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FerrofluidsFerrofluids
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Overview
• Definitions• Engineering• Applications
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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
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Ferrofluids: Magnetic Liquids
Liquid That Responds to a Magnetic Field
=
Colloidal Suspension of Superparamagnetic Magnetic Material
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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• Currently applications of Ferrofluids in space have been replaced by more economical fluids.
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Physics
• Ferromagnetismisamagneticdipolethatisfromthealignmentofunpairedelectronspinsinelementssuchasiron,cobalt,andnickel.Inthisexperimentwewillsynthesizemagneticnanoparticlesfromironchloridesandthendisperseintoatetramethylammoniumhydroxidesurfactanttoformacolloidalsuspension
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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
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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
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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
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Unique Properties
• Stick to Magnets• Take on 3-Dimensional Shape of a
Magnetic Field• Change Density in Proportion to
Magnetic Field Strength
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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
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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= −
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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.
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Damping: Speakers
See how a speaker works at:http://electronics.howstuffworks.com/speaker6.htm
Rosensweig, R. E. Scientific American 1982, 247, 136-45.
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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
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Seals
Rosensweig, R. E. Scientific American 1982, 247, 136-45.
VacuumAtmosphere
Permanent Magnet
Ferrofluid
Rotating Shaft
MagneticallyPermeable Material
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Ferrofluid Preparation
• Step 1• Step 2• Step 3• Step 4• Step 5• Step 6
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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
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1M FeCl3 should be used within one week of preparation.
2M FeCl2 should be used within one week of preparation.
Ferrofluids Step 2
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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
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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
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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
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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
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INGAS
• In20.5Ga67Sn12.5
• In25Ga62Sn13
• In21.5Ga68.5Sn10 – Galinstan® (GerathermMedical AG)
Melting: -19÷÷÷÷10°СBoiling: >1300 °С
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Ferrofluid with metallic matrix
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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
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31
Ferrohydrodynam
ic
Instabilities In
DC
Magnetic Fields
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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.
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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
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34
Ferrofluid
Drops in
Rotating
Magnetic
Fields
FerrohydrodynamicDrops
A Gallery ofInstabilities
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Ferrofluid Spiral / Phase
Transformations
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(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
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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
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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≪
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( )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
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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
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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
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( ) ( ) 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
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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
,
,
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Schematic diagram for the Poiseuille geometry
( )0
h
yQ u z dz= ∫2D volume flow rate
Modeling Results for the Poiseuille Flow Geometry
44
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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
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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
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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
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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)