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

11

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

?

13

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

14

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

16

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

17

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

19

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

22

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.