1
drops in motion
Frieder MugelePhysics of Complex Fluids
University of Twente
the physics of electrowettingand its applications
2
wetting & liquid microdroplets
50 µm
H. Gau et al. Science 1999lvLpp κσ2==∆lv
slsvY σ
σσθ
−=cos
capillary equation Young equation
3
electrowetting: the switch on the wettability
voltage
4
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
5
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
6
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)
7
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
8
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
9
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
10
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
12
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
15
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
18
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
21
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
23
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.
24
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
25
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
26
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)
27
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.
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