FerrofluidsFerrofluids

Overview

• Definitions• Engineering• Applications

Definition

• A ferrofluid is a specific type of liquid which responds to a magnetic field. Ferrofluids are composed of nanoscale magnetic particles suspended in a carrier fluid. The solid particles are generally stabilized with an attached surfactant layer. Ferrofluids are extremely stable meaning that they will not cluster together even in extremely strong magnetic fields

Ferrofluids: Magnetic Liquids

Liquid That Responds to a Magnetic Field

=

Colloidal Suspension of Superparamagnetic Magnetic Material

History of Ferrofliuds

• In the 1960’s Stephen Pappell at NASA first developed ferrofluids as a method for controlling fluids in space.

• Magnets and/or magnetic fields were used to control this magnetic fluid.

• Currently applications of Ferrofluids in space have been replaced by more economical fluids.

Physics

• Ferromagnetismisamagneticdipolethatisfromthealignmentofunpairedelectronspinsinelementssuchasiron,cobalt,andnickel.Inthisexperimentwewillsynthesizemagneticnanoparticlesfromironchloridesandthendisperseintoatetramethylammoniumhydroxidesurfactanttoformacolloidalsuspension

Berger, P.; Adelman, N. B.; Beckman, K. J.; Campbell, D. J.; Ellis, A. B.; Lisensky, G. C. Journal of Chemical Education 1999, 76, 943-8.

How Does A Magnetic Liquid Work?

ElectrostaticRepulsion

2FeCl3 + FeCl2 + 8NH3 + 4H2O →Fe3O4 + 8NH4Cl

Tetramethylammonium Cation(NH4

+)

HydroxideAnion(OH-)

~ 10nm

Chemistry

• The formation of ferrofluid involves various types of forces that hold the components together. For example, magnetite is held together by ionic interactions. Ionic attractions between hydroxide anions and tetramethylammonium cations allow colloidal suspension of the magnetite in the solution. Without the tetramethyl ammonium hydroxide as a surfactant, the magnetite nanoparticles tend to cluster together. Therefore it is necessary to have the appropriate surfactant to stabilize an aqueous ferrofluid

Synthesis of Magnetite NanocrystalsSynthesis of Magnetite NanocrystalsFeCl3 + 3NH4OH → FeO(OH) + 3NH4Cl + H2O

2FeO(OH) + Fe(OH)2→ Fe3O4 + 2H2O

Processes:1) Nucleation 2) Growth 3) Termination

→→

+

++

+ +

+

++

+ +

+

+

+

+

+

++

+

+

FeCl2 + 2NH4OH → Fe(OH)2 + 2NH4Cl

• Fe(III) coordinates to 6 water molecules andFe(II) coordinates to 4 water molecules (notshown) until the solid forms

• The water molecules on the periphery of the magnetite are ultimately replaced by tetramethylammonium hydroxide

Unique Properties

• Stick to Magnets• Take on 3-Dimensional Shape of a

Magnetic Field• Change Density in Proportion to

Magnetic Field Strength

13

Ferrofluid Magnetic Properties

Water-based Ferrofluidµ0Ms = 203 Gauss

φ = 0.036 ; χ0 = 0.65, ρ=1.22 g/cc, η≈7 cp dmin≈5.5 nm, dmax≈11.9 nmτB=2-10 µs, τN=5 ns-20 ms

Isopar-M Ferrofluidµ0Ms = 444 Gauss

φ = 0.079 ; χ0 = 2.18, ρ=1.18 g/cc, η≈11 cp dmin≈7.7 nm, dmax≈13.8 nmτB=7-20 µs, τN=100 ns-200 s

14

Langevin Equation

Measured magnetization (dots) for four ferrofluids containing magnetite particles (Md = 4.46x105

Ampere/meter or equivalently µoMd = 0.56 Tesla) plotted with the theoretical Langevin curve (solid line).

The data consist of Ferrotec Corporation ferrofluids: NF 1634 Isopar M at 25.4o C, 50.2o C, and 100.4o C

all with fitted particle size of 11 nm; MSG W11 water-based at 26.3o C and 50.2o C with fitted particle size

of 8 nm; NBF 1677 fluorocarbon-based at 50.2o C with fitted particle size of 13 nm; and EFH1 (positive α

only) at 27o C with fitted particle size of 11 nm. All data falls on or near the universal Langevin curve

indicating superparamagnetic behavior.

1[ coth ]

s

M

Mα

α= −

Applications

• Inks• money

• Biomedical• attach drugs to magnetic particles,

proposed artificial heart• Damping

• speakers, graphic plotters, instrumentgauges

• Seals• gas lasers, motors, blowers, hard drives

Berger, P.; Adelman, N. B.; Beckman, K. J.; Campbell, D. J.; Ellis, A. B.; Lisensky, G. C. Journal of Chemical Education 1999, 76, 943-8.

Damping: Speakers

See how a speaker works at:http://electronics.howstuffworks.com/speaker6.htm

Rosensweig, R. E. Scientific American 1982, 247, 136-45.

Damping: Rotating Shafts

Ray, K.; Moskowitz, B.; Casciari, R. Journal of Magnetism and Magnetic Materials 1995, 149, 174-180.

Cross-sectional view of a ferrofluid viscous inertia damper

Energy band gap apparatus

Seals

Rosensweig, R. E. Scientific American 1982, 247, 136-45.

VacuumAtmosphere

Permanent Magnet

Ferrofluid

Rotating Shaft

MagneticallyPermeable Material

Ferrofluid Preparation

• Step 1• Step 2• Step 3• Step 4• Step 5• Step 6

Dissolve 67.58g FeCl3.6H2O in 250ml of 2M HCl.

Dissolve 39.76g FeCl2.4H2O in 100ml of 2M HCl.

Ferrofluids Step 1

Modified from Berger et al, Journal of Chemical Education, 1999, 26, 7, 943-948

1M FeCl3 should be used within one week of preparation.

2M FeCl2 should be used within one week of preparation.

Ferrofluids Step 2

Combine 3ml of FeCl2solution and 12ml of FeCl3solution and fill a burette with 150ml of 0.7M ammonium hydroxide solution.

Add ammonia very slowly whilst stirring. A black precipitate of magnetite will form.

Ferrofluids Step 3

After addition is complete, stop stirring and use a strong magnet (Nd2Fe12B) to settle the black precipitate to the bottom of the flask.

Decant off the water and add fresh water. Rinse the precipitate and again decant off the water. Repeat three times to remove excess ammonia.

Ferrofluids Step 4

Transfer the viscous liquid to a weighing boat using a little extra water if necessary. Use a magnet on the base of the weighing boat to remove excess water.

Add 24ml of tetramethylammonium hydroxide (25% solution) and stir with a glass rod

Ferrofluids Step 5

Hold a magnet on the base of the weighing boat and let the solid settle to the bottom. Decant off any excess liquid to leave a very viscous black liquid.

The viscous liquid should form spikes if a magnet is held underneath the weighing boat. You may need to adjust the amount of water.

Ferrofluids Step 6

INGAS

• In20.5Ga67Sn12.5

• In25Ga62Sn13

• In21.5Ga68.5Sn10 – Galinstan® (GerathermMedical AG)

Melting: -19÷÷÷÷10°СBoiling: >1300 °С

Ferrofluid with metallic matrix

Mechanical Applications

• Ferrofluids are used in many ways mechanically. They are used in applications such as gaslasers, motors, and blowers. In some of these applications the ferrofluid is held in place by a strong magnet and separate by two different pressured chambers.They are also used as substances for vibrational dampening in electronic applications

31

Ferrohydrodynam

ic

Instabilities In

DC

Magnetic Fields

32

Labyrinthine Instability in Magnetic

Fluids

Stages in magnetic fluid labyrinthine patterns in a vertical cell, 75 mm on a side with 1 mm gap, with magnetic field ramped from zero to 535 Gauss. [R.E. Rosensweig, Magnetic Fluids, Scientific American, 1982, pp. 136-145,194]

Magnetic fluid in a thin layer with uniform magnetic field applied tangential to thin dimension.

33

Rotating Magnetic Fields

Observed magnetic field distribution in the 3 phase AC stator

a. One pole pair stator b. Two pole pair stator

Uniform Non-uniform

µ → ∞

RO

v rθ b g

η ζ η, , 'Ferrofluid

ω z rb gx

y

z

Surface Current Distribution

( )Re fj t

zK Ke θΩ −=µ →∞

RO

η ζ η, , 'Ferrofluid

ω z (r)x

y

z

( )v rθ

( 2 )Re fj t

zK Ke θΩ −=

Surface Current Distribution

34

Ferrofluid

Drops in

Rotating

Magnetic

Fields

FerrohydrodynamicDrops

A Gallery ofInstabilities

35

Ferrofluid Spiral / Phase

Transformations

36

(a) Von Quincke’s rotor consists of a highly insulating cylinder that is free to rotate and that is placed in slightly conducting oil between parallel plate electrodes. As DC high voltage is raised, at a critical voltage the cylinder spontaneously rotates in either direction; (b) The motion occurs because the insulating rotor charges like a capacitor with positive surface charge near the positive electrode and negative surface charge near the negative electrode. Any slight rotation of the cylinder in either direction results in an electrical torque in the same direction as the initial displacement.

4. Dielectric Analog: Von Quincke’s Rotor

(Electrorotation)

Von Quincke’sRotor

Von Quincke’sRotor

37

Definition of Quincke Rotation: Spontaneous rotation of insulating particles (or

cylinders) suspended in a slightly conducting liquid subjected to a DC electric field

with the field strength exceeding some critical value (Jones, 1984, 1995)

2 1

2 1

ε εσ σ

>

wherei

ii

ετσ

=

is the charge relaxation time

in each region

0Ω > when

More on Quincke’s Rotor (Electrorotation)

Two Competing Forces (Torques):

The electrical torque and the fluid viscous torque exerted on the particle

38

The electric torque( )

( )( )( )3 2

1 0 1 2

2 21 2 2 1

6 1

1 2 1 2 1MW

e

MW

R ET p E

πε τ τ τε ε σ σ τ

− Ω= × =

+ + + Ω

For a small perturbation of rotation to grow, the equation of angular motion for the

particle is re-written as (Jones, 1995):

( )( )( )( )

3 21 0 1 2 3

02 21 2 2 1

6 18

1 2 1 2 1MW

MW

R EdI R

dt

πε τ τ τπη

ε ε σ σ τ

−Ω = − Ω

+ + + Ω

The bracket term should have a value larger than zero for the small perturbation to

grow (Jones, 1995), thus

2 1τ τ>

Torques Exerted on a Micro-particle

The fluid viscous torque 308vT Rπη= − Ω Re 1≪

39

( )0 12

1 1 2 2 1

81

2 3critEη σσ

σ ε σ τ τ

= + −

2

0 1MWcrit

E

Eτ

Ω = ± −

0 critE E>

@0.5e critT E

@e critT E

@ 2e critT E

visT

Competition of the Viscous and Electric Torques

Steady

1 2

1 2

2

2MW

ε ετσ σ

+=

+

Maxwell-Wagner Relaxation Time

40

E 0E =

0E ≠

Experiments have shown that for a given pressure gradient, the Poiseuille flow rate can be

increased (Lemaire et al., 2006) by introducing micro-particle electrorotation into the fluid

flow via the application of an external direct current (DC) electric field.

5. Flow Rate Enhancement using Electrorotation

From Hsin-Fu Huang PhD Thesis research, supervised by M. Zahn

6. Continuum Analysis for Couette & Poiseuille

Flows with Internal Micro-particle Electrorotation

The Couette flow geometry

Stress balance0

s eff eff z yMW

Ui T i

h

γτ η ητ

∗

= = = ⋅ ⋅

The Poiseuille flow geometry

( )0

h

yQ u z dz= ∫2D volume flow rate

41

( ) ( ) 22t e

Dvp P E v v

Dtρ ζ ω β η= −∇ + ⋅∇ + ∇× + ∇ ∇ ⋅ + ∇

( ) ( ) 22 2 ' 't

DI P E v

Dt

ωρ ζ ω β ω η ω= × + ∇× − + ∇ ∇ ⋅ + ∇

( ) ( ) ( )1eq

MW

DP Pv P P P P

Dt tω

τ∂= + ⋅∇ = × − −∂

0v∇⋅ =

( ) ( )0 0, , , , , ,y zeq eq i i y eq i i zP P n E i P n E iε σ ε σ= +

Polarization Relaxation

Equilibrium Polarization

Continuity

Linear Momentum (Dahler & Scriven, 1961,

1963; Condiff & Dahler,

1964; Rosensweig, 1997)

Angular Momentum(Dahler & Scriven, 1961,

1963; Condiff & Dahler,

1964; Rosensweig, 1997)

No-slip boundary conditions

Field conditions: free-to-spin, symmetry, stable rotation

Incompressible flow: treating as a single phase continuum

n Particle # density

EQS & Electro-neutrality (Haus & Melcher, 1989)

0E∇ × ≈ 0D∇ ⋅ ≈

Lobry & Lemaire, 1999; He, 2006; Lemaire et al., 2008

Spin field BCs:

2v

βω = ∇× 0 1β≤ ≤Kaloni, 1992; Lukaszewicz, 1999; Rinaldi, 2002; Rinaldi & Zahn, 2002

1 2

1 2

2

2MW

ε ετσ σ

+=

+

01.5ζ φη∼

( )0 1 2.5η η φ+∼

eη ζ η= + 2' hη η∼

Zaitsev & Shliomis, (1969);

Rosensweig, (1997)

The Continuum Governing Equations

42

z

y

x

R

,

,

r

1ε 1σ

2ε 2σ

Electric potential and field solutions to a spherical particle subjected to a uniform DC electric field

rotating at an angular velocity of .Ω2 0∇ Φ =

( ) ( ) ( ) ( ), ,R r

rr

θ φ θ φΦ = Θ ΨLaplace’s equation with spherical harmonics

(Jackson, 1999)

( )0 0, cos sinz rr E E i E i iθθ θ→ ∞ → = −

( ) ( ), , , ,R Rθ φ θ φ− +Φ = Φf

f f fn J v Kt

ρρ Σ

∂⋅ + + ∇ ⋅ = −

∂

BCs (Cebers, 1980; Melcher, 1981; Pannacci, 2006) ( ) (sin cos cos )f f f x r fK V i Ri R i iθ φσ σ σ φ θ φ= = Ω × = − Ω +

( ) ( )1 2, , , ,f r rn J E R E Rσ θ φ σ θ φ+ −⋅ = −

( ) ( )1 2, , , ,f r rE R E Rσ ε θ φ ε θ φ+ −= −

Ω

†0 zE E i=

θ

φ

The proposed “rotating coffee cup model” for the retarding polarization relaxation equations with its

accompanying (quasi-static) equilibrium retarding polarization (Huang, 2010; Huang, Zahn, & Lemaire, 2010a, b):

Ω

xω

0E

( ) ( ) ( )1eq

MW

DP Pv P P P P

Dt tω

τ∂= + ⋅∇ = × − −∂

2 1 2 1

1 2 1 231 02 2

2 24

1z

eqMW x

P R n E

σ σ ε εσ σ ε ε

πετ

− −− + + =+ Ω

2 1 2 1

1 2 1 231 02 2

2 24

1

MW xy

eqMW x

P R n E

σ σ ε ετσ σ ε ε

πετ

− −Ω − + + = −+ Ω

0

0

2

0 ,

0,

11 c

c

cMW

E E

E E

EEτ

≥

<

± −Ω =

( )0 12

1 1 2 2 1

81

2 3cEη σσ

σ ε σ τ τ

= + −

Retaining macroscopic fluid spin

Including microscopic particle rotation

Polarization Relaxation & Equilibrium Polarization

43

,

,

Schematic diagram for the Poiseuille geometry

( )0

h

yQ u z dz= ∫2D volume flow rate

Modeling Results for the Poiseuille Flow Geometry

44

Zero spin viscosity Poiseuille flow velocity profiles compared with experimental results found from the

literature (Peters et al., 2010)

81 5.4 10 S mσ −= ×

Lemaire experimental results are from Fig. 9 of Peters et al., J. Rheol., pp.311, (2010)

Cusp structure for zero spin viscosities

1.8cE kV mm≈

Zero electric field solution of

Poiseuille parabolic profile

' 0η =

5974.6p Pa

L m

∆ ≈

The zero spin viscosity

solutions of our present

continuum mechanical field

equations over predicts the

value of the spin velocity

profile and has a cusp in the

mid-channel position, which is

not consistent with

experimental measurements

done by Peters et al. (2010).

However, the order of

magnitude is correct.

Comparison of Poiseuille Velocity Profile Results

Huang, (2010)

0.05φ =

45

Finite spin viscosity small spin velocity Poiseuille flow rate results compared with experimental/theoretical

results found from the literature (Lemaire et al., 2006) Lemaire theory/experimental results are from Figs. 5 and 6 of

Lemaire et al., J. Electrostat., pp. 586, (2006)

HT: Huang theory (solid line)

LT: Lemaire theory (dashed line)

LE: Lemaire experiment (dotted line)8

1 4 10 S mσ −= ×1.3cE kV mm≈

1β =

( )2 20' 1 2.5h hη η η φ≈ ≈ +

Finite spin viscosity results do not

involve ad hoc fitting!

Comparison of Poiseuille Flow Rate Results

0.05φ = 0.1φ =

Huang, (2010)46

Note: if we use particle diameter for spin viscosity,

Three orders of magnitude less than best fit value.

Likely supports ER fluid parcel physical picture

Finite spin viscosity small spin velocity Poiseuille flow velocity profiles compared with experimental

results found from the literature (Peters et al., 2010)

81 5.4 10 S mσ −= × 1β = 2 10' 0.012 2.96 10h N sη η −≈ ≈ × ⋅

61.8483 10 1.8cE V m kV mm= × ≈ 1.8cE kV mm=round and substitute to

analytic solution

Lemaire experimental results are from Fig. 9 of

Peters et al., J. Rheol., pp.311, (2010)

Note: At this pressure gradient, MAX spin

velocity is not necessarily small. We are

kind of pushing the limit of small spin

velocities

Zero electric field solution of

Poiseuille parabolic profile

Agreement achieved for the all voltages

considered! (Rounding of critical electric field

strength is only within 3%)

2 13' 6.7 10d N sη η −≈ = × ⋅

Ultrasound velocity profile measurements from Prof. Lemaire’s group likely support our finite spin viscosity theory

combined with our new rotating coffee cup polarization model.

Huang Analytic Solutions V.S.

Lemaire Numeric Solutions

Best fit, within spin viscosity values calculated

by He (2006) and Elborai (2006) for ferrofluids

Huang, 2010

Comparison of Poiseuille Velocity Profile Results

5974.6p Pa

L m

∆ ≈

0.05φ =

47

References

• voh.chem.ucla.edu/classes/Magnetic_fluids/pdf/Ferrofluids.ppt

• www.chemlabs.bris.ac.uk/outreach/resources/Ferrofluids.ppt

• http://www.slideworld.com/slideshows.aspx/Ferrofluids-ppt-426340

• http://www.slideshare.net/vponsamuel/aqueous-ferrofluid (method)