dropsin motion the physicsof electrowetting and itsapplications

Frieder Mugele

Physicsof ComplexFluids University of Twente

1 wetting& liquid microdroplets

50 µm

capillaryequation Young equation s -s Dp = p = 2ks cosq = sv sl L lv Y s H. Gauet al. Science 1999 2 lv electrowetting: the switch on the wettability

voltage

3 someapplicationsof EW

tunablelenses EW displays (varioptic, Philips) (Philips à liquavista)

250 µm Kuiper and Hendriks, APL 2004 courtesyof R. Hayes

micromechanicalactuation lab-on-a-chip

4 outline

q introduction q electrowetting basics q historic note q origin of the EW effect q electromechanical model q contact angle saturation q physical principles and challenges of EW devices q FUNdamentalfluid dynamics with EW q contact angle hysteresis in EW q contact line motion in ambient oil q electrowetting driven drop oscillations and mixing flows q channel-based microfluidic systems with EW functionality q conclusion

5 the origin

1875: Annalesde Chimieet de Physique

englishtranslation: in Mugele&Baret J. Phys. Cond. Matt. 17, R705-R774 (2005)

Gabriel Lippmann (1845-1921) Nobel prize1908

6 1891: interferometriccolorphotography Lippmann‘sexperimenton electrocapillarity H g / 2 S O4 Ds

voltage[Daniell]

First law—the capillaryconstantat the mercury/dilutedsulfuricacidinterfaceisa function of the electricaldifferenceat the surface. s = f (U )

7 effective surface tension

2s cosqY capillary depression (Jurin): DpL = = r g Dh = ph H2SO4 R

Dh 2 Dh = Dh(U ) ® s = s (U ) = s 0 -aU U

Hg build-up of a Debye layer ------à electrostatic energy/area double layer capacitance: + + + + + + 1 2 e 0e Eel = cU c = 2 lD

c total free energy (per unit area): F(U ) = s (U ) = s - U 2 0 2 ¶s Lippmann eq.: r = - ¶U no dielectric!

8 modern electrowetting equation „on dielectric“

basic setup: slv s conductiveliquid U ------sv + + + + + +ssl insulator counterelectrode Berge 1993

“Electrowetting on dielectric (EWOD)”

low voltage: electrowetting equation: parabolic behavior cos(q(U)) = high voltage: contactangle 1 e 0e 2 saturation cosqY + U 2 ds lv advancing receding h electrowetting number water in silicone oil 9 examples of EW-curves

1 e 0e 2 electrowetting equation: cos(q (U )) = cosqY + U 2 ds lv

s [mJ/m2]] macro 2.0 water 38 gelatin (2%; 40°C) 20 0,8 milk 18 1.5 SDS (0.7%) 7 0,4 Triton-x 100 (0.1%) 4.4 ) ) U U ( ( 1.0 q q Triton 0,0

SDS

c os milk c o s -0,4

D 0.5 gelatin a water -0,8 0.00 5 10 15 0 8000 16000 24000 2 5 2 /g (210 2 / ) U woU (V V) m N

Teflon AF-coated ITO glass in silicone oil; AC voltage 10 Banpurkar et al., Langmuir 2008 EW as microdroptensiometer

Liquid Interface gwo (EW drop tensiometer gwo (Temperature = 23oC) (mN/m) (Du Noüyring) (mN/m) Planar Interdigitated Electrode Electrode

O H2O/silicone oil (qY=169 ) calibration calibration 38± 0.2 O H2O/ mineral oil (168 ) 48.8± 0.5 47.3± 0.7 48.0± 0.2 O H2O/ air (62 ) 72.4 ±0.6 72.0±0.2 72.6± 0.5 O H2O/ n-hexadecane (169 ) 52.9±0.7 48.5±0.6 53.3±0.5 Aqu. Gelatin (2 % )/ mineral oil (160O) 24.1±0.6 24.8±0.7 23.3 ± 0.4 Aqu. Gelatin (2 %)/silicone oil (167O) 20.1±0.8 20.4±0.8 20.2 ± 0.5 Aqu. SDS (0.7 %)/ silicone oil (165O) 7.5± 0.3 7.5± 0.8 7.0± 0.4 Aqu. CTAB (0.1 %)/mineral oil (164O) 6.5± 0.5 7.5± 0.8 7.1 ± 0.4 Aqu. Triton X-100 (0.1%)/ silicone oil (163O) 4.7±0.3 5.6±0.5 4.4 ± 0.4 Aqu. Glycerin (50% )/ silicone oil (169O) 32.8±0.8 35.0±0.7 33.0 ± 0.5 Milk / silicone oil (167 O) 19.4±0.7 18.6±0.9 17.9± 0.1 yeast protein (1% )/ silicone oil (167O) 20.0±0.5 15.7±0.7 18.7± 1.0

à interfacial tension measurements for nLdrops consistent with bulk values 11Banpurkar et al., Langmuir 2008 originof EW

+ ++ + +++++ U r E 1 r r G = ås i Ai - ò D × EdV i 2

e 0 r 2 e 0e r 2 Maxwell stress: p = - E(r ) » ås i Ai - AslU el i 2d 2

æ ee 0 2 ö e 0 r 2 = s lv Alv + çs sl - U -s sv ÷Asl Dp = s ×k - E(r) è 2d ø lv 2

s eff sl ?

modifiedYoung equation modifiedcapillaryequation

12 local equilibrium surface profiles

iterative calculation: 2D geometry • initial profile (fixed qA) • field distribution (FEM) • force balance → refinedprofile

! r e 0 r 2 h¢¢(r) r 1. local force balance pel (x) = E(r) = g lv × r = pcap (r) 2 1+ h¢(r)2

~ A h ! 2. freeenergyminimization F = cosq L + ds - dV (Ñf)2 = min Y sl ò r ò B e (r )

13 numericalresults

surfaceprofiles curvature/ Maxwell stress -0,4 n e = 1: 2 e = 2: liquid -0,6 x 102 -0,8

el h 0,4 0,5 0,6 0,7 1 a / p q Y/ p

air l o g P h 100 (0, .2, .4, …, 1.2)

0 0 1 2 3 -4 -2 0 h/d 10 10 10 ins log h/d 2 0 06 ins q localcontactangle = Young‘sangle q divergent curvaturenearcontactline: k ~ p ~ hn ; -1 < n < 0

E u r o P h y s Le tt el

q range of surface distortions: ≈dins no contact angle saturation (in 2-dim model) B ueh r l e t a . P R L 20 03 B i en a e t l . 14 experimental verification

h = 0 h ≈ 0.5 h ≈ 1

d= 10µm

d= 50µm

d= 150µm

15 Mugele, Buehrle, J.Phys.Cond.Matt2007 relation between local and apparent c.a.

apparent c.a. 2D geometry

local c.a.

qB =qY cos(q (U )) = cosqY +h

à apparent c.a. follows EW equation 16 equivalence of force balance & energy minimization

S

+ ¥ ee ++ 0 2 fx,el = r ×Ex dz= U ò 2d + + + + ++ 0 x

total force: Maxwell stress tensor: f x = Txk nk dA (per unitlength) òS

ee 0 2 = U = s lvh 2d force / unit length à T.B. Jones

slv f s independent of drop shape! el sl s 17 sv reconciliation

+ + + ++++++ U r E 1 r r F = s A - D× EdV å i i ò i 2 macroscopicpicture microscopicpicture

e 0 r 2 e 0e r 2 Maxwell stress: p = - E(r ) » ås i Ai - AslU el i 2d 2

æ ee 0 2 ö e 0 r 2 = s lv Alv + çs sl - U -s sv ÷Asl Dp = s ×k - E(r) è 2d ø lv 2 h>>d electrical force s eff f = p (z) dz sl / unit length el ò el 0 modifiedYoung equation modifiedcapillaryequation

à both pictures are equivalent on a scale >> dins 18 contact angle saturation: the mystery of EW

what causes deviations from EW equation at high voltage?

advancing 1 e 0e 2 receding cos(q (U )) = cosqY + U 2 ds lv

break safe operation down , J . A p l P h ys 2 00 1) H e y es ,

diverging electric fields can cause S e y r at ( dielectric breakdown of coating!

19 refined version: local breakdown at contact line

potential

magnitude of field

self-consistent calculation of calculated EW curve field and surface configuration including saturation + local breakdown upon

exceeding VT

(Papathanasiou et al. Appl. Phys. Lett. 2005, J20. Appl. Phys. 2008, Langmuir 2009) charge trapping

permanent injection (or adsorption) of charges produces irreversibility and screens charges from surface beyond

threshold voltage VT:

à AC voltage suppresses ion adsorption

(V21erheijen, Prins, Langmuir 1999) contactlineinstability

2d Coulomb explosion: balance of capillary energy and electrostatic energy

top view: ++ +++++ + + + ++++

water-silanizedglass ; f= 200 Hz 100 µm

Berge et al. Eur. Phys. J. B 1999; 22 Mugele, Herminghaus Appl. Phys. Lett. 2002 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 pressure q 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 line q c.a. saturation can be minimized by use of high quality substrates, AC voltage, ambient oil.

23 outline

q introduction q electrowetting basics q origin of the EW effect q electromechanical model q contact angle saturation q challenges and physical principles of EW devices q FUNdamentalfluid dynamics with EW q contact angle hysteresis in EW q contact line motion in ambient oil q electrowetting driven drop oscillations and mixing flows q channel-based microfluidic systems with EW functionality q conclusion

24 someapplicationsof EW

tunablelenses EW displays (varioptic, Philips) (Philips à liquavista)

250 µm Kuiper and Hendriks, APL 2004 courtesyof R. Hayes

micromechanicalactuation lab-on-a-chip

25 challenges for EW-based microfluidic systems

detachment / •reproducible drop size drop generation: •high throughput

•high speed droplet motion: •low voltage

drop merging & splitting: •reproducibility •drop size control

mixing: •high mixing speed

contamination •preventing evaporation •controlling adsorption (e.g. proteins) 26 drop actuation

fel patternedelectrodes ee 0 2 W = s lv Alv + (s sl - s sv )Asl - U Adrop -el (x ) F 2d r r r Þ F = -ÑW = ò ((s sv -s sl ) + fel (r )) n ds ¶A U1 << U2 sl

counter-acting forces: -bulk viscous dissipation -contact line friction

typicaldesign: sandwichgeometry à no wiresrequired

pioneering work: R. Fair (Duke Univ.): Pollack et al. Appl. Phys. Lett. 2000 Wheeler et al. 27 CJ Kim (UCLA): Cho et al. JMEMS 2003