drops in motion Frieder Mugele the physics of electrowetting and its applications Physics of Complex Fluids University of Twente

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1 drops in motion the physics of electrowetting and its applications Frieder Mugele Physics of Complex Fluids niversity of Twente 1

2 electrowetting: the switch on the wettability voltage

3 outline q q q q q introduction electrowetting basics q historic note q origin of the EW effect q electromechanical model q contact angle saturation physical principles and challenges of EW devices FNdamental fluid 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 conclusion 3

4 the origin 1875: Annales de Chimie et de Physique english translation: in Mugele&Baret J. Phys. Cond. Matt. 17, R705-R774 (005) Gabriel Lippmann ( ) Nobel prize : interferometric color photography

5 Lippmann s experiment on electrocapillarity σ Hg/HSO4 voltage [Daniell] First law the capillaryconstantat the mercury/diluted sulfuricacid interfaceis a function of the electrical differenceat the surface. σ f ( ) 5

6 effective surface tension H SO 4 capillary depression (Jurin): p L σ cosθ R Y ρ g h ph h h h( ) σ σ ( ) σ α 0 Hg build-up of a Debye layer electrostatic energy/area 1 Eel c double layer capacitance: ε c 0 ε λ D total free energy (per unit area): F( ) σ ( ) σ c 0 no dielectric! 6

7 modern electrowetting equation on dielectric basic setup: σ lv σ sl σ sv conductive liquid insulator counter electrode Berge 1993 Electrowetting on dielectric (EWOD) 7 electrowetting equation: cos( θ( )) cosθ Y electrowetting number 1 ε 0ε dσ h lv water in silicone oil low voltage: parabolic behavior high voltage: contact angle saturation advancing receding

8 examples of EW-curves electrowetting equation: cos( θ ( )) cosθ Y 1 ε 0 dσ ε lv cos θ () cos θ().0 0, ,4 0, , , /γ wo (10 5 V m/n) α (V ) water gelatin (%; 40 C) milk SDS (0.7%) Triton-x 100 (0.1%) Triton SDS milk gelatin water σ macro [mj/m ]] Banpurkar et al., Langmuir 008 Teflon AF-coated ITO glass in silicone oil; AC voltage

9 EW as microdrop tensiometer Liquid Interface (Temperature 3 o C) Planar Electrode γ wo (EW drop tensiometer (mn/m) Interdigitated Electrode γ wo (Du Noüy ring) (mn/m) H O/silicone oil (θ Y 169 O ) calibration calibration 38± 0. H O/ mineral oil (168 O ) 48.8± ± ± 0. H O/ air (6 O ) 7.4 ± ±0. 7.6± 0.5 H O/ n-hexadecane (169 O ) 5.9± ± ±0.5 Aqu. Gelatin ( % )/ mineral oil (160 O ) 4.1± ± ± 0.4 Aqu. Gelatin ( %)/silicone oil (167 O ) 0.1± ± ± 0.5 Aqu. SDS (0.7 %)/ silicone oil (165 O ) 7.5± ± ± 0.4 Aqu. CTAB (0.1 %)/mineral oil (164 O ) 6.5± ± ± 0.4 Aqu. Triton X-100 (0.1%)/ silicone oil (163 O ) 4.7± ± ± 0.4 Aqu. Glycerin (50% )/ silicone oil (169 O ) 3.8± ± ± 0.5 Milk / silicone oil (167 O ) 19.4± ± ± 0.1 yeast protein (1% )/ silicone oil (167 O ) 0.0± ± ± Banpurkar et al., Langmuir 008 interfacial tension measurements for nl drops consistent with bulk values

10 origin of EW G i σ i A i E r 1 r r D EdV σ A i i i ε 0ε d r A sl Maxwell stress: p el ε r E( ) 0 r εε 0 σ lv Alv σ sl σ d σ sl eff sv A sl? p σ lv κ ε r E( ) 0 r modified Young equation modified capillary equation 10

11 local equilibrium surface profiles D geometry iterative calculation: initial profile (fixed θ A ) field distribution (FEM) force balance refined profile 1. local force balance p el ( x) 0 r ε! E( ) γ lv r h ( ) r 1 h ( ) p cap r ( ). free energy minimization ~ A η! F cosθ L ds ( ) min ( ) dv φ ε Y sl r B 11

12 numerical results surface profiles curvature / Maxwell stress x 1 liquid air η (0,.,.4,, 1.) log P el η ν -0,4 ε 1: ε : -0,6-0,8 0,4 0,5 0,6 0,7 α / π θ Y / π Buehrle et al. PRL 003 Bienia et al. EuroPhysLett h/d ins q local contact angle Young s angle q divergent curvature near contact line: κ ~ p el ~ h ν ; -1 < ν < 0 q range of surface distortions: d ins no contact angle saturation (in -dim model) log h/d ins

13 experimental verification η 0 η 0.5 η 1 d 10µm d 50µm d 150µm 13 Mugele, Buehrle, J.Phys.Cond.Matt 007

14 relation between local and apparent c.a. D geometry apparent c.a. cos( θ ( )) cosθ η Y local c.a. θ B θ Y 14 apparent c.a. follows EW equation

15 equivalence of force balance & energy minimization S f x, el 0 ρ E dz x εε 0 d x total force: (per unit length) f x T Σ xk n k da Maxwell stress tensor: εε 0 d σ lv η T.B. Jones force / unit length σ lv independent of drop shape! f el σ sl 15 σ sv

16 reconciliation ε 0ε σ i Ai d i r macroscopic picture A sl F i σ E r i A i 1 r r D EdV Maxwell stress: microscopic picture p el ε r E( ) 0 r εε 0 σ lv Alv σ sl σ d σ sl eff sv A sl h>> d electrical force / unit length fel 0 p p σ el ( z) dz modified Young equation modified capillary equation lv ε κ r E( ) 0 r 16 both pictures are equivalent on a scale >> d ins

17 contact angle saturation: the mystery of EW what causes deviations from EW equation at high voltage? advancing receding cos( θ ( )) cosθ Y 1 ε 0ε dσ lv diverging electric fields can cause dielectric breakdown of coating! break down safe operation (Seyrat, Heyes, J. Appl. Phys. 001) 17

18 refined version: local breakdown at contact line potential magnitude of field self-consistent calculation of field and surface configuration local breakdown upon calculated EW curve including saturation exceeding V T (Papathanasiou et al. Appl. Phys. Lett. 005, J. 18Appl. Phys. 008, Langmuir 009)

19 contact line instability d Coulomb explosion: balance of capillary energy and electrostatic energy top view: water-silanized glass ; f 00 Hz 100 µm 19 Berge et al. Eur. Phys. J. B 1999; Mugele, Herminghaus Appl. Phys. Lett. 00

20 AC- vs. DC-EW: frequency-dependence EW equation: cos( θ( )) cosθ Y 1 ε 0ε dσ lv RMS σ 0.7 µs/cm 70V rms f AC khz 0

21 finite-conductivity effects in AC-EW -0,7 5 µs/cm 0 µs/cm 300 µs/cm -0,7-0,7 ( 1mM NaCl) cos θ -0,8-0,8 f 0, 100kHz -0,8-0,9-0,9-0,9-1, , (V ) -1, conducticvity

22 modeling equivalent circuit ~ 0 droplet ~ 0 insulator loc loc << 0 due to Ohmic losses f ( ω) loc σ 0 1 ω 1 R l C d α f cosθ ( ω) (cosθ cosθ Y cosθ Y ε ε σ ) 0 d fσ ( ω) lvd 0 α 1 ω R l 0 C d

23 results α f(ω) (10-4 V - ) 1, 0,8 0,4 µs/cm 5.1 µs/cm 17 µs/cm 300 µs/cm 0, ω / (πσ) (khz m/s) few mm of salt perfect conductivity (up to a few tens of khz) 3

24 summary electrowetting basics contact angle reduction arises from minimization of interfacial and electrostatic energy (maximum of capacitance) 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 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. 4