Physicsof ComplexFluids University of Twente · 0 2 p r h r h r pel x E r lv cap r r r r = + ′...
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1 drops in motion Frieder Mugele Physics of Complex Fluids University of Twente the physics of electrowetting and its applications
Transcript of Physicsof ComplexFluids University of Twente · 0 2 p r h r h r pel x E r lv cap r r r r = + ′...
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drops in motion
Frieder MugelePhysics of Complex Fluids
University of Twente
the physics of electrowettingand its applications
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wetting & liquid microdroplets
50 µm
H. Gau et al. Science 1999lvLpp κσ2==∆lv
slsvY σ
σσθ
−=cos
capillary equation Young equation
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electrowetting: the switch on the wettability
voltage
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some applications of EW
Kuiper and Hendriks, APL 2004
tunable lenses(varioptic, Philips)
250 µm
EW displays(Philips à liquavista)
micromechanical actuation lab-on-a-chip
courtesy of R. Hayes
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outline
q introductionq electrowetting basics
q historic noteq origin of the EW effectq electromechanical modelq contact angle saturation
q physical principles and challenges of EW devicesq FUNdamental fluid dynamics with EW
q contact angle hysteresis in EWq contact line motion in ambient oilq electrowetting driven drop oscillations and mixing
flowsq channel-based microfluidic systems with EW
functionality
q conclusion
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the origin
Gabriel Lippmann(1845-1921)
Nobel prize 1908
1875: Annales de Chimie et de Physique
1891: interferometric color photography
english translation: in Mugele&BaretJ. Phys. Cond. Matt. 17, R705-R774 (2005)
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Lippmann‘s experiment on electrocapillarity
First law—the capillary constant at the mercury/diluted sulfuric acid interface is a functionof the electrical difference at the surface.
voltage [Daniell]∆
σ Hg/
H2S
O4
)(Uf=σ
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effective surface tension
capillary depression (Jurin):
no dielectric!
Hg
H2SO4 Rp Y
Lθσ cos2
=∆ hphg =∆= ρ
∆h 20)()( UUUhh ασσσ −==→∆=∆
+ + + + + + - - - - - -
build-up of a Debye layer à electrostatic energy/area double layer capacitance:
D
cλ
εε 0=2
21 cUEel =
U
total free energy (per unit area): 20 2
)()( UcUUF −== σσ
Lippmann eq.: U∂∂
−=σ
ρ
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modern electrowetting equation „on dielectric“
conductive liquidinsulatorcounter electrode
UU - - - - - -+ + + + + +σsl
σsv
σlvbasic setup:
“Electrowetting on dielectric (EWOD)”
Berge 1993
electrowettingnumber
advancingreceding
high voltage:contact angle saturation
low voltage: parabolic behavior
20
21cos
))(cos(
Ud
U
lvY σ
εεθ
θ
+
=
electrowetting equation:
η
water in silicone oil
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examples of EW-curves20
21cos))(cos( U
dU
lvY σ
εεθθ +=electrowetting equation:
0 8000 16000 24000
-0,8
-0,4
0,0
0,4
0,8 water gelatin (2%; 40°C) milk SDS (0.7%) Triton-x 100 (0.1%)
cos
θ (U
)
U2 (V2)
α
σmacro [mJ/m2]]3820187
4.4
0 5 10 150.0
0.5
1.0
1.5
2.0
Triton SDS milk gelatin water
∆
cos
θ(U
)
U2/γwo(105 V
2m/N)
Teflon AF-coated ITO glass in silicone oil; AC voltageBanpurkar et al., Langmuir 2008
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EW as microdrop tensiometer
18.7± 1.015.7±0.720.0±0.5yeast protein (1% )/ silicone oil (167O)
17.9± 0.1 18.6±0.919.4±0.7Milk / silicone oil (167 O)
33.0 ± 0.5 35.0±0.732.8±0.8Aqu. Glycerin (50% )/ silicone oil (169O)
4.4 ± 0.45.6±0.54.7±0.3Aqu. Triton X-100 (0.1%)/ silicone oil (163O)
7.1 ± 0.47.5± 0.86.5± 0.5Aqu. CTAB (0.1 %)/mineral oil (164O)
7.0± 0.47.5± 0.87.5± 0.3Aqu. SDS (0.7 %)/ silicone oil (165O)
20.2 ± 0.520.4±0.820.1±0.8Aqu. Gelatin (2 %)/silicone oil (167O)
23.3 ± 0.424.8±0.724.1±0.6Aqu. Gelatin (2 % )/ mineral oil (160O)
53.3±0.548.5±0.652.9±0.7H2O/ n-hexadecane (169O)
72.6± 0.572.0±0.272.4 ±0.6H2O/ air (62 O)
48.0± 0.2 47.3± 0.748.8± 0.5H2O/ mineral oil (168O)
38± 0.2calibrationcalibrationH2O/silicone oil (θY=169O)
InterdigitatedElectrode
PlanarElectrode
γwo(Du Noüy ring) (mN/m)
γwo (EW drop tensiometer(mN/m)
Liquid Interface (Temperature = 23oC)
à interfacial tension measurements for nL drops consistent with bulk values
Banpurkar et al., Langmuir 2008
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origin of EW
dVEDAGi
ii ∫∑ ⋅−=rr
21
σ
U
Er
20
2UA
dA sl
r
iii
εεσ −≈ ∑
slsvsllvlv AUd
A
−−+= σ
εεσσ 20
2
σsleff
+++
+ +++ + +
2)(20 rEp lv
rεκσ −⋅=∆
Maxwell stress: 2)(2
0 rEpelrε
−=
modified capillary equationmodified Young equation
?
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local equilibrium surface profiles
1. local force balance )()(1
)()(2
)(2
0 2 rprh
rhrExp caplvelr
r
rr
=′+
′′⋅== γ
ε !
2. free energy minimization min!
)()(
cos~ 2 =∇−+= ∫∫ φε
ηθ dV
rdsLF
A
BslY r
2D geometryiterative calculation:• initial profile (fixed θA)• field distribution (FEM)• force balance → refined profile
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numerical results
0 1 2 30
1
2
h/dins
x
η
liquid
air
q local contact angle = Young‘s angle
q divergent curvature near contact line: κ ~ pel ~ hν ; -1 < ν < 0
q range of surface distortions: ≈dins no contact angle saturation
(in 2-dim model)
10-4 10-2 100
100
102
log
P ellog h/d
ins
η
surface profiles curvature / Maxwell stress
0,4 0,5 0,6 0,7
-0,8
-0,6
-0,4ε = 1: ε = 2:
ν
α / πθ Y/ π
(0, .2, .4, …, 1.2)
Bueh
rle e
t al.
PRL
2003
Bien
ia e
t al.
Euro
Phys
Lett
2006
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experimental verification
η = 0 η ≈ 0.5 η ≈ 1
d = 10µm
d = 50µm
d = 150µm
Mugele, Buehrle, J.Phys.Cond.Matt 2007
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relation between local and apparent c.a.
2D geometry
YB θθ =ηθθ += YU cos))(cos(
apparent c.a.
local c.a.
à apparent c.a. follows EW equation
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equivalence of force balance & energy minimization
+
++
++++ + +
Σ
total force:(per unit length)
Maxwell stress tensor:
ησεε
lvd
U
dAnTf kxkx
==
= ∫Σ
2
2
0
independent of drop shape !
σlv
σsv
σslfel
à T.B. Jones
x
2
0,
2
0 UdzEfd
xelxεε
ρ =⋅=∫∞
force / unit length
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reconciliation
dVEDAFi
ii ∫∑ ⋅−=rr
21
σ
U
Er
+++
+ +++ + +
electrical force / unit length ∫
>>
=dh
elel dzzpf0
)(
20
2UA
dA sl
r
iii
εεσ −≈ ∑
slsvsllvlv AUd
A
−−+= σ
εεσσ 20
2
σsleff
modified Young equation
macroscopic picture
2)(20 rEp lv
rεκσ −⋅=∆
Maxwell stress: 2)(2
0 rEpelrε
−=
modified capillary equation
microscopic picture
à both pictures are equivalent on a scale >> dins
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contact angle saturation: the mystery of EW
advancingreceding
what causes deviations from EW equation at high voltage?
safe operationbreakdown
(Sey
rat,
Hey
es, J
. App
l. Ph
ys. 2
001)
diverging electric fields can cause dielectric breakdown of coating!
20
21cos))(cos( U
dU
lvY σ
εεθθ +=
20
refined version: local breakdown at contact line
(Papathanasiou et al. Appl. Phys. Lett. 2005, J. Appl. Phys. 2008, Langmuir 2009)
self-consistent calculation of field and surface configuration
+local breakdown upon exceeding VT
potential
magnitude of field
calculated EW curve including saturation
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charge trapping
(Verheijen, Prins, Langmuir 1999)
permanent injection (or adsorption) of charges produces irreversibility and screens charges from surface beyond threshold voltage VT:
à AC voltage suppresses ion adsorption
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water-silanized glass ; f= 200 Hz 100 µm
2d Coulomb explosion:balance of capillary energy and electrostatic energy
++ ++
++++
+++ +++
top view:
contact line instability
Berge et al. Eur. Phys. J. B 1999;Mugele, Herminghaus Appl. Phys. Lett. 2002
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summary – electrowetting basics
n contact angle reduction arises from minimization of interfacial and electrostatic energy (maximum of capacitance)
n equilibrium shape is determined by local balance of Maxwell stress and Laplace pressureq local contact angle = Young‘s angle
q diverging curvature near contact line
q equivalence of force balance and effective surface tension approach on scales >> d
n contact angle saturation arises from non-linearities in diverging electric fields at contact lineq c.a. saturation can be minimized by use of high quality substrates, AC
voltage, ambient oil.
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outline
q introductionq electrowetting basics
q origin of the EW effectq electromechanical modelq contact angle saturation
q challenges and physical principles of EW devices
q FUNdamental fluid dynamics with EWq contact angle hysteresis in EWq contact line motion in ambient oilq electrowetting driven drop oscillations and mixing
flowsq channel-based microfluidic systems with EW
functionality
q conclusion
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some applications of EW
Kuiper and Hendriks, APL 2004
tunable lenses(varioptic, Philips)
250 µm
EW displays(Philips à liquavista)
micromechanical actuation lab-on-a-chip
courtesy of R. Hayes
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challenges for EW-based microfluidic systemsdetachment / drop generation:
droplet motion:
drop merging & splitting:
mixing:
contamination
• reproducible drop size• high throughput
• high speed• low voltage
• high mixing speed
• reproducibility• drop size control
• preventing evaporation• controlling adsorption (e.g. proteins)
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drop actuation
F
U1 << U2
patterned electrodes( ) )(xAU
dAAW eldropslsvsllvlv −−−+= 20
2εε
σσσ
( )∫∂
+−=−∇=⇒slA
elslsv dsnrfWF rrr)()( σσ
typical design: sandwich geometryà no wires required
pioneering work: R. Fair (Duke Univ.): Pollack et al. Appl. Phys. Lett. 2000CJ Kim (UCLA): Cho et al. JMEMS 2003
counter-acting forces: - bulk viscous dissipation- contact line friction
fel
Wheeler et al.
