Magnetic fluid rheology and flows · 2019. 11. 20. · Magnetic fluid rheology and flows Carlos...

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Current Opinion in Colloid & Interface

Magnetic fluid rheology 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 Ricob 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 magnetization

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 resonance imaging; (3) use of the

antisymmetric part of the viscous stress 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 magnetic field.

Recent advances in magnetic fluid rheology and flows are reviewed including extensions of the governing magnetization relaxation and

ferrohydrodynamic equations with a viscous stress tensor that has an antisymmetric part due to spin velocity; derivation of the magnetic

susceptibility tensor in a ferrofluid 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 viscosity; 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 fluids; Ferrofluids; Ferrohydrodynamics; Magnetization; Magnetic susceptibility; Magnetic forces; Magnetic torques; Magnetoviscosity;

Magnetic thermodiffusion; Magnetic Soret effect

1. Introduction to magnetic fluids

1.1. Ferrofluid composition

Magnetic fluids, also called ferrofluids, are synthesized

colloidal mixtures of non-magnetic carrier liquid, typically

water or oil, containing single domain permanently magne-

tized particles, typically magnetite, with diameters of order

1359-0294/$ - see front matter D 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.cocis.2005.07.004

* Corresponding author. Tel.: +1 617 253 4688; fax: +1 617 258 6774.

E-mail addresses: [email protected] (C. Rinaldi),

[email protected] (A. Chaves), [email protected] (S. Elborai),

[email protected] (X. He), [email protected] (M. Zahn).1 Tel.: +1 787 832 4040/3585; fax: +1 787 834 3655/+1 787 265 3818.2 Tel.: +1 617 253 5019; fax: +1 617 258 6774.

5 –15 nm and volume fraction up to about 10%

[1&&,2&&,3&,4&,5&].

Brownian motion keeps the nanoscopic particles from

settling under gravity, and a surfactant layer, such as oleic

acid, or a polymer coating surrounds each particle to provide

short range steric hindrance and electrostatic repulsion

between particles preventing particle agglomeration [6&].

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

[2&&,8]. Recent experiments and analysis show that magnetic

dipole forces in strong magnetic fields cause large nano-

particles to form chains and aggregates that can greatly

affect macroscopic properties of ferrofluids even for low

nanoparticle concentration [9–12]. Small angle neutron

Science 10 (2005) 141 – 157

C. Rinaldi et al. / Current Opinion in Colloid & Interface Science 10 (2005) 141–157142

scattering (SANS) distinguishes between magnetic and non-

magnetic components of ferrofluids allowing density,

composition, and magnetization profiles to be precisely

determined [13,14]. Nanoparticle dynamics, composition,

and magnetic relaxation affect magnetic fluid rheology

which can be examined using magnetic field induced

birefringence [15–19].

The study and applications of ferrofluids, invented in

the mid-1960s, involve the multidisciplinary sciences of

chemistry, fluid mechanics, and magnetism. Because of the

small particle size, ferrofluids involved nanoscience and

nanotechnology from their inception. With modern advan-

ces in understanding nanoscale systems, current research

focuses on synthesis, characterization, and functionaliza-

tion of nanoparticles with magnetic and surface properties

tailored for application as micro/nanoelectromechanical

sensors, actuators, and micro/nanofluidic devices [20&];

and for such biomedical applications as [20&,21&&] nano-

biosensors, targeted drug-delivery vectors [22], magneto-

cytolysis of cancerous tumors, hyperthermia [23],

separations and cell sorting, magnetic resonance imaging

[24,25], immunoassays [26], radiolabelled magnetic fluids

[27], and X-ray microtomography for three dimensional

analysis of magnetic nanoparticle distribution in biological

applications, a crucial parameter for therapeutic evaluation

[28].

1.2. Applications

Conventional ferrofluid applications use DC magnetic

fields from permanent magnets for use as liquid O-rings in

rotary and exclusion seals, film bearings, as inertial

dampers in stepper motors and shock absorbers, in

magnetorheological fluid composites, as heat transfer

fluids in loudspeakers, in inclinometers and accelerome-

ters, for grinding and polishing, in magnetocaloric pumps

and heat pipes [1&&,2&&,3&,4&,5&], and as lubrication in

improved hydrodynamic journal bearings [29]. Ferrofluid

is used for cooling over 50 million loudspeakers each year.

Almost every computer disk drive uses a magnetic fluid

rotary seal for contaminant exclusion and the semiconduc-

tor industry uses silicon crystal growing furnaces that

employ ferrofluid rotary shaft seals. Ferrofluids are also

used for separation of magnetic from non-magnetic

materials and for separating materials by their density by

using a non-uniform magnetic field to create a magnetic

pressure distribution in the ferrofluid that causes the fluid

to act as if it has a variable density that changes with

height. Magnetic materials move to the regions of

strongest magnetic field while non-magnetic materials

move to the regions of low magnetic field with matching

effective density. Magnetomotive separations use this

selective buoyancy for mineral processing, water treatment

[30], and sink-float separation of materials, one novel

application being the separation of diamonds from beach

sand.

2. Governing ferrohydrodynamic equations

2.1. Magnetization

2.1.1. Langevin magnetization equilibrium

Ferrofluid equilibrium magnetization is accurately

described by the Langevin equation for paramagnetism

[1&&,2&&,3&,4&,5&,31&&]

M0 ¼ MS cotha �1

a

� �; a ¼ l0mH=kT ð1Þ

where in equilibrium M̄0 and H̄ are collinear; Ms=Nm =

Md/ is the saturation magnetization when all magneticdipoles with magnetic nanoparticle volume Vp and magnet-

ization Md have moment m =MdVp aligned with H̄; N is

the number of magnetic dipoles per unit volume; and / isthe volume fraction of magnetic nanoparticles in the

ferrofluid. For the typically used magnetite nanoparticle

(Md=4.46�105 A/m or l0Md=0.56 T), a representativevolume fraction of / =4% with nanoparticle diameterd =10 nm (Vp =5.25�10�25 m3) gives a ferrofluidsaturation magnetization of l0Ms=l0Md/ =0.0244 T andN =/ /Vp�7.6�1022 magnetic nanoparticles/m3.

At low magnetic fields the magnetization is approx-

imately linear with H̄

M̄M 0

H̄H¼ v0 ¼ l0m2N= 3kTð Þ ¼

p18kT

� �/l0M

2d d

3 ð2Þ

where v0 is the magnetic susceptibility, related to magneticpermeability as l =l0(1+v0). For our representative num-bers at room temperature we obtain v0�0.42 and l /l0�1.42. When the initial magnetic permeability is large,the interaction of magnetic moments is appreciable so that

Eq. (2) is no longer accurate. Shliomis [31&&,1&&] considers

the case of monodispersed particles and uses a method

similar to that used in the Debye–Onsager theory of polar

fluids to replace Eq. (2) with

v0 2v0 þ 3ð Þv0 þ 1

¼ l0m2N= kTð Þ ¼k

6kT

� �/l0M

2d d

3: ð3Þ

Langevin magnetization measurements in the linear low

field region (ab1) provide an estimate of the largestmagnetic particle diameters and in the high field saturation

regime (aH1) gives an estimate of the smallest magneticdiameters [1&&,32&]

limaH1

M0

MS,1� 1

a¼ 1� 6kT

kl0MdHd3

limab1

M0

MS,

a3¼ kl0MdHd

3

18kTð4Þ

This method allows estimation of the ferrofluid mag-

netic nanoparticle size range using a magnetometer. Other

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

[33].

2.1.2. Magnetization relaxation

When the ferrofluid is at rest and the magnetization is

not in equilibrium due to time transients or time varying

magnetic fields, the conventional magnetization equation

for an incompressible fluid derived by Shliomis is

[31&&,34&&]

BM̄M

Btþ v̄vIlð ÞM̄M � x̄x � M̄M þ

M̄M � M̄M 0� �

s¼ 0 ð5Þ

where s is a relaxation time constant, v̄ is the ferrofluidlinear flow velocity, and x̄ is the ferrofluid spin velocitywhich is an average particle rotation angular velocity.

Soon after Eq. (5) was derived, another magnetization

equation was derived microscopically using the Fokker–

Planck equation in the mean field approximation [35&&].

Defining half the flow vorticity as X̄X ¼ 12l� v̄v, the two

magnetization equations are in good agreement when

Xsb1, but (5) leads to non-physical results for XsH1.Another analysis by Felderhof used irreversible thermody-

namics of ferrofluids with hydrodynamics and the full set

of Maxwell equations to derive a closely related but not

identical equation to Eq. (5) [36&,37&]. Shliomis [38&,39&]

states that Felderhof’s relaxation equation leads to an

incorrect limiting value of rotational viscosity when the

Langevin parameter a in Eq. (1) becomes large whileFelderhof [40&] replies that Shliomis’ approximate theory

for dilute ferrofluids does not apply in the dense regime

and has limited validity in the dilute regime. Recent

rotational measurements with an applied DC magnetic

field perpendicular to capillary Poiseuille flow agree with

the Shliomis result and differ from Felderhof’s result

[41&]. Earlier similar measurements with an alternating

magnetic field had a qualitative fit to the Shliomis

rotational viscosity result but required a frequency

dependent fitting parameter to successfully fit theory and

experiment [42].

More recently, Shliomis has derived a third magnet-

ization equation from irreversible thermodynamics which

describes magnetoviscosity in the entire range of magnetic

field strength and flow vorticity [43&]. It is stated that this

new magnetization equation is an improvement over that

of Ref. [35&&] by being valid even far from equilibrium. Yet

another analysis by Müller and Liu uses standard non-

equilibrium thermodynamics with magneto-dissipative

effects to derive a magnetization relaxation equation using

their ferrofluid dynamics theory [44]. They state that

Shliomis’ Debye theory of Eq. (5) and his effective-field

theory approach are special cases of the new set of

equations.

2.1.3. Magnetization relaxation time constants

When a DC magnetic field H̄ is applied to a ferrofluid,

just like a compass needle, each magnetic nanoparticle

with magnetic moment m̄ experiences a torque l0m̄� H̄which tends to align m̄ and H̄. There are two important

time constants that determine how long it takes m̄ to align

with H̄,

sB ¼ 3gVh=kT ; sN ¼ s0e KVp=kTð Þ: ð6Þ

The Brownian rotational relaxation time, sB, describesthe hydrodynamic process when the magnetic moment is

fixed to the nanoparticle and surfactant layer of total

hydrodynamic volume Vh, including surfactant or other

surface coatings, and the whole nanoparticle rotates in a

fluid of viscosity g to align m̄ and H̄. The Néel timeconstant, sN, is the characteristic time for the magneticmoment inside the particle to align with H̄, due to flipping

of atomic spins without particle rotation. The parameter K is

the particle magnetic anisotropy and Vp is the volume of

particle magnetic material. The literature gives different

values for the anisotropy constant K of magnetite, over the

range of 23,000 to 100,000 J m�3 while s0 approximatelyequals 10�9 s. Recent work has used Mossbauer spectro-

scopy to show that the value of K is size dependent,

increasing as particle size decreases and gives a value of

K =78,000 J m�3 for 12.6 nm diameter magnetic nano-

particles [45&]. Other work has measured the effective

anisotropy constant in diluted ferrofluids using electron spin

resonance spectrometry and AC complex magnetic suscept-

ibility measurements [46]. The total magnetic time constant

s including both Brownian and Néel relaxation is given byRefs. [1&&,2&&,3&,4&,5&,31&&]

1

s¼ 1

sBþ 1

sN`s ¼ sBsN

sB þ sN: ð7Þ

The time constant s is dominated by the smaller of sBor sN. For K =78,000 J m

�3 with 12.6 nm diameter

magnetic nanoparticles at T=300 K, sN¨368 ms. For aferrofluid with representative suspending medium viscosity

of g =0.001 Pa-s and with a surfactant thickness d =2 nm,sB�1.7 ls. For these parameters we see that the effectivetime constant is dominated by sB. Torque measurementswith ferrofluid particles of order 10 nm diameter have

estimated, by comparison to theory, effective magnetic

relaxation times of the order of the computed Brownian

relaxation time [47&,48&]. Brownian and Néel relaxation are

lossy processes leading to energy dissipation so that the

complex magnetic susceptibility has an imaginary part.

These losses lead to heat generation using time varying

magnetic fields which can be used for localized treatment

of cancerous tumors [21&&,23].

In rotating magnetic fields, the time constant s of Eq.(7) results in the magnetization direction lagging H̄,

therefore a time average torque acts on each nanoparticle

causing the particles and surrounding fluid to spin. This

leads to new physics as the fluid behaves as if it is filled

with nanosized gyroscopes that stir and mix the fluid


balanced by the non-symmetric part of the viscous stress

tensor.

Rotational Brownian motion of ferrofluid nanoparticles

in a time dependent magnetic field can have thermal noise

induced rotation due to rectification of thermal fluctuations

[49,50]. A plastic sphere filled with ferrofluid was

suspended on a fiber and placed in a horizontal magnetic

field of the form H =HDC+H1[cos xt +asin(2xt+b)].When the magnetic field was turned on, the sphere rotated.

The explanation given was that rotation was due to thermal

ratchet behavior [50]. However, Shliomis describes the true

cause of rotation to be a magnetic torque due to the

nonlinearity of ferrofluid magnetization as given by Eq. (1)

[51].

2.2. Complex magnetic susceptibility

We consider the low field linear region of the Langevin

curve so that in equilibrium M̄0=v0H̄, with v0 given by Eqs.(2) or (3). We examine the sinusoidal steady state magnet-

ization response for a uniform magnetic field at radian

frequency Xf in the ferrofluid layer with planar Couette flowshown in Fig. 1, with upper surface driven at constant

velocity V in the z direction. The ferrofluid flow velocity is

then of the form m̄ =mz(x)īz. The magnetization is independ-ent of y and z because the applied magnetic field is assumed

uniform. Then the second term of Eq. (5) is zero. For

magnetization and magnetic field driven at field frequency

Xf, the complex amplitude sinusoidal steady state forms ofH̄ and M̄ are

H̄H ¼ Re ĤH xīx þ ĤH zīz�e jXf tg��

M̄M ¼ Re M̂M xīx þ M̂M zīz�e jXf tg:��

ð8Þ

Phase shifts between M̄ and H̄ components cause a

non-zero torque, T̄=l0M̄� H̄, which will result in a timeaverage spin velocity of the form x̄ =xy(x)ī y. Thecomplex magnetic susceptibility tensor is then found by

x

Ferrofluid

d

y

v ωyz

Fig. 1. A planar ferrofluid layer between rigid walls, in planar Couette flow driven

by uniform x and z directed DC magnetic fields.

solving M̄ as a function of H̄ in Eq. (5) in the linear limit

of Eqs. (2) or (3)

M̂M xM̂M z

� �¼ v0

jXf s þ 1� �2 þ xys� �2h i

jXf s þ 1� �

xys� xys jXf s þ 1

� �� ĤH xĤH z

� �:

ð9Þ

If xy=0, the tensor relationship reduces to a complexscalar magnetic susceptibility

v ¼ v V� jvW ¼ M̄MH̄H

¼ v01þ jXf s� �`v V

¼ v01þ Xf s

� �2h i ; vW ¼ v0Xf s1þ Xf s

� �2h i ð10Þwhere vV is the real part of v related to magnetic field energystorage and vW is the imaginary part of v which causespower dissipation. Note that vW has a peak value of v0 /2when Xf s =1. Spectroscopy measurements of the real andimaginary parts of v as a function of frequency provideinformation about the magnetization dynamics [52–54&,55–

57]. Other work uses a kinetic approach to microrheology

that adds stress retardation (mechanical memory) to a

viscoelastic fluid or weak gel containing a ferrosuspension

to produce new and interesting non-Newtonian properties

and dynamic susceptibility effects [58].

2.3. Heating

Increasing concentrations of ferrofluid magnetic material

have a greater rate of heating and higher temperature

increase when placed in an alternating magnetic field [59].

The time average dissipated power per unit volume for

fields at sinusoidal radian frequency Xf is [60–62]

< Pd > ¼ Re1

2l0jXf

ˆ̄MM̄MM I ˆ̄HH̄HHT� �

ð11Þ

where the superscript asterisk (*) denotes a complex

conjugate.

Hz

z

V

Hx or Bx

by the x =d surface moving at z directed velocity V, is magnetically stressed


For an oscillating magnetic field with Ĥx = Ĥz =H0 and

magnetization given in Eq. (9) for a ferrofluid with spin

velocity xy, the time average dissipated power is then

< Pd > ¼l0v0H

20X

2f s 1þ X2f � x2y

� �s2

h i1þ 2 X2f þ x2y

� �s2 þ X2f � x2y

� �2s4

� � :ð12Þ

In a clockwise rotating field with Ĥx =H0 and Ĥz =� jH0,the dissipated power is

< Pd > ¼l0v0H

20Xf s Xf þ xy

� �1þ Xf þ xy

� �2s2

h i1þ 2 X2f þ x2y

� �s2 þ X2f � x2y

� �2s4

� � :ð13Þ

Note that the magnetic susceptibility in Eqs. (9) and (10)

and the dissipated power in Eqs. (11)– (13) can be

modulated by magnetic field amplitude, frequency, phase

and direction and by control of the spin velocity which itself

can be set by flow vorticity and by magnetic field

parameters such as amplitude and frequency of a rotating

uniform magnetic field.

2.4. Conservation of linear and angular momentum

equations

In time transient or dynamic flow conditions, fluid

viscosity causes the magnetization M̄ to lag the magnetic

field H̄. When M̄ and H̄ are not collinear, the torque density

T=l0M̄� H̄ leads to novel flow phenomena because theviscous stress tensor has an anti-symmetric part. The general

pair of force and torque equations for ferrofluids are then

[1&&,2&&,3&,4&,5&,34&&]

qBm̄mBt

þ m̄mIlð Þm̄m�

¼ �lpþ l0M̄M IlH̄H þ 2fl� x̄x

þ k þ g � fð Þl lIm̄mð Þ þ g þ fð Þl2m̄mð14Þ

IBx̄xBt

þ m̄mIlð Þx̄x�

¼ l0M̄M � H̄H þ 2f l� v̄v � 2x̄xð Þ

þ k Vþ g Vð Þl lIx̄xð Þ þ g Vl2x̄xð15Þ

where q is the fluid mass density, I is the fluid moment ofinertia density, v̄ is the linear flow velocity, x̄ is the spinvelocity, and p is the hydrodynamic pressure. The viscosity

coefficients are the usual shear viscosity g and the dilationalviscosity k while gV and kV are the analogous shear and bulkcoefficients of spin viscosity. The coefficient f is called thevortex viscosity and from microscopic theory for dilute

suspensions obeys the approximate relationship, f =1.5g/,

where / is the volume fraction of particles [63,34&&]. Recentwork has performed computer simulations of ferrofluid

laminar pipe flows to show magnetic field induced drag

reduction [64,65] and fluorescent microscale particle image

velocimetry was developed for ferrofluid micro-channel

flows [66].

Most practical ferrofluid flows are incompressible, so

that l I v̄ =0, and are viscous dominated so that inertialeffects are negligible. Flow geometry often results in

l I x̄ =0, as is the case in Fig. 1 where x̄ =xy(x)īy.Dimensional analysis gives g V̈ g: 2/2 where : is of the

order of the distance between particles and / is the particleand surfactant volume fraction. Because, with usual volume

fractions of order / =0.01, the distance : is comparable toparticle diameter of order 10 nm, gV becomes very small andso is often neglected in Eq. (15). In these limits and

assuming viscous dominated flow, Eqs. (14) and (15) can be

combined to the simpler forms:

0,�lpþ l0M̄M IlH̄H þl02l� M̄M � H̄H

� �þ gl2v̄v ð16Þ

x̄x,l0 M̄M � H̄H� �

4fþ 1

2l� v̄v: ð17Þ

Note that the spin velocity depends on magnetic torque

and flow vorticity. Using Eqs. (16) and (17) in Eq. (5)

yields

BM̄M

Btþ v̄vIlð ÞM̄M ¼ X̄X � M̄M �

M̄M � M̄M 0� �

s

� 14f

l0M̄M � M̄M� H̄H� �

; X̄X ¼ 12l� v̄v:

ð18Þ

Recent work by Rosensweig has extended Eqs. (14)

and (15) based on integral balance equations and

thermodynamics without arbitrary definitions of electro-

magnetic energy density and stress. The analysis included

electric and magnetic fields using the Minkowski expres-

sion, D̄� B̄, for electromagnetic momentum density andused an appropriate formulation of entropy production in

which the electromagnetic field is distinguished from

equilibrium. The usual constitutive relationships result

from the analysis without any empirical assumptions,

including the magnetization relaxation Eqs. (5) and (18)

[67&]. Rosensweig then further extended the analysis to

include Galilean relativity effects to first order in the ratio

of fluid velocity to light speed [68&].

A similar analysis was performed by Felderhof,

following the semirelativistic hydrodynamic equations of

motion of de Groot and Mazur [69], based on the choice

of e0l0Ē� H̄ for electromagnetic momentum density[36&,70&]. The Rosensweig and Felderhof analyses are

on the whole very similar, and in the limit of small v /c,

the two analyses are identical.


3. Magnetic forces and torques

3.1. Magnetic force density

The magnetic force density acting on an incompressible

ferrofluid is

F̄F ¼ l0 M̄M Il� �

H̄H ð19Þ

so that ferrofluids move in the direction of increasing

magnetic field strength. In a uniform magnetic field there is

no magnetic force. When M̄ and H̄ are collinear, this force

density modifies Bernoulli’s equation for inviscid and

irrotational steady flow to [1&&]

pþ 12

qjv̄vj2 � qḡg Ir̄r � l0Z H0

MdH ¼ constant ð20Þ

where |v̄| is the magnitude of the fluid velocity, ḡ is the

gravitational acceleration vector, and r̄=xīx+yīy + zīz is the

position vector. The magnetic term is the magnetic

contribution to fluid pressure and describes such magnetic

Fig. 2. Ferrofluid instabilities in DC magnetic fields for an Isopar-M based ferroflu

diameter magnet behind a small ferrofluid droplet surrounded by propanol to pre

magnetic field perpendicular to ferrofluid layer. The peaks initiate in a hexagonal a

weight and surface tension—(b) 200 Gauss, (c) 330 Gauss, (d) 400 Gauss; (e– f)

Gauss vertical magnetic field [71,72].

field effects as the shape of a ferrofluid meniscus; flow and

instabilities of a ferrofluid jet such as for magnetic fluid

inkjet printing; operation of magnetic fluid seals, bearings,

load supports; sink-float separations; magnetic fluid

nozzles; and magnet self-levitation in a ferrofluid

[1&&,3&,4&].

Ferrofluids exhibit a wide range of very interesting lines,

patterns, and structures that can develop from ferrohydro-

dynamic instabilities as shown in Fig. 2 [20&,71,72].

The magnetic field gradient force density in Eq. (19)

has been used for precise positioning and transport of

ferrofluid for sealing, damping, heat transfer, and liquid

delivery systems [73–75]. Smooth and continuous pump-

ing of ferrofluid in a tube or channel can be achieved by

a traveling wave non-uniform magnetic field generated by

a spatially traveling current varying sinusoidally in time

with a sinusoidal spatial variation along the duct axis

[76,77]. Magnetic forces on ferrofluids have been used

for adaptive optics to shape deformable mirrors [78,79];

as a ferrofluid cladding layer in development of a tunable

in-line optical-fiber modulator [80]; use as a flat panel

display cell where the luminance is magnetically con-

id with saturation magnetization of about 400 Gauss. (a) 1200 Gauss 5 mm

vent ferrofluid wetting of 1 mm gap glass plates; (b–d) peak pattern with

rray when the magnetic surface force exceeds the stabilizing effects of fluid

labyrinth instability with ferrofluid between 1 mm gap glass plates in 250


trolled through the ferrofluid film thickness [81]; as a

microfluidic MEMS-based light modulator [82]; for

magnetic control of the Plateau rule of the angle between

contacting films in 2D foams [83]; for magnetic control

of bubble size and transport in ferrofluid foams for

microfluidic and ‘‘lab-on-a-chip’’ applications and for

possible zero gravity experiments using the magnetic

field gradient force to precisely balance gravity so that

bubbles are free floating in ferrofluid [84]; for magnetic

field control of ferrofluid in a cavitating flow in a

converging–diverging nozzle [85]; and for studies of

longitudinal and transverse tangential magnetic fields on

ferrofluid capillary rise [86]. Applied electric fields can

also exert forces in ferrofluids to control suspension

rheological properties [87–89].

3.2. Torque-driven flows

In a rotating magnetic field, the magnetization relaxation

time constants of Eqs. (6) and (7) create a phase difference

between magnetization and magnetic field so that M̄ and H̄

are not in the same direction. This causes a magnetic torque

density

T̄T ¼ l0M̄M � H̄H ð21Þ

which causes the magnetic nanoparticles and surrounding

fluid to spin as given in Eq. (17). The concerted action

of order 1022–1023 spinning nanoparticles/m3 can cause

fluid pumping [90,91&,92&] and other interesting ferrofluid

flows [93&,94] and microdrop behavior shown in Fig. 3

[95&,96&,97&].

To emphasize magnetic torque effects, the effective

viscosity of ferrofluid was studied using the rotating uniform

Fig. 3. A ferrofluid drop between Hele–Shaw cell glass plates with 1.1 mm gap has

DC (0–250 Gauss) magnetic fields. The ferrofluid is surrounded by equal propor

smearing. (a) The vertical DC field is first applied to form the labyrinth pattern and

spiral pattern; (b) the counter-clockwise rotating field is applied first to hold the dr

to about 100 Gauss, the continuous fluid drop abruptly transitions to discrete drop

pattern further; (c) various end-states of spirals, and (d) droplet patterns [95&].

magnetic field generated by a two-pole three-phase motor

stator winding with a Couette viscometer used as a torque

meter [47&,48&]. When a fixed spindle rotation speed is

selected, the viscometer applies the necessary torque in order

to keep it rotating at the specified speed. When the magnetic

field co-rotates with the spindle immersed in ferrofluid, the

magnetic-field-induced shear stress on the spindle is in the

direction opposite to spindle rotation, making it harder to

turn the spindle at the specified speed so that the viscometer

applies a higher torque and it records an increase of effective

ferrofluid viscosity as shown in Fig. 4 [48&]. When the

magnetic field counter-rotates relative to the spindle, the

magnetic-field-induced shear stress on the spindle is in the

same direction as spindle rotation, so that it is easier to rotate

the spindle at the specified speed; therefore the viscometer

applies a lower torque, and the viscometer records a

decrease of effective ferrofluid viscosity as also shown in

Fig. 4. When the torque in Fig. 4 is negative, the effective

viscosity is negative [48&,98–106]. Other torque measure-

ments used a stationary spindle with ferrofluid inside the

spindle, outside the spindle, or simultaneously inside and

outside the spindle [48&]. The approximate magnetic-field-

induced time average torque on the spindle for ferrofluid

entirely outside the spindle is [48&]

T,� 8kR2Lc2l0v0 1þ v0ð ÞH2Xs

v0 þ 2ð Þ2 þ c2v0 4þ 2v0 þ v0c2ð Þ

ð22Þ

where R is the radius of the outer cylinder, c is the ratio ofthe inner cylinder radius to the outer radius of the

ferrofluid container, Xf is the radian frequency of theapplied magnetic field with rms amplitude H, s is theeffective magnetization relaxation time, v0 is the equili-

simultaneous applied in-plane rotating (20 Gauss rms at 25 Hz) and vertical

tions by volume of water and isopropyl alcohol (propanol) to prevent glass

then a counter-clockwise rotating field is applied to form a slowly rotating

op together with no labyrinth and then as the DC magnetic field is increased

lets, while further increase of the magnetic field to 250 Gauss changes the

Fig. 4. Torque required to rotate a spindle surrounded with ferrofluid as a

function of rotating magnetic field amplitude, frequency, and rotation

direction with respect to the 100 RPM rotation of the spindle [48&].


brium ferrofluid magnetic susceptibility, and l0=4p�10�7 henries/meter is the magnetic permeability of free

space. The approximate magnetic field induced torque on

the spindle for ferrofluid entirely inside the spindle is

[107,48&]

T,� 2Xf sv0l0H2V 1�sv0l0H

2

2f

� �ð23Þ

where f =1.5g/ is the vortex viscosity and g is the fluidviscosity. Magnetic field and shear dependent changes in

ferrofluid viscosity have many possible applications in

damping technologies [108&,109].

Fig. 5. The change in magnetoviscosity versus related DC magnetic field Hx or ma

imposed magnetic flux density Bx, magnetic susceptibility vm =1.55 was used in

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

magnetic flux 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 ofposition inside the ferrofluid flow, while magnetic flux

density Bx will always be spatially uniform in the planar

channel as l I B̄ =0, no matter the flow profile in thegeometry of Fig. 1 [104,106]. Extensions of this work

include AC magnetic fields for Couette and Poiseuille flows

with magnetic field components along and perpendicular to

the duct axis [104,113&].

For the planar Couette flow shown in Fig. 1, with x

directed magnetic field only (Hz =0), the change in

magnetoviscosity

Dg ¼ f 1þ 2xydV

� �ð24Þ

is plotted as the multivalued functions versus Hx or Bxmagnetic parameters in Fig. 5 [106]. For a DC magnetic

field, the effective viscosity always increases with magnetic

gnetic flux density Bx parameters PH or PB for various values of Vs /d. Forthe plots for oil-based ferrofluid Ferrotec EFH1 [106].


field amplitude. For AC magnetic fields, the effective

viscosity can decrease, even through zero and negative

values [48&,104].

The size distribution of nanoparticles in ferrofluid is very

important to various shear flows in a magnetic field. A

gradient magnetic field causes large particles to diffuse to

the strong field region while smaller particles have a weaker

effect. Rheometer measurements of viscosity show that

large particles and agglomerates have a strong magnetic

field dependence on viscosity increase which depends on

shear rate, while the smaller particle fluid has only a small

viscosity increase and smaller shear-rate dependence

[114,115].

Another rotating magnetic probe was developed to

measure the local viscoelasticity on microscopic scales

based on the alignment of dipolar chains of submicron

magnetic particles in the direction of an applied magnetic

field [116]. Proposed continuing work is to investigate the

rheological properties of the interior of a cell using this

magnetic rotational microrheology method [117].

4.2. Ultrasound velocity profile measurements

Because ferrofluids are opaque, an ultrasound velocity

profile method was developed for use with ferrofluids

[118&,119&,120&,121&]. The sound velocity in ferrofluid

increases slightly with magnetic field strength and ultra-

sound frequency while the velocity slightly decreases with

increasing angle between magnetic field and ultrasound

propagation direction and with weight concentration of

magnetic particles [122&].

An Ultrasonic Doppler Velocimeter (UDV) measured the

bulk velocity of ferrofluid in a cylindrical container, with

and without a top, with flow driven by a uniform rotating

magnetic field, as shown in Fig. 6. The measurements show

that a counter-clockwise rotating magnetic field causes a

Fig. 6. Spin-up flow profiles at mid-height excited by a magnetic field rotating co

free top surface and (b) with a cover on the container, so that there is no free top su

linear profiles of a fluid in rigid body co-rotation with the applied magnetic field,

velocity of the bulk flows in the central region co-rotate with the respective mag

surface angular velocities are larger and counter-rotate with the magnetic field at ¨

central region co-rotate with the magnetic field at larger velocities than in (a) with

rigid-body-like counter-clockwise rotation of ferrofluid at a

constant angular velocity. Only in a thin layer near the

cylinder wall does the no-slip condition force the fluid flow

to differ from rigid-body rotation.

The free ferrofluid/air interface at the surface of the vessel

with no top is observed to rotate in the clockwise direction,

opposite to the bulk rotation. The experiments show that

while the ferrofluid bulk slowly co-rotates with the applied

magnetic field, the ferrofluid free surface counter-rotates

with the applied magnetic field at higher rotational speed

than the bulk. With a fixed top on the ferrofluid free surface,

the volume flow velocity is generally higher than for a free

surface which counter-rotates to the volume flow.

Rosensweig et al. observed the velocity of the free

surface of ferrofluid flow in a uniform rotating magnetic

field driven by magnetic shear stresses in meniscus regions

[123&]. When the meniscus of the ferrofluid free surface was

concave, the ferrofluid surface flow counter-rotated to the

driven magnetic field; when the meniscus of ferrofluid free

surface was flat, the ferrofluid surface flow was stationary;

and when the meniscus of the ferrofluid free surface was

convex, the ferrofluid surface flow co-rotated with the

driven magnetic field. Because ferrofluid is opaque,

measurement of the bulk flow profiles was not possible.

All the surface flow observations were made by placing

tracer particles on the top rotating surface. Based on these

observations, Rosensweig concluded that volume flow

effects were negligible. However, the ultrasound velocity

measurements in Fig. 6 show that there is a significant

volume flow, even without a free top interface.

4.3. Interfacial phenomena

Further experimental measurements of meniscus height,

h =n(0), and shape n(x), were performed using narrowdiameter laser beam reflections from the meniscus interface

unter-clockwise at 200 Hz for various magnetic field amplitudes; (a) with a

rface. The central flow velocity profiles for (a) and (b) are approximately the

dropping to zero at the wall over a thin boundary layer. In (a), the angular

netic fields from high to low at ¨14, 8, 4, and 1 rpm while the respective

48, 36, 22, and 9 rpm. In (b), the angular velocity of the bulk flows in the

the respective magnetic fields from high to low at ¨20, 12, 5, and 1 rpm.

Fig. 7. The experimental optical setup for measuring ferrofluid meniscus

shape [124&].


as a function of DC applied magnetic fields, as shown in

Fig. 7. The angle of deflection of the laser beam from the

vertical allows the computation of the shape of the ferrofluid

meniscus [124&].

Three applied magnetic field configurations were used,

as shown in Fig. 8. A meniscus forms on the sides of a glass

slide immersed in the center of a vessel with negligibly

small field gradients. Fig. 9 shows for both oil and water-

based ferrofluids that applied magnetic field in configura-

tion a has practically no effect on the meniscus shape. As

expected, with a uniform magnetic field tangent to the

interface, the shape of the interface matches the non-

magnetic meniscus shape

x

a¼ 1ffiffiffi

2p cosh�1

ffiffiffi2

p

n=a� cosh�1

ffiffiffi2

p

h=a

�

þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2� h

a

� 2s�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2� n

a

� 2sð25Þ

where a =(2r /qg)1 / 2 is the capillary length for ferrofluid ofmass density q and surface tension r, with g being theacceleration of gravity. Fig. 9 shows that applied horizontal

magnetic field in configuration b lowers the height of a

Fig. 8. The three magnetic field configurations of the ferr

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

from the liquid bridge [128]; while other measurements

compared the shape response of ferrofluid droplets, a

magnetorheological fluid, and a composite magnetic fluid

with nanometer and micron sized particles in low frequency

alternating magnetic fields up to 5 Hz [129].

The Weissenberg effect is the rise of a free surface of a

viscoelastic fluid at a rotating rod due to normal stress forces

[130]. For magnetic fluids the height of the fluid surface at

the rod also depends on the length and quantity of fluid

particle chains, the strength of the applied magnetic field

parallel to the surface, the concentration of larger magnetic

particles, and the shear rate.

4.4. Hele–Shaw cell flows

In a porous medium, the local average fluid velocity is

described by Darcy’s law

0 ¼ �lp� bv̄v þ F̄F ð26Þ

where p is the hydrodynamic pressure, b =g /j is the ratioof fluid viscosity g to the permeability j which depends onthe geometry of the particles and interstitial space, and F̄ is

the total external force density, typically due to gravity and

magnetization given by Eq. (19).

A Hele–Shaw cell consists of two parallel walls a small

distance d apart, and is used for two-dimensional flows

where the flow velocity only has components parallel to the

ofluid meniscus experimentally investigated [124&].

Fig. 9. Measured meniscus shape for the three configurations of applied magnetic field. The top row shows oil-based ferrofluid (v0�1.55) results while thebottom row shows water-based ferrofluid (v0�0.67) results [124&].


walls. The mean flow between the walls is then also

described by Eq. (26) where b =12g /d2 and j =d2 /12. Aferrofluid drop in a Hele–Shaw cell forms an intricate

labyrinth when a uniform DC magnetic field is applied

perpendicular to the walls as shown in Fig. 2e–f. Typical

labyrinth analyses are usually approximately based on a

minimization of the free energy as a sum of magnetostatic

and interfacial tension energies, including the effects of

demagnetizing magnetic fields typically assuming that the

magnetization is linear with H̄, as in Eq. (2). Recent work

has generalized the free energy analysis to nonlinear

magnetization characteristics, particularly using the Lange-

vin magnetization of Eq. (1) [131].

Fig. 3 shows interesting Hele–Shaw cell ferrofluid

drop responses to simultaneous vertical DC and horizontal

rotating uniform magnetic fields [95&,96&,97&]. Other

ferrofluid Hele–Shaw cell flows investigated azimuthal

magnetic fields from a long straight current-carrying wire

along the axis perpendicular to the walls with a time-

dependent gap [132,133]; labyrinthine instability in mis-

cible magnetic fluids in a horizontal Hele–Shaw cell with

a vertical magnetic field [134]; theory and experiments of

interacting ferrofluid drops [135&]; numerical simulations

[136] and measurements [137] of viscous fingering

labyrinth instabilities; fingering instability of an expanding

air bubble in a horizontal Hele–Shaw cell [138] and of a

rising bubble in a vertical Hele–Shaw cell [139]; finger-

ing instabilities of a miscible magnetic fluid droplet in a

rotating Hele–Shaw cell [140]; theory and experiments of

the Rayleigh–Taylor instability [141&]; and natural con-

vection of magnetic fluid in a bottom-heated square

Hele–Shaw cell with two insulated side walls with heat

transfer measurements and liquid crystal thermography

[142].

4.5. Flow instabilities

4.5.1. Jet and sheet flows

The behavior of an initially circular cross-section

ferrofluid jet impacting a solid circular surface to create

an expanding sheet flow in the presence of a magnetic field

was investigated [143]. A horizontal magnetic field trans-

verse to a vertical ferrofluid jet axis changes the jet cross-

section from circular to elliptical, with long axis in the

direction of the applied magnetic field. As the transverse

magnetic field is increased, the expanding sheet also

becomes approximately elliptically shaped but with long

axis perpendicular to the magnetic field, which is transverse

to the long axis of the jet cross-section, as shown in Fig. 10.

At large magnetic fields, the sheet forms sharp tips and fluid

chains emerge from its corners. The prime cause of the

change in sheet shape is the influence of the magnetic field

on the jet shape. If an initially elliptical non-magnetic jet

strikes a circular impactor, the expanding sheet is similarly

elliptical but with its long axis also perpendicular to that of

the jet.

If the applied magnetic field is vertical, and thus

perpendicular to the expanding circular sheet, the sheet

(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].


diameter decreases with increasing magnetic field B. A

simple approximate Bernoulli analysis including magnetic

surface forces predicts the sheet radius to be

r ¼ rT 1�B2

qU21

l0� 1

l

� � �; rT ¼

qUQ4kr

ð27Þ

where rT is the Taylor radius with B =0, l is the ferrofluidmagnetic permeability, l0 is the magnetic permeability ofthe free space surrounding the sheet, q is the ferrofluiddensity, U is the ferrofluid sheet velocity, Q is the jet flow

rate, and r is the interfacial surface tension [143].

4.5.2. Kelvin–Helmholtz instability

The classic instability of the planar interface between

two superposed fluids with a relative horizontal velocity is

called the Kelvin–Helmholtz instability. The moving

ferrofluid sheet flow of Section 4.5.1 has magnetically

coupled upper and lower interfaces which can become

Kelvin–Helmholtz unstable. A planar sheet model,

generalized to include a magnetic field B perpendicular

to both interfaces, is formulated to examine the effects of

magnetic fields on interfacial stability for a fluid layer of

thickness d moving with horizontal velocity U [143].Letting n1 be the upwards deflection of the upperinterface and n2 be the upwards deflection of the lowerinterface, a linear stability analysis shows that there are

two interfacial modes with n1 /n2=T1. For interfacial

deflections of the form n1,2=Re[n̂1,2ej(xt-kz)] the disper-

sion relation is

q0x2

kþ q x � kUð Þ

2

k

coth kd=2ð Þtanh kd=2ð Þ

� � rk2

þk l � l0ð Þ2B2 coshkd þ ll0 sinhkdF1

h ilsinhkd l2 þ l20 þ 2ll0cothkd

� �¼ 0 n1=n2 ¼ k1 ð28Þ

where q0 is the density of the surrounding air. Interfacialdeflections are unstable if x22. Application of a mag-netic field component parallel to the sheet interfaces tends

to stabilize the sheet flow [143].

The stability of Kelvin–Helmholtz waves propagating

on the interface between two magnetic fluids stressed by

an oblique magnetic field has also been analyzed for free

fluids [144] and for fluids streaming through porous media

[145&].

4.5.3. Other flow instabilities

The Rayleigh–Maragoni–Bénard instability of a ferro-

fluid in a vertical magnetic field was studied combining

& of special interest.&& of outstanding interest.


aspects of volume and surface forces due to heating, flow

rheology, and magnetism [146].

The Faraday instability is the parametric generation of

standing waves on the free surface of a fluid subjected to

vertical vibrations. The initially flat free surface of the fluid

becomes unstable at a critical intensity of the vertical

vibrations. The Faraday instability has been used to study

the rheological properties of ferrofluids caused by strong

dipole interactions that lead to the formation of magnetic

particle chains elongated in the direction of the horizontal

magnetic field [147]; and used with a vertical oscillating

magnetic field to parametrically excite standing surface

waves with no mechanically imposed vertical vibrations

together with a vertical DC magnetic field to tune the fluid

parameters [148]. Later work used both a vertical DC

magnetic field with a mechanical exciter to vertically shake

the test cell [149] to obtain a novel pattern of standing twin

peaks due to the simultaneous excitation of two different

wave numbers.

4.6. Thermodiffusion (Soret effect)

In a multicomponent mixture, a temperature gradient

leads to diffusive concentration gradients due to the

coupling between heat and mass transport, known as the

Soret effect. The Soret effect has a strong dependence on

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

imposed across a flat ferrofluid layer with a transverse

magnetic field causes a concentration gradient of magnetic

nanoparticles. The mass and temperature gradient causes a

magnetization gradient resulting in a magnetic field

gradient which redistributes the magnetic particles with

mixing. Unlike a homogeneous single component fluid

which has a stationary instability, the two component

ferrofluid system has a double-diffusive oscillatory insta-

bility [160].

Recent work used a vertical laser beam to create a hot

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.

With a vertical magnetic field the initially round hot spot

changed to various polygon shapes, said to be caused by

convectively unstable roll cells. Shliomis [162] offered

another explanation where the hot spot is initially a non-

magnetic ‘‘bubble’’ within a magnetic fluid which is the

inverse of the labyrinth instability shown in Figs. 3a and

2e–f. Using the magnetic Bond number criterion for

labyrinth instability, Shliomis obtained very good agreement

with the labyrinth theory.

Calculation of the thermomagnetic force on a prolate

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-

ature gradient at an angle to the magnetic force [163].

5. Conclusions

This magnetic fluid rheology and flows review has

presented recent advances in fundamental theory; ferrofluid

flows and instabilities; thermal effects and applications; and

practical device and biomedical applications. Of special

importance are the better understanding of the significant

effects of magnetic particle aggregation; modern electrical,

mechanical, optical, and radiation measurement methods to

determine important rheological parameters; extensions of

the governing magnetization and ferrohydrodynamic equa-

tions including theoretical and experimental investigations

and applications of the antisymmetric part of the viscous

stress tensor; magnetic control of the magnetic susceptibility

tensor for heating applications with ferrofluids with non-

zero spin velocity; recent advances in biomedical applica-

tions of drug delivery, hyperthermia, and magnetic reso-

nance imaging; effective magnetoviscosity analysis and

measurements, including zero and negative values and not

just viscosity reduction; ultrasound velocity profile meas-

urements of spin-up flow showing counter-rotating surface

and volume flows in a uniform rotating magnetic field;

theory and measurements of ferrofluid meniscus shape for

tangential and perpendicular magnetic fields; and new

analysis and measurements of ferrohydrodynamic flows,

instabilities, and thermodiffusion (Soret effect) phenomena.

Acknowledgments

For the MIT authors, this work was partially supported

by the Thomas and Gerd Perkins Professorship at MIT and

by generous MIT alumnus Thomas F. Peterson. Ferrotec

Corporation is acknowledged for providing ferrofluids used

in MIT experiments and Brookfield Corporation is acknowl-

edged for providing a viscometer. The University of Puerto

Rico at Mayaguez authors were supported by the US

National Science Foundation (CTS-0331379) and by the

Petroleum Research Fund (ACS-PRF 40867-G 9).

References and recommended readings

[1]&&

R.E. Rosensweig, Ferrohydrodynamics. New York: Cambridge

University Press, 1985: republished by New York: Dover Publica-

tions, 1997.

[2]&&

S. Odenbach, Magnetoviscous Effects in Ferrofluids, Springer,

Berlin, 2002.

[3]&

B. Berkovski, V. Bashtovoy (Eds.), Magnetic Fluids and Applica-

tions, Begell House, New York, 1996.

[4]&

B.M. Berkovsky, V.F. Medvedev, M.S. Krakov, Magnetic Fluids

Engineering Applications, Oxford University Press, Oxford, 1993.

[5]&

E. Blums, A. Cebers, M.M. Maiorov, Magnetic Fluids, Walter de

Gruyter, Berlin, 1997.


[6]&

S.W. Charles, The preparation of magnetic fluids, in: S. Odenbach

(Ed.), Ferrofluids, Magnetically Controllable Fluids and Their

Applications, Springer, Berlin, 2002, pp. 3–18.

[7] I. Bolshakova, M. Bolshakov, A. Zaichenko, A. Egorov, The

investigation of the magnetic fluid stability using the devices with

magnetic field microsensors, JMMM 289 (2005) 108–110.

[8] G. Bossis, O. Volkova, S. Lacis, A. Meunier, Magnetorheology:

fluids, structures and rheology, in: S. Odenbach (Ed.), Ferrofluids,

Magnetically Controllable Fluids and Their Applications, Springer,

Berlin, 2002, pp. 202–230.

[9] A. Zubarev, Statistical physics of non-dilute ferrofluids, in: S.

Odenbach (Ed.), Ferrofluids, Magnetically Controllable Fluids and

Their Applications, Springer, Berlin, 2002, pp. 143–161.

[10] M.I. Morozov, M.I. Shliomis, Magnetic fluid as an assembly of

flexible chains, in: S. Odenbach (Ed.), Ferrofluids, Magnetically

Controllable Fluids and Their Applications, Springer, Berlin, 2002,

pp. 162–184.

[11] A.Y. Zubarev, L.Y. Iskakova, On the theory of structural trans-

formations in magnetic fluids, Colloid J 65 (6) (2003) 703–710.

[12] A.O. Ivanov, S.S. Kantorovich, Structure of chain aggregates in

ferrocolloids, Colloid J 65 (2) (2003) 166–176.

[13] A. Wiedenmann, Magnetic and crystalline nanostructures in ferro-

fluids as probed by small angle neutron scattering, in: S. Odenbach



[14] F. Gazeau, E. Dubois, J.-C. Bacri, Boué, A. Cebers, R. Perzynski,

Anisotropy of the structure factor of magnetic fluids under a field

probed by small-angle neutron scattering, Phys Rev E 65 (2002)

1–15 (031403).

[15] M.H. Sousa, E. Hasmonay, J. Depeyrot, F.A. Tourinho, J.-C.

Bacri, E. Dubois, et al., NiFe2O4 nanoparticles in ferrofluids:

evidence of spin disorder in the surface layer, JMMM 242-245

(2002) 572–574.

[16] Y.L. Raikher, V.I. Stepanov, J.-C. Bacri, R. Perzynski, Orientational

dynamics in magnetic fluids under strong coupling of external and

internal relaxations, JMMM 289 (2005) 222–225.

[17] Y.L. Raikher, V.I. Stepanov, J.-C. Bacri, R. Perzynski, Orientational

dynamics of ferrofluids with finite magnetic anisotropy of the

particles: relaxation of magneto-birefringence in crossed fields, Phys

Rev E 66 (2002) 1–14 (021203).

[18] D.K. Kim, D. Kan, T. Veres, F. Normadin, J.K. Liao, H.H. Kim, et

al., Monodispersed Fe–Pt nanoparticles for biomedical applica-

tions, J Appl Phys 97 (2005) 1–3 (10Q918).

[19] F. Shen, C. Poncet-Legrand, S. Somers, A. Slade, C. Yip, A.M.

Duft, et al., Properties of a novel magnetized alginate for

magnetic resonance imaging, Biotechnol Bioeng 83 (3) (2003)

282–292.

[20]&

C. Rinaldi, T. Franklin, M. Zahn, T. Cader, Magnetic nanoparticles

in fluid suspension: ferrofluid applications, Dekker Encyclopedia of

Nanoscience and Nanotechnology, Marcel Dekker, New York, 2004,

pp. 1731–1748.

[21]&&

S. Mornet, S. Vasseur, F. Grasset, E. Duguet, Magnetic nanoparticle

design for medical diagnosis and therapy, J Mater Chem 14 (2004)

2161–2175.

[22] R. Ganguly, A.P. Gaind, S. Sen, I.K. Puri, Analyzing ferrofluid

transport for magnetic drug targeting, JMMM 289 (2005) 331–334.

[23] R. Müller, R. Hergt, M. Zeisberger, W. Gawalek, Preparation of

magnetic nanoparticles with large specific loss power for heating

applications, JMMM 289 (2005) 13–16.

[24] J.W.M. Bulte, Magnetic nanoparticles as markers for cellular MR

imaging, JMMM 289 (2005) 423–427.

[25] L.F. Gamarra, G.E.S. Brito, W.M. Pontuschka, E. Amaro, A.H.C.

Parma, G.F. Goya, Biocompatible superparamagnetic iron oxide

nanoparticles used for contrast agents: a structural and magnetic

study, JMMM 289 (2005) 439–441.

[26] G. Glockl, V. Brinkmeier, K. Aurich, E. Romanus, P. Weber, W.

Weitschies, Development of a liquid phase immunoassay by time-

dependent measurements of the transient magneto-optical birefrin-

gence using functionalized magnetic nanoparticles, JMMM 289

(2005) 480–483.

[27] R. Aquino, J.A. Gomes, F.A. Tourinho, E. Dubois, R. Perzynski,

G.J. da Silva, et al., Sm and Y radiolabeled magnetic fluids:

magnetic and magneto-optical characterization, JMMM 289 (2005)

431–434.

[28] O. Brunke, S. Odenbach, C. Fritsche, I. Hilger, W.A. Kaiser,

Determination of magnetic particle distribution in biomedical

applications by X-ray microtomography, JMMM 289 (2005)

428–430.

[29] T.A. Osman, G.S. Nada, Z.S. Safar, Effect of using current-carrying-

wire models in the design of hydrodynamic journal bearings

lubricated with ferrofluids, Tribol Lett 11 (2001) 61–70.

[30] S. Jakabsky, M. Lovas, A. Mockovciakova, S. Hredzak, Utilization

of ferromagnetic fluids in mineral processing and water treatment, J

Radioanal Nucl Chem 246 (3) (2000) 543–547.

[31]&&

M.I. Shliomis, Magnetic fluids, Soviet Phys Uspekhi 17 (2) (1974)

153–169.

[32] R.W. Chantrell, J. Popplewell, S.W. Charles, Measurements of

particle size distribution parameters in ferrofluids, IEEE Trans Magn

14 (1978) 975–977.

[33] P. Kop*anský, M. Timko, I. Poto*ova, M. Koneracká, A. Juŕiková, N.Tomaxovi*ova, et al., The determination of the hydrodynamicdiameter of magnetic particles using FRS experiment, JMMM 289

(2005) 97–100.

[34]&&

M.I. Shliomis, Effective viscosity of magnetic suspensions, Soviet

Phys JETP 34 (6) (1972) 1291–1294.

[35]&&

M.A. Martsenyuk, Y.L. Raikher, M.I. Shliomis, On the kinetics of

magnetization of suspensions of ferromagnetic particles, Soviet

Phys JETP 38 (2) (1974) 413–416.

[36]&

B.U. Felderhof, H.J. Kroh, Hydrodynamics of magnetic and

dielectric fluid in interaction with the electromagnetic field, J Chem

Phys 110 (15) (1999) 7403–7411.

[37]&

B.U. Felderhof, Magnetoviscosity and relaxation in ferrofluids, Phys

Rev E 62 (3) (2000) 3848–3854.

[38]&

M. Shliomis, Comment on Fmagnetoviscosity and relaxation inferrofluids_, Phys Rev E 64 (2001) 1–6 (063501).

[39]&

M.I. Shliomis, Ferrohydrodynamics: retrospective and issues, in:



[40]&

B.U. Felderhof, Reply to ‘‘comment on Fmagnetoviscosity and

relaxation in ferrofluids_’’, Phys Rev E 6406 (2001) 1–4 (063502).

[41]&

R. Patel, R.V. Upadhyay, R.V. Mehta, Viscosity measurements of a

ferrofluid: comparison with various hydrodynamic equations, J Col-

loid Interface Sci 263 (2003) 661–664.

[42] A. Zeuner, R. Richter, I. Rehberg, Weak periodic excitation of a

magnetic fluid capillary flow, JMMM 201 (1999) 321–323.

[43]&

M. Shliomis, Ferrohydrodynamics: testing a third magnetization

equation, Phys Rev E 64 (R) (2001) 1–4 (060501).

[44] H.W. Müller, M. Liu, Ferrofluid dynamics, in: S. Odenbach (Ed.),

Ferrofluids, Magnetically Controllable Fluids and Their Applica-

tions, Springer, Berlin, 2002, pp. 112–123.

[45]&

A.F. Lehlooh, S.H. Mahmood, J.M. Williams, On the particle size

dependence of the magnetic anisotropy energy, Physica B 321 (2002)

159–162.

[46] P.C. Fannin, I. Malaescu, C.N. Marin, The effective anisotropy

constant of particles within magnetic fluids as measured by magnetic

resonance, JMMM 289 (2005) 162–164.

[47]&

A.D. Rosenthal, C. Rinaldi, T. Franklin, M. Zahn, Torque

measurements in spin-up flow of ferrofluids, J Fluids Eng 126

(2004) 198–205.

[48]&

C. Rinaldi, F. Gutman, X. He, A.D. Rosenthal, M. Zahn, Torque

measurements on ferrofluid cylinders in rotating magnetic fields,

JMMM 289 (2005) 307–310.

[49] A. Engel, P. Reimann, Thermal ratchet effects in ferrofluids, Phys

Rev E 70 (2004) 1–15 (051107).


[50] A. Engel, H.W. Müller, P. Reimann, A. Jung, Ferrofluids as thermal

ratchets, Phys Rev Lett 91 (6) (2003) 1–4 (060602).

[51] M.I. Shliomis, Comment on ‘‘ferrofluids as thermal ratchets’’, Phys

Rev Lett 92 (18) (2003) 1, (188901).

[52] P.C. Fannin, C.N. Marin, I. Malaescu, A.T. Giannitsis, Micro-

wave absorption of composite magnetic fluids, JMMM 289

(2005) 78–80.

[53] A.T. Giannitsis, P.C. Fannin, S.W. Charles, Nonlinear effects in

magnetic fluids, JMMM 289 (2005) 165–167.

[54]&

P.C. Fannin, Characterisation of magnetic fluids, J Alloys Compd

369 (2004) 43–51.

[55] P.C. Fannin, Y.P. Kalmykov, S.W. Charles, Investigation of subsid-

iary loss-peaks in the frequency dependent susceptibility profiles of

magnetic fluids, JMMM 289 (2005) 133–135.

[56] P.C. Fannin, Magnetic spectroscopy as an aide in understanding

magnetic fluids, in: S. Odenbach (Ed.), Ferrofluids, Magnetically

Controllable Fluids and Their Applications, Springer, Berlin, 2002,

pp. 19–32.

[57] B. Fischer, B. Huke, M. Lücke, R. Hempelmann, Brownian

relaxation of magnetic colloids, JMMM 289 (2005) 74–77.

[58] Y.L. Raikher, V.V. Rusakov, Theoretical models for AC-field

probing of complex magnetic fluids, JMMM 258–259 (2003)

459–463.

[59] D.K. Kim, M.S. Amin, S. Elborai, S.-H. Lee, Y. Koseoglu, M. Zahn,

et al., Energy absorption of superparamagnetic iron oxide nano-

particles by microwave irradiation, J Appl Phys 97 (2005) 1–3

(10J510).

[60] R.E. Rosensweig, Heating magnetic fluid with an alternating

magnetic field, JMMM 252 (2002) 370–374.

[61] R.E. Rosensweig, Role of internal rotations in selected magnetic

fluid applications, Magnetohydrodynamics 36 (4) (2000) 303–316.

[62] P.C. Fannin, C.N. Marin, I. Malaescu, A.T. Giannitsis, Micro-

wave absorption of composite magnetic fluids, JMMM 289

(2005) 78–80.

[63] H. Brenner, Rheology of two-phase systems, Annual Rev Fluid Mech

2 (1970) 137–176.

[64] D.M. Ramos, F.R. Cunha, Y.D. Sobral, J.L.A. Fontoura Rodrigues,

Computer simulations of magnetic fluids in laminar pipe flows,

JMMM 289 (2005) 238–241.

[65] F.R. Cunha, Y.D. Sobral, Asymptotic solution for pressure-driven

flows of magnetic fluids in pipes, JMMM 289 (2005) 314–317.

[66] N.T. Nguyen, Z.G. Wu, X.Y. Huang, C.-Y. Wen, The application of

APIV technique in the study of magnetic flows in a micro-channel,JMMM 289 (2005) 396–398.

[67]&

R. Rosensweig, Basic equations for magnetic fluids with internal

rotations, in: S. Odenbach (Ed.), Ferrofluids, Magnetically Controllable

Fluids and Their Applications, Springer, Berlin, 2002, pp. 61–84.

[68]&

R. Rosensweig, Continuum equations for magnetic and dielec-

tric fluids with internal rotations, J Chem Phys 121 (3) (2004)

1228–1242.

[69] S.R. de Groot, P. Mazur, Non-equilibrium Thermodynamics, North-

Holland Amsterdam, 1962, also re-published by New York: Dover,

1984.

[70]&

B.U. Felderhof, Relativistic hydrodynamics of magnetic and dielec-

tric fluids in interaction with the electromagnetic field, J Chem Phys

120 (8) (2004) 3598–3603.

[71] C. Rinaldi, M. Zahn, Ferrohydrodynamic instabilities in dc magnetic

fields, J Vis 7 (1) (2004) 8.

[72] M. Zahn, Magnetic fluid and nanoparticle applications to nano-

technology, J Nanopart Res 3 (2001) 73–78.

[73] W. He, S.J. Lee, D.C. Jiles, D.H. Schimidt, D. Porter, R. Shinar,

Design of high-magnetic field gradient sources for controlling

magnetically induced flow of ferrofluid in microfluidic systems, J

Appl Phys 93 (10) (2003) 7459–7461.

[74] Y. Melikhov, S.J. Lee, D.C. Jiles, D.H. Schimidt, M.D. Porter, R.

Shinar, Microelectromagnetic ferrofluid-based actuator, J Appl Phys

93 (10) (2003) 8438–8440.

[75] N. Saga, T. Nakamura, Elucidation of propulsive force of

microrobot using magnetic fluid, J Appl Phys 91 (10) (2002)

7003–7005.

[76]&

L. Mao, H. Koser, Ferrohydrodynamic pumping in spatially

traveling sinusiodally time-varying magnetic fields, JMMM 289

(2005) 199–202.

[77] K. Zimmermann, I. Zeidis, V.A. Naletova, V.A. Turkov, V.E.

Bachurin, Locomotion based on a two-layers flow of magnetizable

nanosuspensions, JMMM 290-291 (part2) (2005) 808–810.

[78] P.R. Laird, R. Bergamasco, V. Bérubé, E.F. Borra, J. Gingras, A.

Ritcey, et al., Ferrofluid based deformable mirrors—a new approach

to adaptive optics using liquid mirrors, in: P.L. Wizinowich, D.

Bonaccini (Eds.), Adaptive Optical System. Technologies II, Pro-

ceedings of SPIEvol. 4839, SPIE, WA, 2003, pp. 733–740.

[79] P.R. Laird, E.F. Borra, R. Begamasco, J. Gingras, L. Truong, A.M.

Ritcey, Deformable mirrors based on magnetic liquids, in: D.B.

Calia, B.L. Ellerbroek, (Eds.), Advancements in Adaptive Optics,

Proceedings of SPIEvol. 5490, PIE, WA, 2004, pp. 1493–1501.

[80] J.J. Chieh, S.Y. Yang, Y.H. Chao, H.E. Horng, C.-Y. Hong, H.C.

Yang, Dynamic response of optical-fiber modulator by using

magnetic fluid as a cladding layer, J Appl Phys 97 (2005) 1–4

(043104).

[81] J.-W. Seo, S.-M. Jeon, S.H. Park, H.-S. Lee, An experimental and

numerical investigation of flat panel display cell using magnetic

fluid, JMMM 252 (2002) 353–355.

[82] J.-W. Seo, H. Kim, S. Sung, Design and fabrication of a magnetic

microfluidic light modulator using magnetic fluid, JMMM 272-276

(2004) e1787–e1789.

[83] E. Janiaud, J.-C. Bacri, A. Cebers, F. Elias, Magnetic forces in 2D

foams, JMMM 289 (2005) 215–218.

[84] W. Drenckhan, F. Elias, S. Hutzler, D. Weaire, E. Janiaud, J.-C.

Bacri, Bubble size control and measurement in the generation of

ferrofluid foams, J Appl Phys 93 (12) (2003) 10078–10083.

[85] J. Ishimoto, S. Kamiyama, Numerical study of cavitating flow of

magnetic fluid in a vertical converging–diverging nozzle, JMMM

289 (2005) 26–263.

[86] V. Bashtovoi, G. Bossis, P. Kuzhir, A. Reks, Magnetic field effect on

capillary rise of magnetic fluids, JMMM 289 (2005) 376–378.

[87] J.G. Veguera, Y.I. Dikansky, Periodical structure in a magnetic fluid

under the action of an electric field and with a shear flow, JMMM

289 (2005) 87–89.

[88] V.A. Naletova, V.A. Turkov, V.V. Sokolov, A.N. Tyatyuskin, The

interaction of the particles of magnetizable suspensions with a wall

(wall-adjacent effect) in uniform electric and magnetic fields,

JMMM 289 (2005) 367–369.

[89] V.A. Naletova, V.A. Turkov, A.N. Tyatyuskin, Spherical body in a

magnetic fluid in uniform electric and magnetic fields, JMMM 289

(2005) 370–372.

[90] R. Krauh, B. Reimann, R. Richter, I. Rehberg, Fluid pumped bymagnetic stress, Appl Phys Lett 86 (2005) 1–3 (024102).

[91]&

A.P. Krekhov, M.I. Shliomis, S. Kamiyama, Ferrofluid pipe flow in

an oscillating magnetic field, Phys Fluids 17 (2005) 1–8 (033105).

[92]&

K.R. Schumacher, I. Sellien, G.S. Knoeke, T. Cader, B.A. Finlayson,

Experiment and simulation of laminar and turbulent ferrofluid pipe

flow in an oscillating magnetic field, Phys Rev E 67 (2003) 1–11

([026308]).

[93]&

B.U. Felderhof, Flow of a ferrofluid down a tube in an oscillating

magnetic field, Phys Rev E 64 (2001) 1–7 ([021508]).

[94] M.I. Shliomis, M.A. Zaks, Nonlinear dynamics of a ferrofluid

pendulum, Phys Rev Lett 93 (4) (2004) 1–4 (047202).

[95]&

C. Lorenz, M. Zahn, Hele–Shaw ferrohydrodynamics for rotating

and dc axial magnetic fields, Phys Fluids Gallery Fluid Motion 15 (S4

No. 9) (2003) (see also S4, http://pof.aip.org/pof/gallery/2003toc.jsp).

[96]&

S. Rhodes, J. Perez, S. Elborai, S.-H. Lee, M. Zahn, Ferrofluid spiral

formations and continuous-to-discrete phase transitions under simul-

taneously applied DC axial and AC in-plane rotating magnetic fields,

JMMM 289 (2005) 353–355.

http://pof.aip.org/pof/gallery/2003toc.jsp


[97]&

S.M. Elborai, D.K. Kim, X. He, S.-H. Lee, S. Rhodes, M. Zahn, Self-

forming, quasi-two-dimensional magnetic fluid patterns with applied

in-phase-rotating and DC-axial magnetic fields, J Appl Phys 97

(2005) 1–3 (10Q303).

[98] M.I. Shliomis, K.I. Morozov, Negative viscosity of ferrofluid under

alternating magnetic-field, Phys Fluids 6 (1994) 2855–2861.

[99] A. Zeuner, R. Richter, I. Rehberg, Experiments on negative and

positive magnetoviscosity in an alternating magnetic field, Phys Rev

E 58 (1998) 6287–6293.

[100] M. Zahn, L.L. Pioch, Magnetizable fluid behavior with effective

positive, zero or negative dynamic viscosity, Indian J Eng Mat Sci 5

(1998) 400–410.

[101] M. Zahn, L.L. Pioch, Ferrofluid flows in ac and traveling wave

magnetic fields with effective positive, zero or negative dynamic

viscosity, JMMM 201 (1999) 144–148.

[102] J.-C. Bacri, R. Perzynski, M.I. Shliomis, G.I. Burde, Negative-

viscosity effect in a magnetic fluid, Phys Rev Lett 75 (1) (1995)

2128–2131.

[103] R.E. Rosensweig, ‘‘Negative viscosity’’ in a magnetic fluid, Science

271 (5249) (1996) 614–615.

[104] M. Zahn, D.R. Greer, Ferrohydrodynamic pumping in spatially

uniform sinusoidally time-varying magnetic fields, JMMM 149 (1)

(1995) 165–173.

[105] A. Zeuner, R. Richter, I. Rehberg, On the consistency of the standard

model for magnetoviscosity in an alternating magnetic field, JMMM

201 (1999) 191–194.

[106] X. He, S.M. Elborai, D.K. Kim, S.H. Lee, M. Zahn, Effective

magnetoviscosity of planar-couette magnetic fluid flow, J Appl Phys

97 (2005) 1–3 (10Q302).

[107] C. Rinaldi, Continuum modeling of polarizable systems. PhD thesis

in the Department of Chemical Engineering, Massachusetts Institute

of Technology, 2002.

[108]&

S. Odenbach, S. Thurm, Magnetoviscous effects in ferrofluids, in: S.

Odenbach (Ed.), Ferrofluids, magnetically controllable fluids and

their applications, Springer, Berlin, 2002, pp. 185–201.

[109] V. Bashtovoi, O. Lavrova, T. Mitkova, V. Polevikov, L. Tobiska,

Flow and energy dissipation in a magnetic fluid drop around a

permanent magnet, JMMM 289 (2005) 207–210.

[110] H. Kikura, J. Matsushita, O. Hirashima, M. Aritomi, I. Nakatani,

Flow visualization and particle size determination of primary

clusters in a water-based magnetic fluid, JMMM 289 (2005)

392–395.

[111] S. Odenbach, Ferrofluids-magnetically controlled suspensions, Col-

loids Surf A Physicochem Eng Asp 217 (2003) 171–178.

[112] M. Kroell, M. Pridoehl, G. Zimmermann, L. Pop, S. Odenbach, A.

Hartwig, Magnetic and rheological characterization of novel ferro-

fluids, JMMM 289 (2005) 21–24.

[113]&

C. Rinaldi, M. Zahn, Effects of spin viscosity on ferrofluid flow

profiles in alternating and rotating magnetic fields, Phys Fluids 14 (8)

(2002) 2847–2870.

[114] S. Thurm, S. Odenbach, Magnetic separation of ferrofluids, JMMM

252 (2002) 247–249.

[115] L.M. Pop, S. Odenbach, A. Wiedenmann, N. Matoussevitch, H.

Bönnemann, Microstructure and rheology of ferrofluids, JMMM 289

(2005) 303–306.

[116] C. Wilhelm, J. Browaeys, A. Ponton, J.-C. Bacri, Rotational

magnetic particles microrheology: the Maxwellian case, Phys Rev

E 67 (2003) 1–10 (011504).

[117] C. Wilhelm, F. Gazeau, J.-C. Bacri, Rotational magnetic endosome

microrheolgy: viscoelastic architecture inside living cells, Phys Rev

E 67 (2003) 1–12 (061908).

[118]&

Y. Takeda, Velocity profile measurement by ultrasonic Doppler

method, Exp Therm Fluid Sci 10 (1995) 444–453.

[119]&

H. Kikura, Y. Takeda, T. Sawada, Velocity profile measurements of

magnetic fluid flow using ultrasonic Doppler method, JMMM 201

(1999) 276–280.

[120]&

H. Kikura, M. Aritomi, Y. Takeda, Velocity measurement on Taylor–

Couette flow of a magnetic fluid with small aspect ratio, JMMM 289

(2005) 342–345.

[121]&

T. Sawada, H. Nishiyama, T. Tabata, Influence of a magnetic field

on ultrasound propagation in a magnetic fluid, JMMM 252 (2002)

186–188.

[122]&

M. Motozawa, T. Sawada, Influence of magnetic field on

ultrasonic propagation velocity in magnetic fluids, JMMM 289

(2005) 66–69.

[123]&

R.E. Rosensweig, J. Popplewell, R.J. Johnston, Magnetic fluid

motion in rotating field, JMMM 85 (1990) 171–180.

[124]&

R.E. Rosensweig, S. Elborai, S.-H. Lee, M. Zahn, Theory and

measurements of ferrofluid meniscus shape in applied uniform

horizontal and vertical magnetic fields, JMMM 289 (2005)

192–195.

[125] E.G. Megalios, N. Kapsalis, J. Paschalidis, A.G. Papathanasiou, A.G.

Boudouvis, A simple optical device for measuring free surface

deformations of nontransparent liquids, J Colloid Interface Sci 288

(2005) 508–512.

[126] M.S. Amin, S.M. Elborai, S.-H. Lee, X. He, M. Zahn, Surface

tension measurement techniques of magnetic fluids at an interface

between different fluids using perpendicular field instability, J Appl

Phys 97 (2005) 1–3 (10R308).

[127] V. Sofonea, W.-G. Früh, A. Cristea, Lattice Boltzmann model for the

simulation of interfacial phenomena in magnetic fluids, JMMM 252

(2002) 144–146.

[128] A. Rothert, R. Richter, Experiments on the breakup of a liquid bridge

of magnetic fluid, JMMM 201 (1999) 324–327.

[129] S. Sudo, A. Nakagawa, K. Shimada, H. Nishiyama, Shape response

of functional drops in alternating magnetic fields, JMMM 289 (2005)

321–324.

[130] K. Melzner, S. Odenbach, Investigation of the Weissenberg effect

in ferrofluids under microgravity conditions, JMMM 252 (2002)

250–252.

[131] J. Richardi, M.P. Pileni, Nonlinear theory of pattern formation in

ferrofluid films at high field strengths, Phys Rev E 69 (2004) 1–9

(016304).

[132] R.M. Oliveira, J.A. Miranda, Magnetic fluid in a time-dependent gap

Hele–Shaw cell, JMMM 289 (2005) 360–363.

[133] J.A. Miranda, R.M. Oliveira, Time dependent gap Hele–Shaw cell

with a ferrofluid: evidence for an interfacial singularity inhibition by

a magnetic field, Phys Rev E 69 (2004) 1–5 (066312).

[134] M. Igonin, A. Cebers, Labyrinthine instability of miscible magnetic

fluids, JMMM 252 (2002) 293–295.

[135]&

D.P. Jackson, Theory, experiment, and simulations of a symmetric

arrangement of quasi-two-dimensional magnetic fluid drops, JMMM

289 (2005) 188–191.

[136] C.-Y. Chen, H.-J. Wu, L. Hsu, Numerical simulations of labyrinthine

instabilities on a miscible elliptical magnetic droplet, JMMM 289

(2005) 364–366.

[137] W. Herreman, P. Molho, S. Neveu, Magnetic field effects on viscous

fingering of a ferrofluid in a radial Hele–Shaw cell, JMMM 289

(2005) 356–359.

[138] I. Drikis, A. Cebers, Viscous fingering in magnetic fluids: numerical

simulation of radial Hele–Shaw flow, JMMM 201 (1999) 339–342.

[139] A. Tatulchenkov, A. Cebers, Shapes of a gas bubble rising in the

vertical Hele–Shaw cell with magnetic liquid, JMMM 289 (2005)

373–375.

[140] C.-Y. Chen, H.-J. Wu, Fingering instabilities of a miscible

magnetic droplet on a rotating Hele–Shaw cell, JMMM 289

(2005) 339–341.

[141]&

G. Pacitto, C. Flament, J.-C. Bacri, M. Widom, Rayleigh–Taylor

instability with magnetic fluids: experiment and theory, Phys Rev E

62 (6) (2000) 7941–7948.

[142] C.-Y. Wen, W.-P. Su, Natural convection of magnetic fluid in a

rectangular Hele–Shaw cell, JMMM 289 (2005) 299–302.


[143] T.A. Franklin, Ferrofluid flow phenomena. Master’s Thesis in the

Department of Electrical Engineering and Computer Science;

Massachusetts Institute of Technology: Cambridge, MA, 2003.

[144] K. Zakaria, Nonlinear dynamics of magnetic fluids with a relative

motion in the presence of an oblique magnetic field, Physica A 327

(2003) 221–248.

[145]&

Y.O. El-Dib, A.Y. Ghaly, Destabilizing effect of time-dependent

oblique magnetic field on magnetic fluids streaming in porous media,

J Colloid Interface Sci 269 (2004) 224–239.

[146] M. Hennenberg, B. Weyssow, S. Slavtchev, V. Alexandrov, T.

Desaive, Rayleigh–Marangoni–Bénard instability of a ferrofluid

layer in a vertical magnetic field, JMMM 289 (2005) 268–271.

[147] V.V. Mekhonoshin, A. Lange, Chain-induced effects in the Faraday

instability on ferrofluids in a horizontal magnetic field, Phys Fluids

16 (4) (2004) 925–935.

[148] T. Mahr, I. Rehberg, Magnetic Faraday instability, Europhys Lett 43

(1) (1998) 23–28.

[149] B. Reimann, T. Mahr, R. Richter, I. Rehberg, Standing twin peaks

due to non-monotonic dispersion of Faraday waves, JMMM 201

(1999) 303–305.

[150] A. Lange, Magnetic Soret effect: application of the ferrofluid

dynamics theory, Phys Rev E 70 (2004) 1–6 ([046308]).

[151] T. Völker, S. Odenbach, Thermodiffusion in magnetic fluids, JMMM

289 (2005) 289–291.

[152] S. Odenbach, T. Völker, Thermal convection in a ferrofluid supported

by thermodiffusion, JMMM 289 (2005) 122–125.

[153] T. Völker, E. Blums, S. Odenbach, Thermodiffusion in magnetic

fluids, JMMM 252 (2002) 218–220.

[154] A.J. Silva, M. Gonçalves, S.M. Shibli, Thermodiffusion study in

ferrofluids through collinear mirage effect, JMMM 289 (2005)

295–298.

[155] E. Blums, New transport properties of ferrocolloids: magnetic Soret

effect and thermomagnetoosmosis, JMMM 289 (2005) 246–249.

[156] A. Ryskin, H. Pleiner, Influence of a magnetic field on the Soret-

effect-dominated thermal convection in ferrofluids, Phys Rev E 69

(2004) 1–10 (046301).

[157]&

E. Blums, Heat and mass transfer phenomena, in: S. Odenbach (Ed.),

Ferrofluids, Magnetically Controllable Fluids and Their Applica-

tions, Springer, Berlin, 2002, pp. 124–142.

[158] S.I. Alves, A. Bourdon, A.M. Figueiredo Neto, Investigation of the

Soret coefficient in magnetic fluids using the Z-scan technique,

JMMM 289 (2005) 285–288.

[159] J. Lenglet, A. Bourdon, J.-C. Bacri, G. Demouchy, Thermodiffu-

sion in magnetic colloids evidenced and studied by forced

Rayleigh scattering experiments, Phys Rev E 65 (2002) 1–14

(031408).

[160] M.I. Shliomis, B.I. Smorodin, Convective instability of magnetized

ferrofluids, JMMM 252 (2002) 197–202.

[161] W. Luo, T. Du, J. Huang, Novel convective instabilities in a magnetic

fluid, Phys Rev Lett 82 (20) (1999) 4134–4137.

[162] M.I. Shliomis, Comment on ‘‘novel convective instabilities in a

magnetic fluid’’, Phys Rev Lett 87 (5) (2001) 1, (059801).

[163] V.A. Naletova, A.S. Kvitantsev, Thermomagnetic force acting on

a spheroidal body in a magnetic fluid, JMMM 289 (2005)

250–252.

Magnetic fluid rheology and flowsIntroduction to magnetic fluidsFerrofluid compositionApplications

Governing ferrohydrodynamic equationsMagnetizationLangevin magnetization equilibriumMagnetization relaxationMagnetization relaxation time constants

Complex magnetic susceptibilityHeatingConservation of linear and angular momentum equations

Magnetic forces and torquesMagnetic force densityTorque-driven flows

FerrohydrodynamicsMagnetoviscosityUltrasound velocity profile measurementsInterfacial phenomenaHele-Shaw cell flowsFlow instabilitiesJet and sheet flowsKelvin-Helmholtz instabilityOther flow instabilities

Thermodiffusion (Soret effect)

ConclusionsAcknowledgmentsReferences and recommended readings,•

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