Analysis of Electrowetting Phenomena Based on Energy and Electromechanics

() (4) (3) () Analysis of Electrowetting Phenomena Based on Energy and Electromechanics γ Fluid γ γ 3 3 S Droplet S 3 Insulator Electrode S 3 κy 3 3.4. 0 7.3 6. 4.6 - -3 - - 0 3 7. 9.8 6..4 βϕ.8.5. 0.9 0.6 () Analytical Solution(4.) () Linear FVMSolution (3) FEM Solution (4) FVM Solution 0 40 60 80 α (deg.) F t -5.0E-09 -.0E-08 -.5E-08 -.0E-08 0 40 60 80 α (deg.) f ex 0.8 0.6 0.4 0. 0 Fluid Droplet 0.5.5 ε / ε 3

Introduction

Micro Total Analysis System µtotal Analysis System (µtas) Bio-Chip DNA-Chip Lab-On On-a-Chip

µ TAS Electrowetting Injection Transportation Mixing Cultivation Caliper Tech. Corp. Separation Detection

Merits of Electrowetting Low power consumption Low voltage operation c.f. Electrophoresis: ~ kv Reversible operation Droplet based operation

Previous Investigation Lippmann (875) Electrocapiliary. Berge et al. (994) Lippmann Young. Kim et al. (998) Electrowetting Prins et al. (00) Electrocapiliary Science

Principle of Electrowetting

Nomenclature Nonwetting Dewetting Wetting Droplet Wetting

Principle of Electrowetting Lippmann equation: γ = σ V mm Lippmann Young equation: cos α ( V ) = cos α (0) + ε 0ε γ d V d γ + ++ + + + + + + + + + + + + + + ++ + + α + Electrolyte + + + + + ε + +++ + + +++ + + ++ + + +++ + + ++ + +++ + + + + + + + --- - - - - - -- - --- - - - - - -- - - - - - - -- - - -- - - - - - -- ----- Electrode Insulator V

Application (I) Insulator : 700nm Parylene C Hydrophobic material : 00nm Teflon AF Drop size : 0.7 ~.0ml of 00 mm KCl Interval btw. electrodes :.5mm Initiating voltage : 30 ~ 40 V Fast movement above 55 V Average velocity : 3 cm/s

Application (I) Flow of a droplet on a -D array Dispensing of droplets

Application (I) Rotation Mixing

Application (II) M. W. J. Prins et. al., Science, 00.

Application (III) Na SO 4 sol. -bromodecane ~ Hydrophilic region Hydrophobic insulator (teflon/saran TM ) mm B. Berge et. al., Eur. Phys. J. E, 000.

Application (IV) T. D. Blake et.al., Langmuir, 000.

Research Motivation

Saturation and Instability 0-4 M KNO 3 solution (5 µl) 75 µm thickness Teflon tape coated Lippmann Young equation cos α ( V ) = cos α (0) + ε 0ε γ d V

Motivation Conventional Lippmann Young Equation - EDL effect is not considered - Line Tension is not considered electrolyte air + + + + + + + + + + + + + + + ++ + Droplet + electrode insulator ------------------------ - - - - - - cos α ( V ) cos (0) + ε ε γ d 0 = α + EDL + Line Tension V TCL effect

Motivation Detailed Analysis on electrostatic interaction near TCL is necessary Deionized water on silanized glass (d = 80 µm); applied voltage: kv F. Mugele et al., Appl. Phys. Lett., 00

Motivation M. Vallet, M. Vallade, and B. Berge Limiting phenomena for the spreading of water on polymer films by electrowetting, Eur. Phys. J. B, 999.

Objectives EDL (Electrical Double Layer), Line Tension Lippmann Young. TCL EDL. Wetting Tension..

Approaches Analytical Energy approach Electro-Mechanical approach Numerical Line tension Wetting tension Experimental Vertical stress Droplet profile (AFM) Saturation, Instability

Analytical Approaches Energy Approach Electro-Mechanical Approach Numerical Approach Experimental Approach

Total System Fluid γ Zooming γ γ 3 3 S Droplet S 3 S 3 Insulator Electrode

System of Interest y S Fluid () γ Droplet () S 3 γ 3 α γ 3 S 3 x d z Insulator (3) S c

Energy Approach : Method of Analysis Minimum energy principle of thermodynamics Method of variational calculus

Energy Approach y S Free energy of system G tot = G = γ mech + G el S + γ 3S3 + γ 3S3 Ω ε i ϕ + Π( ϕ) tot Fluid () S 3 γ 3 d z γ α γ 3 Insulator (3) Mechanical part Electrostatic part Droplet () S 3 S c x dω c.f. G el = U el TS U el = ε σϕds + dω S ρϕ Ωtot Ω [ Π( ] εϕ ϕ ϕ TS = ) tot dω Ω tot ϕ dω + U

Excess Free Energy Excess free energy and line tension G tot ( c) el ( b) el = πr ( γ cosα + γ γ + g + g ) + πrf Excess free energy? 3 3 Excess free energy t electrolyte air + + + + + + + + + + + + + + + ++ + + λ D electrode insulator ------------------------ - - - - - -

Modified Lippmann Young Equation Introduce variational method G tot ( c) el ( b) el = πr ( γ cosα + γ γ + g + g ) + πrf 3 3 t δg tot = πrδr ( γ cosα + γ 3 γ 3 + g el + gel + Ft / R) = ( c) ( b) 0 Modified Lippmann Young equation cosα cosα ε ( V ϕ 4ε κ βϕ cosh 3 i i = 0 + γ d γ β ) Ft Rγ

Modified Lippmann Young Equation cosα cosα ε ( V ϕ 4ε κ βϕ cosh 3 i i = 0 + γ d γ β ) Effect of EDL Line tension Ft Rγ y Fluid γ Fluid () γ Droplet () F t S Droplet d γ 3 z α Insulator (3) γ 3 ϕ x γ γ 3 3 F t S 3 Insulator S 3 / κ = 3nm, β =υe /(kt)

Analytical Approaches Energy Approach Electro-Mechanical Approach Numerical Approach Experimental Approach

Electro-Mechanical Approach Wetting tension F e = S ( l ) + S T nds ( f ) = S ( l ) { ( Π + ) + } ε ie I ε iee + S ( f ) nds For a perfectly conducting droplet (Kang 00) F e = ε d 3 V cosecα Fluid F e S Droplet

Analytical Approaches Energy Approach Electro-Mechanical Approach Numerical Approach Experimental Approach

Numerical Approach ϕ n = 0 ϕ n = 0 ( l) ( f ) s ϕs ϕ = ( l) n ε ϕ = ε ϕ ( f ) n ϕ = 0 Fluid () ϕ = sinh( βϕ) Droplet () ϕ n = 0 ϕ n = 0 ( f ) ( s) S ϕs ( f ) ( s) n ε3ϕ n ϕ = ε ϕ = ϕ = 0 ( l) ( s) S ϕs ϕ = ( l) n ε ϕ = ε ϕ ( s) n Insulator (3) 3 ϕ n = 0 ϕ =V Dimensionless parameters : ~ x = κx ~ y = κy,, ~ ϕ = υe ϕ /( kt) = βϕ ~ σ = βσ /( εκ),

Electrical Potential Distributions α=0 3 3 α=40 κy κy 0 0 α=70 κy - -3 - - 0 3 3 κx κy - -3 - - 0 3 3 κx 7.06 3.4 9.75 6.09.44 0.00 α=90 0 0 - -3 - - 0 3 κx - -3 - - 0 3 κx V=0.5 Voltage( βϕ = ~ ϕ = 9.5), d = 3nm ( κ d =)

Validation Check(I) Analytical solution Electrical potential at TCL ϕ = sinhϕ ϕ = sinhϕ.8 () () (3) () Analytical Solution(4.) () Linear FVM S olution (3) FEM S olution (4) FVM S olution Fluid () σ m Fluid ().5 (4) βϕ. σ σ TCL 0.9 ϕ( α) [( ε σ + σ / ε ) α / π ] + σ m 0.6 0 40 60 80 α (deg.) σ =, σ =, σ m =, κ = κ, ε / ε = 4 T. Chou, Phys. Rev. Lett., 00.

Validation Check Analytical solution Line tension at TCL 60 l σ 0 50 Analytical Solution(4.3) Numerical Solution 40 α (κβ /ε)f t 30 l 0 σ 0 0 ~ ( e) ( e) εκ Gel = G el = [ tanh( πx) / tanh( αx) ]dx 0 σ 0 0 0 0 40 60 80 α (deg.) σ = σ = σ 0 =

ϕ n = 0 ϕ n = 0 Analytical Solution Numerical Solution Fluid () () ϕ n () ϕ n Fluid () 0.8 ϕ n = 0 d ϕ = sinhϕ dx y d ϕ = sinhϕ dx ϕ n = 0 βϕ 0.6 () n () n ε ϕ ε ϕ = σ ϕ n = 0 m x ϕ n = 0 0.4 0. e βϕ / i = e e βϕ / I βϕ / I + + + ( βϕ ) I / κi x e e ( βϕ ) I / κi x e e 0-8 -4 0 4 8 κx σ m =

(flux) 5 y n S Interface 4 Analytical S olution(4.4) Numerical Solution d Fluid () F e S 3 F ex Fey z α Solid (3) Fs F x n n 3 n Droplet () S 3 Substrate S c x ϕ n (f) (d / V) 3 ϕ ( f ) n σ 0 = ε π u u' = e, s e d 0 u ( ) α α du' 0 0 3 4 5 s/d o ~ α = 60, βϕ = ϕ =9. 5

Computed Line Tension -5.0E-09 -.0E-08 F t F t [N] -.5E-08 -.0E-08 0 40 60 80 α (deg.) cosα cosα Vε 3= 0. 5voltage, 4d ε= iκ3 nm βϕ ( V ϕ ) cosh γ d γ β i = 0 + Ft Rγ

Validity of Perfect-Conductor Assumption For a perfectly conducting droplet Fe = T nds = S ( l ) + S ( f ) ε 3 V d cosecα Horizontal component : Vertical component : Main assumptions F ex = F ey = ε 3 d V ε d 3 V cotα F e S

Effect of EDL α (deg.) f ex 0 40 60 80.000.00.00.003 / 3 = ε ε V 5voltage 0. = nm 3 =, α (deg.) f ey 0 40 60 80 0 3 4 5 cot α Numerical Solution ex f ex V d F ε 3 = ey ey f V d F ε 3 = d, α ϕ ϕ ε ε α ϕ ϕ ε ε sin ~ ~ ~ ~ ~ ~ sin ~ ~ ~ ~ ~ ) ( ) ( 3 3 + Π + = l f S S ex S d s n ds s n f

Electrical Permittivity Fluid 0.8 S ε F e 0.6 f ex ε 3 0.4 0. Droplet 0 0.5.5 ε / ε 3 f ex versus ε / ε 3 for V = 0. 5voltage, d = 3nm

Effect of Shape y Interface Fluid () Droplet () F e (0,.5) (-.95,0.5) (-,0) Solid (3) Substrate x V = 0. 5voltage, d = 3nm, ε / ε 3 =

Validity of Perfect-Conductor Assumption Fluid F e S Droplet Insulator σ V

Analytical Approaches Energy Approach Electro-Mechanical Approach Numerical Approach Experimental Approach

Microscopic Droplet Profile Air α o =3. Bean oil Silicon wafer

Microscopic Droplet Profile Coarse Postioning System Prove Tip Droplet Insulator

Microscopic Droplet Profile α 6.87 o α.95 o α α

Concluding Remarks Derivation of modified Lippmann-Young equation. cosα cosα ε ( V 4ε κ βϕ cosh 3 i i = 0 + γ d γ β Development of microscopic numerical method for solving electrical potential at TCL. - specific adsorption effect. Validation of electromechanical theory. ϕ Measurement of microscopic contact angle. ) Ft Rγ

Gabriel Lippmann (Aug.6, 845 ~ July 3, 9) The Nobel Prize for Physics in 908 Marie Curie Pierre Curie

Application Top Plate (glass) Filler Fluid (silicon oil) droplet Bottom Plate (glass) Ground Electrode (ITO) Hydrophobic Insulation Counter Electrode (chrome)

Free energy = d = 3nm V 0. 5voltage * G ) el : The free energy per unit depth ** EDL : The effect of electrical double layer to the free energy,

Free energy G G ( e) ( b) ( c) el = Gel Gel Gel el = U el TS = Ω tot ε ϕ + Π( ϕ) dω G ( b) el = S3 + S3 y 0 ( b) ( b) + Π = ε i ϕ ( ϕ ) dyds G ( c) 3 ( ϕ ) el = S c ε V d ds [ cosh( υβϕ) ] Π( ϕ) = n kt (b) ϕ : electrical potential of bulk