetic permeability is large, composites, as the interaction of magnetic moments is appreciable so that && && fluids in , in inclinometers and accelerome- Eq. (2) is no longer accurate. Shliomis [31 ,1 ] considers ters, for grinding and polishing, in magnetocaloric pumps the case of monodispersed particles and uses a method and heat pipes [1&&,2&&,3&,4&,5&], and as lubrication in similar to that used in the Debye–Onsager theory of polar improved hydrodynamic journal bearings [29]. Ferrofluid fluids to replace Eq. (2) with is used for cooling over 50 million loudspeakers each year. Almost every computer disk drive uses a magnetic fluid v0ðÞ2v0 þ 3 2 k 2 3 ¼ l0m N=ðÞ¼kT /l0Md d : ð3Þ rotary seal for contaminant exclusion and the semiconduc- v0 þ 1 6kT tor industry uses silicon crystal growing furnaces that employ ferrofluid rotary shaft seals. Ferrofluids are also Langevin magnetization measurements in the linear low used for separation of magnetic from non-magnetic field region (a b1) provide an estimate of the largest materials and for separating materials by their density by magnetic particle diameters and in the high field saturation using a non-uniform magnetic field to create a magnetic regime (a H1) gives an estimate of the smallest magnetic && & distribution in the ferrofluid that causes the fluid diameters [1 ,32 ] to act as if it has a variable density that changes with M 1 6kT height. Magnetic materials move to the regions of lim 0 ,1 À ¼ 1 À aH1 M a l M Hd3 strongest magnetic field while non-magnetic materials S k 0 d move to the regions of low magnetic field with matching 3 M0 a kl0MdHd effective density. Magnetomotive separations use this lim , ¼ ð4Þ ab1 MS 3 18kT selective for mineral processing, water treatment [30], and sink-float separation of materials, one novel This method allows estimation of the ferrofluid mag- application being the separation of diamonds from beach netic nanoparticle size range using a magnetometer. Other sand. methods include transmission electron microscopy, atomic C. Rinaldi et al. / Current Opinion in Colloid & Interface Science 10 (2005) 141–157 143

force microscopy, and forced Rayleigh scattering of light with m¯ experiences a torque l0m¯ ÂH¯ [33]. which tends to align m¯ and H¯ . There are two important time constants that determine how long it takes m¯ to align 2.1.2. Magnetization relaxation with H¯ , When the ferrofluid is at rest and the magnetization is not in equilibrium due to time transients or time varying ðÞKVp=kT sB ¼ 3gVh=kT; sN ¼ s0e : ð6Þ magnetic fields, the conventional magnetization equation for an incompressible fluid derived by Shliomis is The Brownian rotational relaxation time, sB, describes [31&&,34&&] the hydrodynamic process when the magnetic moment is fixed to the nanoparticle and surfactant layer of total BM¯ M¯ À M¯ 0 þ ðÞv¯Il M¯ À x¯ Â M¯ þ ¼ 0 ð5Þ hydrodynamic volume V , including surfactant or other Bt s h surface coatings, and the whole nanoparticle rotates in a where s is a relaxation time constant, v¯ is the ferrofluid fluid of viscosity g to align m¯ and H¯ . The Ne´el time linear flow velocity, and x¯ is the ferrofluid spin velocity constant, sN, is the characteristic time for the magnetic which is an average particle rotation angular velocity. moment inside the particle to align with H¯ , due to flipping Soon after Eq. (5) was derived, another magnetization of atomic spins without particle rotation. The parameter K is equation was derived microscopically using the Fokker– && the particle magnetic anisotropy and Vp is the volume of Planck equation in the mean field approximation [35 ]. particle magnetic material. The literature gives different ¯ 1 l Defining half the flow as X ¼ 2 Â v¯, the two values for the anisotropy constant K of magnetite, over the magnetization equations are in good agreement when range of 23,000 to 100,000 J mÀ 3 while s approximately H 0 Xs b1, but (5) leads to non-physical results for Xs 1. equals 10À 9 s. Recent work has used Mossbauer spectro- Another analysis by Felderhof used irreversible thermody- scopy to show that the value of K is size dependent, namics of ferrofluids with hydrodynamics and the full set increasing as particle size decreases and gives a value of of Maxwell equations to derive a closely related but not À 3 & & & & K =78,000 J m for 12.6 nm diameter magnetic nano- identical equation to Eq. (5) [36 ,37 ]. Shliomis [38 ,39 ] particles [45&]. Other work has measured the effective states that Felderhof’s relaxation equation leads to an anisotropy constant in diluted ferrofluids using electron spin incorrect limiting value of rotational viscosity when the resonance spectrometry and AC complex magnetic suscept- Langevin parameter a in Eq. (1) becomes large while & ibility measurements [46]. The total magnetic time constant Felderhof [40 ] replies that Shliomis’ approximate theory s including both Brownian and Ne´el relaxation is given by for dilute ferrofluids does not apply in the dense regime Refs. [1&&,2&&,3&,4&,5&,31&&] and has limited validity in the dilute regime. Recent rotational measurements with an applied DC magnetic 1 1 1 s s ¼ þ `s ¼ B N : ð7Þ field perpendicular to capillary Poiseuille flow agree with s sB sN sB þ sN the Shliomis result and differ from Felderhof’s result & [41 ]. Earlier similar measurements with an alternating The time constant s is dominated by the smaller of sB À 3 magnetic field had a qualitative fit to the Shliomis or sN. For K =78,000 J m with 12.6 nm diameter rotational viscosity result but required a frequency magnetic nanoparticles at T =300 K, sN¨368 ms. For a dependent fitting parameter to successfully fit theory and ferrofluid with representative suspending medium viscosity experiment [42]. of g =0.001 Pa-s and with a surfactant thickness d =2 nm, More recently, Shliomis has derived a third magnet- sB å1.7 ls. For these parameters we see that the effective ization equation from irreversible thermodynamics which time constant is dominated by sB. Torque measurements describes magnetoviscosity in the entire range of magnetic with ferrofluid particles of order 10 nm diameter have & field strength and flow vorticity [43 ]. It is stated that this estimated, by comparison to theory, effective magnetic new magnetization equation is an improvement over that relaxation times of the order of the computed Brownian && of Ref. [35 ] by being valid even far from equilibrium. Yet relaxation time [47&,48&]. Brownian and Ne´el relaxation are another analysis by Mu¨ller and Liu uses standard non- lossy processes leading to energy dissipation so that the equilibrium thermodynamics with magneto-dissipative complex magnetic susceptibility has an imaginary part. effects to derive a magnetization relaxation equation using These losses lead to heat generation using time varying their ferrofluid dynamics theory [44]. They state that magnetic fields which can be used for localized treatment Shliomis’ Debye theory of Eq. (5) and his effective-field of cancerous tumors [21&&,23]. theory approach are special cases of the new set of In rotating magnetic fields, the time constant s of Eq. equations. (7) results in the magnetization direction lagging H¯ , therefore a time average torque acts on each nanoparticle 2.1.3. Magnetization relaxation time constants causing the particles and surrounding fluid to spin. This When a DC magnetic field H¯ is applied to a ferrofluid, leads to new physics as the fluid behaves as if it is filled just like a compass needle, each magnetic nanoparticle with nanosized gyroscopes that stir and mix the fluid 144 C. Rinaldi et al. / Current Opinion in Colloid & Interface Science 10 (2005) 141–157 balanced by the non-symmetric part of the viscous stress solving M¯ as a function of H¯ in Eq. (5) in the linear limit tensor. of Eqs. (2) or (3) Rotational Brownian motion of ferrofluid nanoparticles Mˆ v jX s þ 1 x s Hˆ x ¼ hi0 f y x : in a time dependent magnetic field can have thermal noise 2 2 Mˆ z À xys jXf s þ 1 Hˆ z induced rotation due to rectification of thermal fluctuations jXf s þ 1 þ xys [49,50]. A plastic sphere filled with ferrofluid was ð9Þ suspended on a fiber and placed in a horizontal magnetic If x =0, the tensor relationship reduces to a complex field of the form H =H +H [cos xt +asin(2xt +b)]. y DC 1 scalar magnetic susceptibility When the magnetic field was turned on, the sphere rotated. The explanation given was that rotation was due to thermal ¯ M Ãv0 ratchet behavior [50]. However, Shliomis describes the true v ¼ vV À jvW ¼ ¼ `vV H¯ 1 þ jX s cause of rotation to be a magnetic torque due to the f nonlinearity of ferrofluid magnetization as given by Eq. (1) v v X s ¼ hi0 ; vW ¼ hi0f ð10Þ [51]. 2 2 1 þ Xf s 1 þ Xf s

2.2. Complex magnetic susceptibility where vV is the real part of v related to magnetic field energy storage and vW is the imaginary part of v which causes We consider the low field linear region of the Langevin power dissipation. Note that vW has a peak value of v0 /2 curve so that in equilibrium M¯ =v H¯ , with v given by Eqs. 0 0 0 when Xf s =1. Spectroscopy measurements of the real and (2) or (3). We examine the sinusoidal steady state magnet- imaginary parts of v as a function of frequency provide ization response for a uniform magnetic field at radian information about the magnetization dynamics [52–54&,55– frequency Xf in the ferrofluid layer with planar Couette flow 57]. Other work uses a kinetic approach to microrheology shown in Fig. 1, with upper surface driven at constant that adds stress retardation (mechanical memory) to a velocity V in the z direction. The ferrofluid flow velocity is viscoelastic fluid or weak gel containing a ferrosuspension then of the form m¯ =mz(x)¯iz. The magnetization is independ- to produce new and interesting non-Newtonian properties ent of y and z because the applied magnetic field is assumed and dynamic susceptibility effects [58]. uniform. Then the second term of Eq. (5) is zero. For magnetization and magnetic field driven at field frequency 2.3. Heating Xf, the complex amplitude sinusoidal steady state forms of H¯ and M¯ are Increasing concentrations of ferrofluid magnetic material have a greater rate of heating and higher temperature ¯ ˆ ¯ ˆ ¯ jXf t H ¼ Re H xix þ H zizŠe g increase when placed in an alternating magnetic field [59]. The time average dissipated power per unit volume for ¯ ˆ ¯ ˆ ¯ jXf t fields at sinusoidal radian frequency Xf is [60–62] M ¼ Re M xix þ M zizŠe g: ð8Þ 1 ˆ ˆ Phase shifts between M¯ and H¯ components cause a < P > ¼ Re l jX M¯ IH¯ T ð11Þ d 2 0 f non-zero torque, T¯ =l0M¯ ÂH¯ , which will result in a time average spin velocity of the form x¯ = xy(x)¯iy.The where the superscript asterisk (*) denotes a complex complex magnetic susceptibility tensor is then found by conjugate.

x

V Ferrofluid

Hx or Bx d

ωy vz Hz y z

Fig. 1. A planar ferrofluid layer between rigid walls, in planar Couette flow driven by the x =d surface moving at z directed velocity V, is magnetically stressed by uniform x and z directed DC magnetic fields. C. Rinaldi et al. / Current Opinion in Colloid & Interface Science 10 (2005) 141–157 145

&& For an oscillating magnetic field with Hˆ x =Hˆ z =H0 and where / is the volume fraction of particles [63,34 ]. Recent magnetization given in Eq. (9) for a ferrofluid with spin work has performed computer simulations of ferrofluid velocity xy, the time average dissipated power is then laminar pipe flows to show magnetic field induced drag hi reduction [64,65] and fluorescent microscale particle image 2 2 2 2 2 velocimetry was developed for ferrofluid micro-channel l0v0H0 Xf s 1 þ Xf À xy s < P > ¼ : flows [66]. d 2 2 2 2 2 2 4 1 þ 2 Xf þ xy s þ Xf À xy s Most practical ferrofluid flows are incompressible, so that l Iv¯ =0, and are viscous dominated so that inertial ð12Þ effects are negligible. Flow geometry often results in l Ix¯ =0, as is the case in Fig. 1 where x¯ =x (x)¯i . In a clockwise rotating field with Hˆ =H and Hˆ =ÀjH , y y x 0 z 0 V¨ : 2 2 : the dissipated power is Dimensional analysis gives g g / where is of the order of the distance between particles and / is the particle hi and surfactant volume fraction. Because, with usual volume l v H2X sX x 1 X x 2s2 0 0 0 f f þ y þ f þ y fractions of order / =0.01, the distance : is comparable to < P > ¼ : d 2 particle diameter of order 10 nm, gV becomes very small and 1 þ 2 X2 þ x2 s2 þ X2 À x2 s4 f y f y so is often neglected in Eq. (15). In these limits and ð13Þ assuming viscous dominated flow, Eqs. (14) and (15) can be combined to the simpler forms: Note that the magnetic susceptibility in Eqs. (9) and (10) and the dissipated power in Eqs. (11)–(13) can be ¯ I ¯ l0 ¯ ¯ 2 0, À lp þ l0M lH þ l  M  H þ gl v¯ ð16Þ modulated by magnetic field amplitude, frequency, phase 2 and direction and by control of the spin velocity which itself l M¯  H¯ 1 can be set by flow vorticity and by magnetic field x¯ , 0 þ l  v¯: ð17Þ parameters such as amplitude and frequency of a rotating 4f 2 uniform magnetic field. Note that the spin velocity depends on magnetic torque and flow vorticity. Using Eqs. (16) and (17) in Eq. (5) 2.4. Conservation of linear and angular yields equations BM¯ M¯ À M¯ 0 In time transient or dynamic flow conditions, fluid þ ðÞv¯Il M¯ ¼ X¯  M¯ À viscosity causes the magnetization M¯ to lag the magnetic Bt s field H¯ . When M¯ and H¯ are not collinear, the torque density 1 ¯ ¯ ¯ ¯ 1 À l0M  M  H ; X ¼ l v¯: T =l0M¯ ÂH¯ leads to novel flow phenomena because the 4f 2 viscous stress tensor has an anti-symmetric part. The general ð18Þ pair of force and torque equations for ferrofluids are then && && & & & && [1 ,2 ,3 ,4 ,5 ,34 ] Recent work by Rosensweig has extended Eqs. (14)  and (15) based on integral balance equations and B m¯ I ¯ I ¯ thermodynamics without arbitrary definitions of electro- q þ ðÞm¯ l m¯ ¼Àlp þ l0M lH þ 2fl  x¯ Bt density and stress. The analysis included þ ðÞk þ g À f llðÞþIm¯ ðÞg þ f l2m¯ electric and magnetic fields using the Minkowski expres- sion, D¯ ÂB¯ , for electromagnetic momentum density and ð14Þ  used an appropriate formulation of entropy production in Bx¯ which the is distinguished from I þ ðÞm¯Il x¯ ¼ l M¯  H¯ þ 2fðÞl  v¯ À 2x¯ Bt 0 equilibrium. The usual constitutive relationships result from the analysis without any empirical assumptions, þ ðÞkV þ gV llðÞþIx¯ gVl2x¯ including the magnetization relaxation Eqs. (5) and (18) ð15Þ [67&]. Rosensweig then further extended the analysis to include Galilean relativity effects to first order in the ratio where q is the fluid mass density, I is the fluid moment of of fluid velocity to light speed [68&]. inertia density, v¯ is the linear flow velocity, x¯ is the spin A similar analysis was performed by Felderhof, velocity, and p is the hydrodynamic pressure. The viscosity following the semirelativistic hydrodynamic equations of coefficients are the usual shear viscosity g and the dilational motion of de Groot and Mazur [69], based on the choice viscosity k while gV and kV are the analogous shear and bulk of e0l0E¯ ÂH¯ for electromagnetic momentum density coefficients of spin viscosity. The coefficient f is called the [36&,70&]. The Rosensweig and Felderhof analyses are vortex viscosity and from microscopic theory for dilute on the whole very similar, and in the limit of small v /c, suspensions obeys the approximate relationship, f =1.5g/, the two analyses are identical. 146 C. Rinaldi et al. / Current Opinion in Colloid & Interface Science 10 (2005) 141–157

3. Magnetic forces and torques field effects as the shape of a ferrofluid meniscus; flow and instabilities of a ferrofluid jet such as for magnetic fluid 3.1. Magnetic force density inkjet printing; operation of magnetic fluid seals, bearings, load supports; sink-float separations; magnetic fluid The magnetic force density acting on an incompressible nozzles; and magnet self-levitation in a ferrofluid ferrofluid is [1&&,3&,4&]. Ferrofluids exhibit a wide range of very interesting lines, ¯ ¯ I ¯ F ¼ l0 M l H ð19Þ patterns, and structures that can develop from ferrohydro- dynamic instabilities as shown in Fig. 2 [20&,71,72]. so that ferrofluids move in the direction of increasing The magnetic field gradient force density in Eq. (19) magnetic field strength. In a uniform magnetic field there is has been used for precise positioning and transport of no magnetic force. When M¯ and H¯ are collinear, this force ferrofluid for sealing, , heat transfer, and liquid density modifies Bernoulli’s equation for inviscid and delivery systems [73–75]. Smooth and continuous pump- irrotational steady flow to [1&&] ing of ferrofluid in a tube or channel can be achieved by Z a traveling wave non-uniform magnetic field generated by H 1 2 I a spatially traveling current varying sinusoidally in time p þ qjv¯j À qg¯ r¯ À l0 MdH ¼ constant ð20Þ 2 0 with a sinusoidal spatial variation along the duct axis [76,77]. Magnetic forces on ferrofluids have been used where |v¯| is the magnitude of the fluid velocity, g¯ is the for adaptive to shape deformable mirrors [78,79]; gravitational acceleration vector, and r¯ =xi¯x +yi¯y +zi¯z is the as a ferrofluid cladding layer in development of a tunable position vector. The magnetic term is the magnetic in-line optical-fiber modulator [80]; use as a flat panel contribution to fluid pressure and describes such magnetic display cell where the luminance is magnetically con-

Fig. 2. Ferrofluid instabilities in DC magnetic fields for an Isopar-M based ferrofluid with saturation magnetization of about 400 Gauss. (a) 1200 Gauss 5 mm diameter magnet behind a small ferrofluid droplet surrounded by propanol to prevent ferrofluid wetting of 1 mm gap glass plates; (b–d) peak pattern with magnetic field perpendicular to ferrofluid layer. The peaks initiate in a hexagonal array when the magnetic surface force exceeds the stabilizing effects of fluid weight and —(b) 200 Gauss, (c) 330 Gauss, (d) 400 Gauss; (e –f) labyrinth instability with ferrofluid between 1 mm gap glass plates in 250 Gauss vertical magnetic field [71,72]. C. Rinaldi et al. / Current Opinion in Colloid & Interface Science 10 (2005) 141–157 147 trolled through the ferrofluid film thickness [81];asa magnetic field generated by a two-pole three-phase motor microfluidic MEMS-based light modulator [82];for stator winding with a Couette viscometer used as a torque magnetic control of the Plateau rule of the angle between meter [47&,48&]. When a fixed spindle rotation speed is contacting films in 2D foams [83]; for magnetic control selected, the viscometer applies the necessary torque in order of bubble size and transport in ferrofluid foams for to keep it rotating at the specified speed. When the magnetic microfluidic and ‘‘lab-on-a-chip’’ applications and for field co-rotates with the spindle immersed in ferrofluid, the possible zero gravity experiments using the magnetic magnetic-field-induced on the spindle is in the field gradient force to precisely balance gravity so that direction opposite to spindle rotation, making it harder to bubbles are free floating in ferrofluid [84]; for magnetic turn the spindle at the specified speed so that the viscometer field control of ferrofluid in a cavitating flow in a applies a higher torque and it records an increase of effective converging–diverging nozzle [85]; and for studies of ferrofluid viscosity as shown in Fig. 4 [48&]. When the longitudinal and transverse tangential magnetic fields on magnetic field counter-rotates relative to the spindle, the ferrofluid capillary rise [86]. Applied electric fields can magnetic-field-induced shear stress on the spindle is in the also exert forces in ferrofluids to control same direction as spindle rotation, so that it is easier to rotate rheological properties [87–89]. the spindle at the specified speed; therefore the viscometer applies a lower torque, and the viscometer records a 3.2. Torque-driven flows decrease of effective ferrofluid viscosity as also shown in Fig. 4. When the torque in Fig. 4 is negative, the effective In a rotating magnetic field, the magnetization relaxation viscosity is negative [48&,98–106]. Other torque measure- time constants of Eqs. (6) and (7) create a phase difference ments used a stationary spindle with ferrofluid inside the between magnetization and magnetic field so that M¯ and H¯ spindle, outside the spindle, or simultaneously inside and are not in the same direction. This causes a magnetic torque outside the spindle [48&]. The approximate magnetic-field- density induced time average torque on the spindle for ferrofluid & ¯ ¯ ¯ entirely outside the spindle is [48 ] T ¼ l0M Â H ð21Þ 2 2 2 which causes the magnetic nanoparticles and surrounding 8kR Lc l0v0ðÞ1 þ v0 H Xs T, À ð22Þ 2 2 2 fluid to spin as given in Eq. (17). The concerted action ðÞv0 þ 2 þ c v0ðÞ4 þ 2v0 þ v0c of order 1022 –1023 spinning nanoparticles/m3 can cause fluid pumping [90,91&,92&] and other interesting ferrofluid where R is the radius of the outer cylinder, c is the ratio of flows [93&,94] and microdrop behavior shown in Fig. 3 the inner cylinder radius to the outer radius of the & & & [95 ,96 ,97 ]. ferrofluid container, Xf is the radian frequency of the To emphasize magnetic torque effects, the effective applied magnetic field with rms amplitude H, s is the viscosity of ferrofluid was studied using the rotating uniform effective magnetization relaxation time, v0 is the equili-

Fig. 3. A ferrofluid drop between Hele–Shaw cell glass plates with 1.1 mm gap has simultaneous applied in-plane rotating (20 Gauss rms at 25 Hz) and vertical DC (0–250 Gauss) magnetic fields. The ferrofluid is surrounded by equal proportions by volume of water and isopropyl alcohol (propanol) to prevent glass smearing. (a) The vertical DC field is first applied to form the labyrinth pattern and then a counter-clockwise rotating field is applied to form a slowly rotating spiral pattern; (b) the counter-clockwise rotating field is applied first to hold the drop together with no labyrinth and then as the DC magnetic field is increased to about 100 Gauss, the continuous fluid drop abruptly transitions to discrete droplets, while further increase of the magnetic field to 250 Gauss changes the pattern further; (c) various end-states of spirals, and (d) droplet patterns [95&]. 148 C. Rinaldi et al. / Current Opinion in Colloid & Interface Science 10 (2005) 141–157

4. Ferrohydrodynamics

4.1. Magnetoviscosity

Magnetic fluids have been used in microfluidic and microchannel devices [110–112]. Theoretical analysis calculates the shear stress for the planar Couette flow in Fig. 1 with a uniform x directed DC magnetic field Hx or density Bx, to evaluate the DC effective magnetoviscosity [106]. If the ferrofluid fills an air-gap of length s and area A of an infinitely magnetically permeable magnetic circuit excited by an N turn coil carrying a DC current I0, then Hx =NI0 /s is spatially uniform for planar Couette flow only as the spin velocity xy is also uniform. For other flow profiles, Hx and xy will be a function of Fig. 4. Torque required to rotate a spindle surrounded with ferrofluid as a position inside the ferrofluid flow, while magnetic flux function of rotating magnetic field amplitude, frequency, and rotation density Bx will always be spatially uniform in the planar direction with respect to the 100 RPM rotation of the spindle [48&]. channel as l IB¯ =0, no matter the flow profile in the geometry of Fig. 1 [104,106]. Extensions of this work brium ferrofluid magnetic susceptibility, and l0 =4p  include AC magnetic fields for Couette and Poiseuille flows 10À 7 henries/meter is the magnetic permeability of free with magnetic field components along and perpendicular to & space. The approximate magnetic field induced torque on the duct axis [104,113 ]. the spindle for ferrofluid entirely inside the spindle is For the planar Couette flow shown in Fig. 1, with x [107,48&] directed magnetic field only (H =0), the change in z sv l H2 magnetoviscosity T, À 2X sv l H 2V 1 À 0 0 ð23Þ f 0 0 2f 2x d Dg ¼ f 1 þ y ð24Þ where f =1.5g/ is the vortex viscosity and g is the fluid V viscosity. Magnetic field and shear dependent changes in is plotted as the multivalued functions versus Hx or Bx ferrofluid viscosity have many possible applications in magnetic parameters in Fig. 5 [106]. For a DC magnetic damping technologies [108&,109]. field, the effective viscosity always increases with magnetic

Fig. 5. The change in magnetoviscosity versus related DC magnetic field Hx or magnetic flux density Bx parameters PH or PB for various values of Vs /d. For imposed magnetic flux density Bx, magnetic susceptibility vm =1.55 was used in the plots for oil-based ferrofluid Ferrotec EFH1 [106]. C. Rinaldi et al. / Current Opinion in Colloid & Interface Science 10 (2005) 141–157 149 field amplitude. For AC magnetic fields, the effective rigid-body-like counter-clockwise rotation of ferrofluid at a viscosity can decrease, even through zero and negative constant angular velocity. Only in a thin layer near the values [48&,104]. cylinder wall does the no-slip condition force the fluid flow The size distribution of nanoparticles in ferrofluid is very to differ from rigid-body rotation. important to various shear flows in a magnetic field. A The free ferrofluid/air interface at the surface of the vessel gradient magnetic field causes large particles to diffuse to with no top is observed to rotate in the clockwise direction, the strong field region while smaller particles have a weaker opposite to the bulk rotation. The experiments show that effect. measurements of viscosity show that while the ferrofluid bulk slowly co-rotates with the applied large particles and agglomerates have a strong magnetic magnetic field, the ferrofluid free surface counter-rotates field dependence on viscosity increase which depends on with the applied magnetic field at higher rotational speed shear rate, while the smaller particle fluid has only a small than the bulk. With a fixed top on the ferrofluid free surface, viscosity increase and smaller shear-rate dependence the volume flow velocity is generally higher than for a free [114,115]. surface which counter-rotates to the volume flow. Another rotating magnetic probe was developed to Rosensweig et al. observed the velocity of the free measure the local on microscopic scales surface of ferrofluid flow in a uniform rotating magnetic based on the alignment of dipolar chains of submicron field driven by magnetic shear stresses in meniscus regions magnetic particles in the direction of an applied magnetic [123&]. When the meniscus of the ferrofluid free surface was field [116]. Proposed continuing work is to investigate the concave, the ferrofluid surface flow counter-rotated to the rheological properties of the interior of a cell using this driven magnetic field; when the meniscus of ferrofluid free magnetic rotational microrheology method [117]. surface was flat, the ferrofluid surface flow was stationary; and when the meniscus of the ferrofluid free surface was 4.2. Ultrasound velocity profile measurements convex, the ferrofluid surface flow co-rotated with the driven magnetic field. Because ferrofluid is opaque, Because ferrofluids are opaque, an ultrasound velocity measurement of the bulk flow profiles was not possible. profile method was developed for use with ferrofluids All the surface flow observations were made by placing [118&,119&,120&,121&]. The sound velocity in ferrofluid tracer particles on the top rotating surface. Based on these increases slightly with magnetic field strength and ultra- observations, Rosensweig concluded that volume flow sound frequency while the velocity slightly decreases with effects were negligible. However, the ultrasound velocity increasing angle between magnetic field and ultrasound measurements in Fig. 6 show that there is a significant propagation direction and with weight concentration of volume flow, even without a free top interface. magnetic particles [122&]. An Ultrasonic Doppler Velocimeter (UDV) measured the 4.3. Interfacial phenomena bulk velocity of ferrofluid in a cylindrical container, with and without a top, with flow driven by a uniform rotating Further experimental measurements of meniscus height, magnetic field, as shown in Fig. 6. The measurements show h =n(0), and shape n(x), were performed using narrow that a counter-clockwise rotating magnetic field causes a diameter laser beam reflections from the meniscus interface

Fig. 6. Spin-up flow profiles at mid-height excited by a magnetic field rotating counter-clockwise at 200 Hz for various magnetic field amplitudes; (a) with a free top surface and (b) with a cover on the container, so that there is no free top surface. The central flow velocity profiles for (a) and (b) are approximately the linear profiles of a fluid in rigid body co-rotation with the applied magnetic field, dropping to zero at the wall over a thin boundary layer. In (a), the angular velocity of the bulk flows in the central region co-rotate with the respective magnetic fields from high to low at ¨14, 8, 4, and 1 rpm while the respective surface angular velocities are larger and counter-rotate with the magnetic field at ¨48, 36, 22, and 9 rpm. In (b), the angular velocity of the bulk flows in the central region co-rotate with the magnetic field at larger velocities than in (a) with the respective magnetic fields from high to low at ¨20, 12, 5, and 1 rpm. 150 C. Rinaldi et al. / Current Opinion in Colloid & Interface Science 10 (2005) 141–157

meniscus, while in vertical magnetic fields the meniscus rises (configuration c). An approximate minimization of free energy model was used including magnetization, surface tension, and gravitation energies, to calculate meniscus height change with magnetic field which compared well to measurements [124&]. Other work used an optical reflection method to measure the height of the perpendicular field instability peaks, like those shown in Fig. 2b–d [125]. The surface tension at an air/ferrofluid interface or at a non-magnetic liquid (propanol)/ferrofluid interface was measured using the perpendicular field instability of Fig. 2b–d by measuring the fluid peak spacing and magnetic field strength at the incipience of instability [126]. Other work used a 2D lattice Boltzmann model to account for the competition between interfacial tension and dipolar forces in ferrofluids [127]; experiments were performed on the time evolution of the breakup of a liquid bridge of ferrofluid in an external magnetic field as it disintegrates, including study of the dynamics of satellite drops emanating Fig. 7. The experimental optical setup for measuring ferrofluid meniscus shape [124&]. from the liquid bridge [128]; while other measurements compared the shape response of ferrofluid droplets, a magnetorheological fluid, and a composite magnetic fluid as a function of DC applied magnetic fields, as shown in with nanometer and micron sized particles in low frequency Fig. 7. The angle of deflection of the laser beam from the alternating magnetic fields up to 5 Hz [129]. vertical allows the computation of the shape of the ferrofluid The Weissenberg effect is the rise of a free surface of a meniscus [124&]. viscoelastic fluid at a rotating rod due to normal stress forces Three applied magnetic field configurations were used, [130]. For magnetic fluids the height of the fluid surface at as shown in Fig. 8. A meniscus forms on the sides of a glass the rod also depends on the length and quantity of fluid slide immersed in the center of a vessel with negligibly particle chains, the strength of the applied magnetic field small field gradients. Fig. 9 shows for both oil and water- parallel to the surface, the concentration of larger magnetic based ferrofluids that applied magnetic field in configura- particles, and the shear rate. tion a has practically no effect on the meniscus shape. As expected, with a uniform magnetic field tangent to the 4.4. Hele–Shaw cell flows interface, the shape of the interface matches the non- magnetic meniscus shape In a porous medium, the local average fluid velocity is pffiffiffi pffiffiffi described by Darcy’s law x 1 2 2 ¼ pffiffiffi coshÀ1 À coshÀ1 0 ¼Àlp À bv¯ þ F¯ ð26Þ a 2 n=a h=a sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where p is the hydrodynamic pressure, b =g /j is the ratio h 2 n 2 of fluid viscosity g to the permeability j which depends on þ 2 À À 2 À ð25Þ a a the geometry of the particles and interstitial space, and F¯ is the total external force density, typically due to gravity and where a =(2r /qg)1/2 is the capillary length for ferrofluid of magnetization given by Eq. (19). mass density q and surface tension r, with g being the A Hele–Shaw cell consists of two parallel walls a small acceleration of gravity. Fig. 9 shows that applied horizontal distance d apart, and is used for two-dimensional flows magnetic field in configuration b lowers the height of a where the flow velocity only has components parallel to the

Fig. 8. The three magnetic field configurations of the ferrofluid meniscus experimentally investigated [124&]. C. Rinaldi et al. / Current Opinion in Colloid & Interface Science 10 (2005) 141–157 151

Fig. 9. Measured meniscus shape for the three configurations of applied magnetic field. The top row shows oil-based ferrofluid (v0 å1.55) results while the & bottom row shows water-based ferrofluid (v0 å0.67) results [124 ]. walls. The mean flow between the walls is then also the Rayleigh–Taylor instability [141&]; and natural con- described by Eq. (26) where b =12g /d2 and j =d2 /12. A vection of magnetic fluid in a bottom-heated square ferrofluid drop in a Hele–Shaw cell forms an intricate Hele–Shaw cell with two insulated side walls with heat labyrinth when a uniform DC magnetic field is applied transfer measurements and liquid crystal thermography perpendicular to the walls as shown in Fig. 2e–f. Typical [142]. labyrinth analyses are usually approximately based on a minimization of the free energy as a sum of magnetostatic 4.5. Flow instabilities and interfacial tension energies, including the effects of demagnetizing magnetic fields typically assuming that the 4.5.1. Jet and sheet flows magnetization is linear with H¯ , as in Eq. (2). Recent work The behavior of an initially circular cross-section has generalized the free energy analysis to nonlinear ferrofluid jet impacting a circular surface to create magnetization characteristics, particularly using the Lange- an expanding sheet flow in the presence of a magnetic field vin magnetization of Eq. (1) [131]. was investigated [143]. A horizontal magnetic field trans- Fig. 3 shows interesting Hele–Shaw cell ferrofluid verse to a vertical ferrofluid jet axis changes the jet cross- drop responses to simultaneous vertical DC and horizontal section from circular to elliptical, with long axis in the rotating uniform magnetic fields [95&,96&,97&].Other direction of the applied magnetic field. As the transverse ferrofluid Hele–Shaw cell flows investigated azimuthal magnetic field is increased, the expanding sheet also magnetic fields from a long straight current-carrying wire becomes approximately elliptically shaped but with long along the axis perpendicular to the walls with a time- axis perpendicular to the magnetic field, which is transverse dependent gap [132,133]; labyrinthine instability in mis- to the long axis of the jet cross-section, as shown in Fig. 10. cible magnetic fluids in a horizontal Hele–Shaw cell with At large magnetic fields, the sheet forms sharp tips and fluid a vertical magnetic field [134]; theory and experiments of chains emerge from its corners. The prime cause of the interacting ferrofluid drops [135&]; numerical simulations change in sheet shape is the influence of the magnetic field [136] and measurements [137] of viscous fingering on the jet shape. If an initially elliptical non-magnetic jet labyrinth instabilities; fingering instability of an expanding strikes a circular impactor, the expanding sheet is similarly air bubble in a horizontal Hele–Shaw cell [138] and of a elliptical but with its long axis also perpendicular to that of rising bubble in a vertical Hele–Shaw cell [139]; finger- the jet. ing instabilities of a miscible magnetic fluid droplet in a If the applied magnetic field is vertical, and thus rotating Hele–Shaw cell [140]; theory and experiments of perpendicular to the expanding circular sheet, the sheet 152 C. Rinaldi et al. / Current Opinion in Colloid & Interface Science 10 (2005) 141–157

(a) B≈0 Gauss (b) B≈200 Gauss

(c) B≈600 Gauss (d) B≈1200 Gauss

Fig. 10. A vertical oil-based ferrofluid jet, with diameter 2.5 mm, impacts a small circular horizontal plate of 10 mm diameter creating a radially expanding thin sheet flow. (a) In zero magnetic field, a circular jet will create a circular sheet; (b) application of the magnetic field transverse to the jet, in the direction of the arrow, causes the jet cross-section to elongate in the direction of the applied field while the sheet distorts to an approximately elliptical shape, but with long-axis perpendicular to the applied magnetic field. (c, d) For large magnetic fields, the sheet becomes very thin and is characterized by sharp tips and fluid chains emerging from its corners [143].

ˆ j(xt-kz) diameter decreases with increasing magnetic field B.A deflections of the form n1,2 =Re[n1,2e ] the disper- simple approximate Bernoulli analysis including magnetic sion relation is surface forces predicts the sheet radius to be  q x2 qxðÞÀ kU 2 cothðÞkd=2  0 þ À rk2 B2 1 1 qUQ k k hitanhðÞkd=2 r ¼ rT 1 À 2 À ; rT ¼ ð27Þ qU l0 l 4kr 2 2 l F kðÞl À l0 B coshkd þ sinhkd 1 l0 þ 2 2 lsinhkdl þ l0 þ 2ll0cothkd where rT is the Taylor radius with B =0, l is the ferrofluid ¼ 0 n =n ¼ k1 ð28Þ magnetic permeability, l0 is the magnetic permeability of 1 2 the free space surrounding the sheet, q is the ferrofluid density, U is the ferrofluid sheet velocity, Q is the jet flow where q0 is the density of the surrounding air. Interfacial rate, and r is the interfacial surface tension [143]. deflections are unstable if x2 <0 as then x is imaginary so that interfacial deflections will grow exponentially with 4.5.2. Kelvin–Helmholtz instability time. Since non-zero B tends to decrease x2, the magnetic The classic instability of the planar interface between field tends to destabilize the interfacial deflections. With two superposed fluids with a relative horizontal velocity is B =0, the n1 /n2 =1 mode becomes unstable at k =0 for called the Kelvin–Helmholtz instability. The moving Weber number We =qU2d /r >2. Application of a mag- ferrofluid sheet flow of Section 4.5.1 has magnetically netic field component parallel to the sheet interfaces tends coupled upper and lower interfaces which can become to stabilize the sheet flow [143]. Kelvin–Helmholtz unstable. A planar sheet model, The stability of Kelvin–Helmholtz waves propagating generalized to include a magnetic field B perpendicular on the interface between two magnetic fluids stressed by to both interfaces, is formulated to examine the effects of an oblique magnetic field has also been analyzed for free magnetic fields on interfacial stability for a fluid layer of fluids [144] and for fluids streaming through porous media & thickness d moving with horizontal velocity U [143]. [145 ]. Letting n1 be the upwards deflection of the upper interface and n2 be the upwards deflection of the lower 4.5.3. Other flow instabilities interface, a linear stability analysis shows that there are The Rayleigh–Maragoni–Be´nard instability of a ferro- two interfacial modes with n1 /n2 =T1. For interfacial fluid in a vertical magnetic field was studied combining C. Rinaldi et al. / Current Opinion in Colloid & Interface Science 10 (2005) 141–157 153 aspects of volume and surface forces due to heating, flow 5. Conclusions rheology, and magnetism [146]. The Faraday instability is the parametric generation of This magnetic fluid rheology and flows review has standing waves on the free surface of a fluid subjected to presented recent advances in fundamental theory; ferrofluid vertical vibrations. The initially flat free surface of the fluid flows and instabilities; thermal effects and applications; and becomes unstable at a critical intensity of the vertical practical device and biomedical applications. Of special vibrations. The Faraday instability has been used to study importance are the better understanding of the significant the rheological properties of ferrofluids caused by strong effects of magnetic particle aggregation; modern electrical, dipole interactions that lead to the formation of magnetic mechanical, optical, and radiation measurement methods to particle chains elongated in the direction of the horizontal determine important rheological parameters; extensions of magnetic field [147]; and used with a vertical oscillating the governing magnetization and ferrohydrodynamic equa- magnetic field to parametrically excite standing surface tions including theoretical and experimental investigations waves with no mechanically imposed vertical vibrations and applications of the antisymmetric part of the viscous together with a vertical DC magnetic field to tune the fluid stress tensor; magnetic control of the magnetic susceptibility parameters [148]. Later work used both a vertical DC tensor for heating applications with ferrofluids with non- magnetic field with a mechanical exciter to vertically shake zero spin velocity; recent advances in biomedical applica- the test cell [149] to obtain a novel pattern of standing twin tions of drug delivery, hyperthermia, and magnetic reso- peaks due to the simultaneous excitation of two different nance imaging; effective magnetoviscosity analysis and wave numbers. measurements, including zero and negative values and not just viscosity reduction; ultrasound velocity profile meas- 4.6. Thermodiffusion (Soret effect) urements of spin-up flow showing counter-rotating surface and volume flows in a uniform rotating magnetic field; In a multicomponent mixture, a temperature gradient theory and measurements of ferrofluid meniscus shape for leads to diffusive concentration gradients due to the tangential and perpendicular magnetic fields; and new coupling between heat and mass transport, known as the analysis and measurements of ferrohydrodynamic flows, Soret effect. The Soret effect has a strong dependence on instabilities, and thermodiffusion (Soret effect) phenomena. magnetic field in ferrofluids [150–157&] and the sign is controlled by the electrostatic charge or surfactant at the nanoparticle interface [158,159]. A temperature gradient Acknowledgments imposed across a flat ferrofluid layer with a transverse magnetic field causes a concentration gradient of magnetic For the MIT authors, this work was partially supported nanoparticles. The mass and temperature gradient causes a by the Thomas and Gerd Perkins Professorship at MIT and magnetization gradient resulting in a magnetic field by generous MIT alumnus Thomas F. Peterson. Ferrotec gradient which redistributes the magnetic particles with Corporation is acknowledged for providing ferrofluids used mixing. Unlike a homogeneous single component fluid in MIT experiments and Brookfield Corporation is acknowl- which has a stationary instability, the two component edged for providing a viscometer. The University of Puerto ferrofluid system has a double-diffusive oscillatory insta- Rico at Mayaguez authors were supported by the US bility [160]. National Science Foundation (CTS-0331379) and by the Recent work used a vertical laser beam to create a hot Petroleum Research Fund (ACS-PRF 40867-G 9). spot on a thin horizontal ferrofluid layer [161]. With a positive Soret coefficient the magnetic nanoparticles dif- fused to colder regions leaving the hot spot transparent. References and recommended readings With a vertical magnetic field the initially round hot spot [1] R.E. Rosensweig, Ferrohydrodynamics. New York: Cambridge changed to various polygon shapes, said to be caused by && convectively unstable roll cells. Shliomis [162] offered University Press, 1985: republished by New York: Dover Publica- tions, 1997. another explanation where the hot spot is initially a non- [2] S. Odenbach, Magnetoviscous Effects in Ferrofluids, Springer, && magnetic ‘‘bubble’’ within a magnetic fluid which is the Berlin, 2002. inverse of the labyrinth instability shown in Figs. 3a and [3] B. Berkovski, V. Bashtovoy (Eds.), Magnetic Fluids and Applica- & 2e–f. Using the magnetic Bond number criterion for tions, Begell House, New York, 1996. [4] B.M. Berkovsky, V.F. Medvedev, M.S. Krakov, Magnetic Fluids labyrinth instability, Shliomis obtained very good agreement & Engineering Applications, Oxford University Press, Oxford, 1993. with the labyrinth theory. [5] E. Blums, A. Cebers, M.M. Maiorov, Magnetic Fluids, Walter de & Calculation of the thermomagnetic force on a prolate Gruyter, Berlin, 1997. spheroidal body immersed in ferrofluid was used as a model of long magnetic nanoparticle aggregates in a non-uniformly heated ferrofluid in an applied magnetic field with temper- & of special interest. ature gradient at an angle to the magnetic force [163]. && of outstanding interest. 154 C. Rinaldi et al. / Current Opinion in Colloid & Interface Science 10 (2005) 141–157

[6] S.W. Charles, The preparation of magnetic fluids, in: S. Odenbach dependent measurements of the transient magneto-optical birefrin- & (Ed.), Ferrofluids, Magnetically Controllable Fluids and Their gence using functionalized magnetic nanoparticles, JMMM 289 Applications, Springer, Berlin, 2002, pp. 3–18. (2005) 480–483. [7] I. Bolshakova, M. Bolshakov, A. Zaichenko, A. Egorov, The [27] R. Aquino, J.A. Gomes, F.A. Tourinho, E. Dubois, R. Perzynski, investigation of the magnetic fluid stability using the devices with G.J. da Silva, et al., Sm and Y radiolabeled magnetic fluids: magnetic field microsensors, JMMM 289 (2005) 108–110. magnetic and magneto-optical characterization, JMMM 289 (2005) [8] G. Bossis, O. Volkova, S. Lacis, A. Meunier, Magnetorheology: 431–434. fluids, structures and rheology, in: S. Odenbach (Ed.), Ferrofluids, [28] O. Brunke, S. Odenbach, C. Fritsche, I. Hilger, W.A. Kaiser, Magnetically Controllable Fluids and Their Applications, Springer, Determination of magnetic particle distribution in biomedical Berlin, 2002, pp. 202–230. applications by X-ray microtomography, JMMM 289 (2005) [9] A. Zubarev, Statistical physics of non-dilute ferrofluids, in: S. 428–430. Odenbach (Ed.), Ferrofluids, Magnetically Controllable Fluids and [29] T.A. Osman, G.S. Nada, Z.S. Safar, Effect of using current-carrying- Their Applications, Springer, Berlin, 2002, pp. 143–161. wire models in the design of hydrodynamic journal bearings [10] M.I. Morozov, M.I. Shliomis, Magnetic fluid as an assembly of lubricated with ferrofluids, Tribol Lett 11 (2001) 61–70. flexible chains, in: S. Odenbach (Ed.), Ferrofluids, Magnetically [30] S. Jakabsky, M. Lovas, A. Mockovciakova, S. Hredzak, Utilization Controllable Fluids and Their Applications, Springer, Berlin, 2002, of ferromagnetic fluids in mineral processing and water treatment, J pp. 162–184. Radioanal Nucl Chem 246 (3) (2000) 543–547. [11] A.Y. Zubarev, L.Y. Iskakova, On the theory of structural trans- [31] M.I. Shliomis, Magnetic fluids, Soviet Phys Uspekhi 17 (2) (1974) && formations in magnetic fluids, Colloid J 65 (6) (2003) 703–710. 153–169. [12] A.O. Ivanov, S.S. Kantorovich, Structure of chain aggregates in [32] R.W. Chantrell, J. Popplewell, S.W. Charles, Measurements of ferrocolloids, Colloid J 65 (2) (2003) 166–176. particle size distribution parameters in ferrofluids, IEEE Trans Magn [13] A. Wiedenmann, Magnetic and crystalline nanostructures in ferro- 14 (1978) 975–977. fluids as probed by small angle neutron scattering, in: S. Odenbach [33] P. Kop*ansky´, M. Timko, I. Poto*ova, M. Koneracka´, A. Jur´ikova´, N. (Ed.), Ferrofluids, Magnetically Controllable Fluids and Their Tomaxovi*ova, et al., The determination of the hydrodynamic Applications, Springer, Berlin, 2002, pp. 33–58. diameter of magnetic particles using FRS experiment, JMMM 289 [14] F. Gazeau, E. Dubois, J.-C. Bacri, Boue´, A. Cebers, R. Perzynski, (2005) 97–100. Anisotropy of the structure factor of magnetic fluids under a field [34] M.I. Shliomis, Effective viscosity of magnetic suspensions, Soviet && probed by small-angle neutron scattering, Phys Rev E 65 (2002) Phys JETP 34 (6) (1972) 1291–1294. 1–15 (031403). [35] M.A. Martsenyuk, Y.L. Raikher, M.I. Shliomis, On the kinetics of && [15] M.H. Sousa, E. Hasmonay, J. Depeyrot, F.A. Tourinho, J.-C. magnetization of suspensions of ferromagnetic particles, Soviet

Bacri, E. Dubois, et al., NiFe2O4 nanoparticles in ferrofluids: Phys JETP 38 (2) (1974) 413–416. evidence of spin disorder in the surface layer, JMMM 242-245 [36] B.U. Felderhof, H.J. Kroh, Hydrodynamics of magnetic and & (2002) 572–574. dielectric fluid in interaction with the electromagnetic field, J Chem [16] Y.L. Raikher, V.I. Stepanov, J.-C. Bacri, R. Perzynski, Orientational Phys 110 (15) (1999) 7403–7411. dynamics in magnetic fluids under strong coupling of external and [37] B.U. Felderhof, Magnetoviscosity and relaxation in ferrofluids, Phys & internal relaxations, JMMM 289 (2005) 222–225. Rev E 62 (3) (2000) 3848–3854. [17] Y.L. Raikher, V.I. Stepanov, J.-C. Bacri, R. Perzynski, Orientational [38] M. Shliomis, Comment on Fmagnetoviscosity and relaxation in & dynamics of ferrofluids with finite magnetic anisotropy of the ferrofluids_, Phys Rev E 64 (2001) 1–6 (063501). particles: relaxation of magneto-birefringence in crossed fields, Phys [39] M.I. Shliomis, Ferrohydrodynamics: retrospective and issues, in: & Rev E 66 (2002) 1–14 (021203). (Ed.), Ferrofluids, Magnetically Controllable Fluids and Their [18] D.K. Kim, D. Kan, T. Veres, F. Normadin, J.K. Liao, H.H. Kim, et Applications, Springer, Berlin, 2002, pp. 85–111. al., Monodispersed Fe–Pt nanoparticles for biomedical applica- [40] B.U. Felderhof, Reply to ‘‘comment on Fmagnetoviscosity and & tions, J Appl Phys 97 (2005) 1–3 (10Q918). relaxation in ferrofluids_’’, Phys Rev E 6406 (2001) 1–4 (063502). [19] F. Shen, C. Poncet-Legrand, S. Somers, A. Slade, C. Yip, A.M. [41] R. Patel, R.V. Upadhyay, R.V. Mehta, Viscosity measurements of a & Duft, et al., Properties of a novel magnetized alginate for ferrofluid: comparison with various hydrodynamic equations, J Col- magnetic resonance imaging, Biotechnol Bioeng 83 (3) (2003) loid Interface Sci 263 (2003) 661–664. 282–292. [42] A. Zeuner, R. Richter, I. Rehberg, Weak periodic excitation of a [20] C. Rinaldi, T. Franklin, M. Zahn, T. Cader, Magnetic nanoparticles magnetic fluid capillary flow, JMMM 201 (1999) 321–323. & in fluid suspension: ferrofluid applications, Dekker Encyclopedia of [43] M. Shliomis, Ferrohydrodynamics: testing a third magnetization & Nanoscience and Nanotechnology, Marcel Dekker, New York, 2004, equation, Phys Rev E 64 (R) (2001) 1–4 (060501). pp. 1731–1748. [44] H.W. Mu¨ller, M. Liu, Ferrofluid dynamics, in: S. Odenbach (Ed.), [21] S. Mornet, S. Vasseur, F. Grasset, E. Duguet, Magnetic nanoparticle Ferrofluids, Magnetically Controllable Fluids and Their Applica- && design for medical diagnosis and therapy, J Mater Chem 14 (2004) tions, Springer, Berlin, 2002, pp. 112–123. 2161–2175. [45] A.F. Lehlooh, S.H. Mahmood, J.M. Williams, On the particle size & [22] R. Ganguly, A.P. Gaind, S. Sen, I.K. Puri, Analyzing ferrofluid dependence of the magnetic anisotropy energy, Physica B 321 (2002) transport for magnetic drug targeting, JMMM 289 (2005) 331–334. 159–162. [23] R. Mu¨ller, R. Hergt, M. Zeisberger, W. Gawalek, Preparation of [46] P.C. Fannin, I. Malaescu, C.N. Marin, The effective anisotropy magnetic nanoparticles with large specific loss power for heating constant of particles within magnetic fluids as measured by magnetic applications, JMMM 289 (2005) 13–16. resonance, JMMM 289 (2005) 162–164. [24] J.W.M. Bulte, Magnetic nanoparticles as markers for cellular MR [47] A.D. Rosenthal, C. Rinaldi, T. Franklin, M. Zahn, Torque & imaging, JMMM 289 (2005) 423–427. measurements in spin-up flow of ferrofluids, J Fluids Eng 126 [25] L.F. Gamarra, G.E.S. Brito, W.M. Pontuschka, E. Amaro, A.H.C. (2004) 198–205. Parma, G.F. Goya, Biocompatible superparamagnetic oxide [48] C. Rinaldi, F. Gutman, X. He, A.D. Rosenthal, M. Zahn, Torque & nanoparticles used for contrast agents: a structural and magnetic measurements on ferrofluid cylinders in rotating magnetic fields, study, JMMM 289 (2005) 439–441. JMMM 289 (2005) 307–310. [26] G. Glockl, V. Brinkmeier, K. Aurich, E. Romanus, P. Weber, W. [49] A. Engel, P. Reimann, Thermal ratchet effects in ferrofluids, Phys Weitschies, Development of a liquid phase immunoassay by time- Rev E 70 (2004) 1–15 (051107). C. Rinaldi et al. / Current Opinion in Colloid & Interface Science 10 (2005) 141–157 155

[50] A. Engel, H.W. Mu¨ller, P. Reimann, A. Jung, Ferrofluids as thermal [75] N. Saga, T. Nakamura, Elucidation of propulsive force of ratchets, Phys Rev Lett 91 (6) (2003) 1–4 (060602). microrobot using magnetic fluid, J Appl Phys 91 (10) (2002) [51] M.I. Shliomis, Comment on ‘‘ferrofluids as thermal ratchets’’, Phys 7003–7005. Rev Lett 92 (18) (2003) 1, (188901). [76] L. Mao, H. Koser, Ferrohydrodynamic pumping in spatially & [52] P.C. Fannin, C.N. Marin, I. Malaescu, A.T. Giannitsis, Micro- traveling sinusiodally time-varying magnetic fields, JMMM 289 wave absorption of composite magnetic fluids, JMMM 289 (2005) 199–202. (2005) 78–80. [77] K. Zimmermann, I. Zeidis, V.A. Naletova, V.A. Turkov, V.E. [53] A.T. Giannitsis, P.C. Fannin, S.W. Charles, Nonlinear effects in Bachurin, Locomotion based on a two-layers flow of magnetizable magnetic fluids, JMMM 289 (2005) 165–167. nanosuspensions, JMMM 290-291 (part2) (2005) 808–810. [54] P.C. Fannin, Characterisation of magnetic fluids, J Alloys Compd [78] P.R. Laird, R. Bergamasco, V. Be´rube´, E.F. Borra, J. Gingras, A. & 369 (2004) 43–51. Ritcey, et al., Ferrofluid based deformable mirrors—a new approach [55] P.C. Fannin, Y.P. Kalmykov, S.W. Charles, Investigation of subsid- to adaptive optics using liquid mirrors, in: P.L. Wizinowich, D. iary loss-peaks in the frequency dependent susceptibility profiles of Bonaccini (Eds.), Adaptive Optical System. Technologies II, Pro- magnetic fluids, JMMM 289 (2005) 133–135. ceedings of SPIEvol. 4839, SPIE, WA, 2003, pp. 733–740. [56] P.C. Fannin, Magnetic spectroscopy as an aide in understanding [79] P.R. Laird, E.F. Borra, R. Begamasco, J. Gingras, L. Truong, A.M. magnetic fluids, in: S. Odenbach (Ed.), Ferrofluids, Magnetically Ritcey, Deformable mirrors based on magnetic , in: D.B. Controllable Fluids and Their Applications, Springer, Berlin, 2002, Calia, B.L. Ellerbroek, (Eds.), Advancements in Adaptive Optics, pp. 19–32. Proceedings of SPIEvol. 5490, PIE, WA, 2004, pp. 1493–1501. [57] B. Fischer, B. Huke, M. Lu¨cke, R. Hempelmann, Brownian [80] J.J. Chieh, S.Y. Yang, Y.H. Chao, H.E. Horng, C.-Y. Hong, H.C. relaxation of magnetic , JMMM 289 (2005) 74–77. Yang, Dynamic response of optical-fiber modulator by using [58] Y.L. Raikher, V.V. Rusakov, Theoretical models for AC-field magnetic fluid as a cladding layer, J Appl Phys 97 (2005) 1–4 probing of complex magnetic fluids, JMMM 258–259 (2003) (043104). 459–463. [81] J.-W. Seo, S.-M. Jeon, S.H. Park, H.-S. Lee, An experimental and [59] D.K. Kim, M.S. Amin, S. Elborai, S.-H. Lee, Y. Koseoglu, M. Zahn, numerical investigation of flat panel display cell using magnetic et al., Energy absorption of superparamagnetic iron oxide nano- fluid, JMMM 252 (2002) 353–355. particles by microwave irradiation, J Appl Phys 97 (2005) 1–3 [82] J.-W. Seo, H. Kim, S. Sung, Design and fabrication of a magnetic (10J510). microfluidic light modulator using magnetic fluid, JMMM 272-276 [60] R.E. Rosensweig, Heating magnetic fluid with an alternating (2004) e1787–e1789. magnetic field, JMMM 252 (2002) 370–374. [83] E. Janiaud, J.-C. Bacri, A. Cebers, F. Elias, Magnetic forces in 2D [61] R.E. Rosensweig, Role of internal rotations in selected magnetic foams, JMMM 289 (2005) 215–218. fluid applications, 36 (4) (2000) 303–316. [84] W. Drenckhan, F. Elias, S. Hutzler, D. Weaire, E. Janiaud, J.-C. [62] P.C. Fannin, C.N. Marin, I. Malaescu, A.T. Giannitsis, Micro- Bacri, Bubble size control and measurement in the generation of wave absorption of composite magnetic fluids, JMMM 289 ferrofluid foams, J Appl Phys 93 (12) (2003) 10078–10083. (2005) 78–80. [85] J. Ishimoto, S. Kamiyama, Numerical study of cavitating flow of [63] H. Brenner, Rheology of two-phase systems, Annual Rev Fluid Mech magnetic fluid in a vertical converging–diverging nozzle, JMMM 2 (1970) 137–176. 289 (2005) 26–263. [64] D.M. Ramos, F.R. Cunha, Y.D. Sobral, J.L.A. Fontoura Rodrigues, [86] V. Bashtovoi, G. Bossis, P. Kuzhir, A. Reks, Magnetic field effect on Computer simulations of magnetic fluids in laminar pipe flows, capillary rise of magnetic fluids, JMMM 289 (2005) 376–378. JMMM 289 (2005) 238–241. [87] J.G. Veguera, Y.I. Dikansky, Periodical structure in a magnetic fluid [65] F.R. Cunha, Y.D. Sobral, Asymptotic solution for pressure-driven under the action of an and with a shear flow, JMMM flows of magnetic fluids in pipes, JMMM 289 (2005) 314–317. 289 (2005) 87–89. [66] N.T. Nguyen, Z.G. Wu, X.Y. Huang, C.-Y. Wen, The application of [88] V.A. Naletova, V.A. Turkov, V.V. Sokolov, A.N. Tyatyuskin, The APIV technique in the study of magnetic flows in a micro-channel, interaction of the particles of magnetizable suspensions with a wall JMMM 289 (2005) 396–398. (wall-adjacent effect) in uniform electric and magnetic fields, [67] R. Rosensweig, Basic equations for magnetic fluids with internal JMMM 289 (2005) 367–369. & rotations, in: S. Odenbach (Ed.), Ferrofluids, Magnetically Controllable [89] V.A. Naletova, V.A. Turkov, A.N. Tyatyuskin, Spherical body in a Fluids and Their Applications, Springer, Berlin, 2002, pp. 61–84. magnetic fluid in uniform electric and magnetic fields, JMMM 289 [68] R. Rosensweig, Continuum equations for magnetic and dielec- (2005) 370–372. & tric fluids with internal rotations, J Chem Phys 121 (3) (2004) [90] R. Krauh, B. Reimann, R. Richter, I. Rehberg, Fluid pumped by 1228–1242. magnetic stress, Appl Phys Lett 86 (2005) 1–3 (024102). [69] S.R. de Groot, P. Mazur, Non-equilibrium Thermodynamics, North- [91] A.P. Krekhov, M.I. Shliomis, S. Kamiyama, Ferrofluid pipe flow in & Holland Amsterdam, 1962, also re-published by New York: Dover, an oscillating magnetic field, Phys Fluids 17 (2005) 1–8 (033105). 1984. [92] K.R. Schumacher, I. Sellien, G.S. Knoeke, T. Cader, B.A. Finlayson, & [70] B.U. Felderhof, Relativistic hydrodynamics of magnetic and dielec- Experiment and simulation of laminar and turbulent ferrofluid pipe & tric fluids in interaction with the electromagnetic field, J Chem Phys flow in an oscillating magnetic field, Phys Rev E 67 (2003) 1–11 120 (8) (2004) 3598–3603. ([026308]). [71] C. Rinaldi, M. Zahn, Ferrohydrodynamic instabilities in dc magnetic [93] B.U. Felderhof, Flow of a ferrofluid down a tube in an oscillating & fields, J Vis 7 (1) (2004) 8. magnetic field, Phys Rev E 64 (2001) 1–7 ([021508]). [72] M. Zahn, Magnetic fluid and nanoparticle applications to nano- [94] M.I. Shliomis, M.A. Zaks, Nonlinear dynamics of a ferrofluid technology, J Nanopart Res 3 (2001) 73–78. pendulum, Phys Rev Lett 93 (4) (2004) 1–4 (047202). [73] W. He, S.J. Lee, D.C. Jiles, D.H. Schimidt, D. Porter, R. Shinar, [95] C. Lorenz, M. Zahn, Hele–Shaw ferrohydrodynamics for rotating & Design of high-magnetic field gradient sources for controlling and dc axial magnetic fields, Phys Fluids Gallery Fluid Motion 15 (S4 magnetically induced flow of ferrofluid in microfluidic systems, J No. 9) (2003) (see also S4, http://pof.aip.org/pof/gallery/2003toc.jsp). Appl Phys 93 (10) (2003) 7459–7461. [96] S. Rhodes, J. Perez, S. Elborai, S.-H. Lee, M. Zahn, Ferrofluid spiral & [74] Y. Melikhov, S.J. Lee, D.C. Jiles, D.H. Schimidt, M.D. Porter, R. formations and continuous-to-discrete phase transitions under simul- Shinar, Microelectromagnetic ferrofluid-based actuator, J Appl Phys taneously applied DC axial and AC in-plane rotating magnetic fields, 93 (10) (2003) 8438–8440. JMMM 289 (2005) 353–355. 156 C. Rinaldi et al. / Current Opinion in Colloid & Interface Science 10 (2005) 141–157

[97] S.M. Elborai, D.K. Kim, X. He, S.-H. Lee, S. Rhodes, M. Zahn, Self- [120] H. Kikura, M. Aritomi, Y. Takeda, Velocity measurement on Taylor– & & forming, quasi-two-dimensional magnetic fluid patterns with applied Couette flow of a magnetic fluid with small aspect ratio, JMMM 289 in-phase-rotating and DC-axial magnetic fields, J Appl Phys 97 (2005) 342–345. (2005) 1–3 (10Q303). [121] T. Sawada, H. Nishiyama, T. Tabata, Influence of a magnetic field & [98] M.I. Shliomis, K.I. Morozov, Negative viscosity of ferrofluid under on ultrasound propagation in a magnetic fluid, JMMM 252 (2002) alternating magnetic-field, Phys Fluids 6 (1994) 2855–2861. 186–188. [99] A. Zeuner, R. Richter, I. Rehberg, Experiments on negative and [122] M. Motozawa, T. Sawada, Influence of magnetic field on & positive magnetoviscosity in an alternating magnetic field, Phys Rev ultrasonic propagation velocity in magnetic fluids, JMMM 289 E 58 (1998) 6287–6293. (2005) 66–69. [100] M. Zahn, L.L. Pioch, Magnetizable fluid behavior with effective [123] R.E. Rosensweig, J. Popplewell, R.J. Johnston, Magnetic fluid & positive, zero or negative dynamic viscosity, Indian J Eng Mat Sci 5 motion in rotating field, JMMM 85 (1990) 171–180. (1998) 400–410. [124] R.E. Rosensweig, S. Elborai, S.-H. Lee, M. Zahn, Theory and & [101] M. Zahn, L.L. Pioch, Ferrofluid flows in ac and traveling wave measurements of ferrofluid meniscus shape in applied uniform magnetic fields with effective positive, zero or negative dynamic horizontal and vertical magnetic fields, JMMM 289 (2005) viscosity, JMMM 201 (1999) 144–148. 192–195. [102] J.-C. Bacri, R. Perzynski, M.I. Shliomis, G.I. Burde, Negative- [125] E.G. Megalios, N. Kapsalis, J. Paschalidis, A.G. Papathanasiou, A.G. viscosity effect in a magnetic fluid, Phys Rev Lett 75 (1) (1995) Boudouvis, A simple optical device for measuring free surface 2128–2131. deformations of nontransparent liquids, J Colloid Interface Sci 288 [103] R.E. Rosensweig, ‘‘Negative viscosity’’ in a magnetic fluid, Science (2005) 508–512. 271 (5249) (1996) 614–615. [126] M.S. Amin, S.M. Elborai, S.-H. Lee, X. He, M. Zahn, Surface [104] M. Zahn, D.R. Greer, Ferrohydrodynamic pumping in spatially tension measurement techniques of magnetic fluids at an interface uniform sinusoidally time-varying magnetic fields, JMMM 149 (1) between different fluids using perpendicular field instability, J Appl (1995) 165–173. Phys 97 (2005) 1–3 (10R308). [105] A. Zeuner, R. Richter, I. Rehberg, On the consistency of the standard [127] V. Sofonea, W.-G. Fru¨h, A. Cristea, Lattice Boltzmann model for the model for magnetoviscosity in an alternating magnetic field, JMMM simulation of interfacial phenomena in magnetic fluids, JMMM 252 201 (1999) 191–194. (2002) 144–146. [106] X. He, S.M. Elborai, D.K. Kim, S.H. Lee, M. Zahn, Effective [128] A. Rothert, R. Richter, Experiments on the breakup of a liquid bridge magnetoviscosity of planar-couette magnetic fluid flow, J Appl Phys of magnetic fluid, JMMM 201 (1999) 324–327. 97 (2005) 1–3 (10Q302). [129] S. Sudo, A. Nakagawa, K. Shimada, H. Nishiyama, Shape response [107] C. Rinaldi, Continuum modeling of polarizable systems. PhD thesis of functional drops in alternating magnetic fields, JMMM 289 (2005) in the Department of Chemical Engineering, Massachusetts Institute 321–324. of Technology, 2002. [130] K. Melzner, S. Odenbach, Investigation of the Weissenberg effect [108] S. Odenbach, S. Thurm, Magnetoviscous effects in ferrofluids, in: S. in ferrofluids under microgravity conditions, JMMM 252 (2002) & Odenbach (Ed.), Ferrofluids, magnetically controllable fluids and 250–252. their applications, Springer, Berlin, 2002, pp. 185–201. [131] J. Richardi, M.P. Pileni, Nonlinear theory of pattern formation in [109] V. Bashtovoi, O. Lavrova, T. Mitkova, V. Polevikov, L. Tobiska, ferrofluid films at high field strengths, Phys Rev E 69 (2004) 1–9 Flow and energy dissipation in a magnetic fluid drop around a (016304). permanent magnet, JMMM 289 (2005) 207–210. [132] R.M. Oliveira, J.A. Miranda, Magnetic fluid in a time-dependent gap [110] H. Kikura, J. Matsushita, O. Hirashima, M. Aritomi, I. Nakatani, Hele–Shaw cell, JMMM 289 (2005) 360–363. Flow visualization and particle size determination of primary [133] J.A. Miranda, R.M. Oliveira, Time dependent gap Hele–Shaw cell clusters in a water-based magnetic fluid, JMMM 289 (2005) with a ferrofluid: evidence for an interfacial singularity inhibition by 392–395. a magnetic field, Phys Rev E 69 (2004) 1–5 (066312). [111] S. Odenbach, Ferrofluids-magnetically controlled suspensions, Col- [134] M. Igonin, A. Cebers, Labyrinthine instability of miscible magnetic loids Surf A Physicochem Eng Asp 217 (2003) 171–178. fluids, JMMM 252 (2002) 293–295. [112] M. Kroell, M. Pridoehl, G. Zimmermann, L. Pop, S. Odenbach, A. [135] D.P. Jackson, Theory, experiment, and simulations of a symmetric & Hartwig, Magnetic and rheological characterization of novel ferro- arrangement of quasi-two-dimensional magnetic fluid drops, JMMM fluids, JMMM 289 (2005) 21–24. 289 (2005) 188–191. [113] C. Rinaldi, M. Zahn, Effects of spin viscosity on ferrofluid flow [136] C.-Y. Chen, H.-J. Wu, L. Hsu, Numerical simulations of labyrinthine & profiles in alternating and rotating magnetic fields, Phys Fluids 14 (8) instabilities on a miscible elliptical magnetic droplet, JMMM 289 (2002) 2847–2870. (2005) 364–366. [114] S. Thurm, S. Odenbach, Magnetic separation of ferrofluids, JMMM [137] W. Herreman, P. Molho, S. Neveu, Magnetic field effects on viscous 252 (2002) 247–249. fingering of a ferrofluid in a radial Hele–Shaw cell, JMMM 289 [115] L.M. Pop, S. Odenbach, A. Wiedenmann, N. Matoussevitch, H. (2005) 356–359. Bo¨nnemann, Microstructure and rheology of ferrofluids, JMMM 289 [138] I. Drikis, A. Cebers, Viscous fingering in magnetic fluids: numerical (2005) 303–306. simulation of radial Hele–Shaw flow, JMMM 201 (1999) 339–342. [116] C. Wilhelm, J. Browaeys, A. Ponton, J.-C. Bacri, Rotational [139] A. Tatulchenkov, A. Cebers, Shapes of a bubble rising in the magnetic particles microrheology: the Maxwellian case, Phys Rev vertical Hele–Shaw cell with magnetic liquid, JMMM 289 (2005) E 67 (2003) 1–10 (011504). 373–375. [117] C. Wilhelm, F. Gazeau, J.-C. Bacri, Rotational magnetic endosome [140] C.-Y. Chen, H.-J. Wu, Fingering instabilities of a miscible microrheolgy: viscoelastic architecture inside living cells, Phys Rev magnetic droplet on a rotating Hele–Shaw cell, JMMM 289 E 67 (2003) 1–12 (061908). (2005) 339–341. [118] Y. Takeda, Velocity profile measurement by ultrasonic Doppler [141] G. Pacitto, C. Flament, J.-C. Bacri, M. Widom, Rayleigh–Taylor & & method, Exp Therm Fluid Sci 10 (1995) 444–453. instability with magnetic fluids: experiment and theory, Phys Rev E [119] H. Kikura, Y. Takeda, T. Sawada, Velocity profile measurements of 62 (6) (2000) 7941–7948. & magnetic fluid flow using ultrasonic Doppler method, JMMM 201 [142] C.-Y. Wen, W.-P. Su, Natural of magnetic fluid in a (1999) 276–280. rectangular Hele–Shaw cell, JMMM 289 (2005) 299–302. C. Rinaldi et al. / Current Opinion in Colloid & Interface Science 10 (2005) 141–157 157

[143] T.A. Franklin, Ferrofluid flow phenomena. Master’s Thesis in the [154] A.J. Silva, M. Gonc¸alves, S.M. Shibli, Thermodiffusion study in Department of Electrical Engineering and Computer Science; ferrofluids through collinear mirage effect, JMMM 289 (2005) Massachusetts Institute of Technology: Cambridge, MA, 2003. 295–298. [144] K. Zakaria, Nonlinear dynamics of magnetic fluids with a relative [155] E. Blums, New transport properties of ferrocolloids: magnetic Soret motion in the presence of an oblique magnetic field, Physica A 327 effect and thermomagnetoosmosis, JMMM 289 (2005) 246–249. (2003) 221–248. [156] A. Ryskin, H. Pleiner, Influence of a magnetic field on the Soret- [145] Y.O. El-Dib, A.Y. Ghaly, Destabilizing effect of time-dependent effect-dominated thermal convection in ferrofluids, Phys Rev E 69 & oblique magnetic field on magnetic fluids streaming in porous media, (2004) 1–10 (046301). J Colloid Interface Sci 269 (2004) 224–239. [157] E. Blums, Heat and mass transfer phenomena, in: S. Odenbach (Ed.), & [146] M. Hennenberg, B. Weyssow, S. Slavtchev, V. Alexandrov, T. Ferrofluids, Magnetically Controllable Fluids and Their Applica- Desaive, Rayleigh–Marangoni–Be´nard instability of a ferrofluid tions, Springer, Berlin, 2002, pp. 124–142. layer in a vertical magnetic field, JMMM 289 (2005) 268–271. [158] S.I. Alves, A. Bourdon, A.M. Figueiredo Neto, Investigation of the [147] V.V. Mekhonoshin, A. Lange, Chain-induced effects in the Faraday Soret coefficient in magnetic fluids using the Z-scan technique, instability on ferrofluids in a horizontal magnetic field, Phys Fluids JMMM 289 (2005) 285–288. 16 (4) (2004) 925–935. [159] J. Lenglet, A. Bourdon, J.-C. Bacri, G. Demouchy, Thermodiffu- [148] T. Mahr, I. Rehberg, Magnetic Faraday instability, Europhys Lett 43 sion in magnetic colloids evidenced and studied by forced (1) (1998) 23–28. Rayleigh scattering experiments, Phys Rev E 65 (2002) 1–14 [149] B. Reimann, T. Mahr, R. Richter, I. Rehberg, Standing twin peaks (031408). due to non-monotonic dispersion of Faraday waves, JMMM 201 [160] M.I. Shliomis, B.I. Smorodin, Convective instability of magnetized (1999) 303–305. ferrofluids, JMMM 252 (2002) 197–202. [150] A. Lange, Magnetic Soret effect: application of the ferrofluid [161] W. Luo, T. Du, J. Huang, Novel convective instabilities in a magnetic dynamics theory, Phys Rev E 70 (2004) 1–6 ([046308]). fluid, Phys Rev Lett 82 (20) (1999) 4134–4137. [151] T. Vo¨lker, S. Odenbach, Thermodiffusion in magnetic fluids, JMMM [162] M.I. Shliomis, Comment on ‘‘novel convective instabilities in a 289 (2005) 289–291. magnetic fluid’’, Phys Rev Lett 87 (5) (2001) 1, (059801). [152] S. Odenbach, T. Vo¨lker, Thermal convection in a ferrofluid supported [163] V.A. Naletova, A.S. Kvitantsev, Thermomagnetic force acting on by thermodiffusion, JMMM 289 (2005) 122–125. a spheroidal body in a magnetic fluid, JMMM 289 (2005) [153] T. Vo¨lker, E. Blums, S. Odenbach, Thermodiffusion in magnetic 250–252. fluids, JMMM 252 (2002) 218–220.