Electrowetting

Microfluidic Applications and Electromechanical Theory Kwan Hyoung Kang Department of Mechanical Engineering Pohang University of Science and Technology [email protected]

Chemistry + Mechanical Engineering = “Chemical

Engineering”

Presented at Department of Chemical Engineering POSTECH 2003. 9. 15

Micro-Total Analysis System (µTAS) ≈ Lab-on-a-chip

Everyone’s a (future) Chemist Rhino?

오! 미안 아가야… rhinovirus, strain 17에 감염되었구나. Sequence data를 방금 전 약국에 보냈거든… 약간의 chicken soup이 괜찮겠고…

(from M. Burns 2002, Science )

Wrist-mounted chem/bio assay

Wrist-mounted chem/bio assay

Distributed

Si Microneedle

Central Unit

1

Microfluidics • Microfluidics = Microhydrodynamics + Surface Chemistry + MEMS Tech.

Liquid handling on sub-millimeter scales • Electroosmotic flow – relatively high voltage ~ 1kV, slow ~ 0.1mm/s

surface force l 2 1 ∝ = volume force l 3 l • Central role in µTAS – – – –

Transport Mixing Separation etc.

• Mechanical syringes and actuator – complicated to fabricate, expensive

Liquid handling on sub-millimeter scales

Surface tension in action

• Creation of gradient in surface tension – Photonic, Thermocapillary – Electric: low cost, fast delivery, relatively easy to implement.

surface force l 2 1 ∝ = volume force l 3 l

(National Geographic Explorer/MSNBC)

Electrowetting control of liquid droplets

Effect of electrical charge on wetting Electrocapillarity and electrocapillary curve

Prof. C.-J. Kim (UCLA) (http://simony.seas.ucla.edu/)

Prof. R. B. Fair (Duke Univ.) (http://www.ece.duke.edu /Research/microfluidics/)

Lippmann eq.: dγ SL = −σ dV

Electrical double layer

2

Gabriel Lippmann (1845~1921)

Young’s equation by energy method

French Experimental Physicist

• The change in surface free energy due to small displacement of the liquid ∆G s = ∆A(γ SL − γ SV o ) + ∆Aγ LV cos(θ − ∆θ )

• At equilibrium

lim ∆A→ 0

One of the first color photo "Parrot" made by Lippmann in 1891.

∆G s =0 ∆A

(γ SL − γ SV o ) + γ LV cos θ = 0

Nobel Prize for Physics in 1908 for producing the first color photographic plate.

Contact angle change by electrocapillarity

Electrocapillarity vs Electrowetting Electrocapillarity

• Young’s equation: γ LV cos θ = γ SV o − γ SL Classification

• Change of surface tension due to charge

V --------

++++

Lippmann equation: dγ SL = −σ dV

cos θ = cos θ o −

γ LV

∫ σ dV ;

o

cos θ = cos θ o −

Contact angle

d

--------

ε

++++

++++

dγ SL = −σ dV

σ ~ εκV

Surface charge γ − γ SL cos θ o = SV γ LV

++++

dγ SL = −σ dV

Surface tension

• Contact angle change 1

Electrowetting

σ = εV / d 1

γ LV

∫ σ dV

cos θ = cos θ o +

εV 2 2γ LV d

Lippmann-Young eqn.

Contact angle control by electrowetting

Contact angle control by electrowetting 10-4 M KNO3 droplet on Teflon AF1600/Parylene C surface

Σ Ω

Sa

d=0.1mm

fluid

dielectric solid electrode

0V

400V

S 12

liquid droplet V

S∞

S 13 Sd

θ

θ Se

Contact angle

10µl 800V

(a) 0V

1kV

1.6kV

(a) 200V

3

Contact angle control by electrowetting

Contact line instability (after saturation) Droplet ejection

Light emission from contact line

Contact angle saturation

1mm

LippmannYoung eqn.

M. Vallet et al. Eur. Phys. J. B, 1999.

H. J. J. Verheijen et al. (Philips Res. Lab. Eindhoven, The Netherlands) (1999) Langmuir 15, 6616.

Electrocapillarity vs Electrowetting

Electrocapillarity vs Electrowetting

Electrocapillarity EW on Polymers

Electrocapillarity EW on Polymers

EW on SAMs

Classification -------

+++++

Capacitance Equiv. dielectric. Thickness Specific adsorption Contact angle hysteresis

++++

------+++++

++++

------+++++

Classification -------

++++

+++++

εκ, ~104 µF/m2

ε/d, ~1 µF/m2

ε/δ, ~103 µF/m2

Applied voltage

κ, ~ 1nm

d, 10µm

δ, ~ 10nm Influential

Influential moderate

Electrochemically inert Depends on polymers

EW on SAMs

++++

------+++++

-------

++++

+++++

++++

0 ~ 5V

0V~1kV

0 ~ 5V

Reversibility

bad

good

bad

Dominant interaction force

Coulombic, Chemical,

Coulombic

Coulombic, Chemical

In general, significant

Electrowetting control of liquid droplets

Actuation of microdroplet by electrowetting “No need for pumps, valves, or even fixed channels. ”

Prof. C.-J. Kim (UCLA) (http://simony.seas.ucla.edu/)

Prof. R. B. Fair (Duke Univ.) (http://www.ece.duke.edu /Research/microfluidics/)

M.G. Pollack et al. (Duke U., Dept Elect. Eng.) (2000) Appl. Phys. Lett. 77, 1725.

4

Splitting of a droplet

Other applications

Droplet: 100mM KCl (≈1µl) ≈1.5mm

Flow of a droplet on a 2-D array

Liquid actuation in microcapillary

Dispensing of droplets

Liquid actuation in microcapillary

M. W. J. Prins,* W. J. J. Welters, J. W. Weekamp, “Fluid Control in Multichannel Structures by Electrocapillary Pressure,” Science, January 12, 2001. M. W. J. Prins,* W. J. J. Welters, J. W. Weekamp, “Fluid Control in Multichannel Structures by Electrocapillary Pressure,” Science, January 12, 2001.

Liquid actuation in microcapillary

Applications

M. W. J. Prins,* W. J. J. Welters, J. W. Weekamp, “Fluid Control in Multichannel Structures by Electrocapillary Pressure,” Science, January 12, 2001.

5

Why electrowetting for lab-on-a-chip?

Digital microfluidics by electrowetting

ƒ Droplet-based microfluidic operations • By programmed electric signals rather than by complex physical structures. • Fabrication process becomes very simple.

Other advantages of electrowetting : fast liquid actuation, low power consumptions. C.-J. Kim et al. (UCLA) (2002)

Mixing of droplet by electrowetting

Prof. R. B. Fair (Duke Univ.) (http://www.ece.duke.edu /Research/microfluidics/)

Optical lens (2)

CMOS Camera

Optical lens (1)

Yang et al. (Bell Lab.) (2003)Adv. Mater. 15(11) 940.

Optical switch for optical network

Benefits • No moving parts, direct electric control • Fast response (0.02s for a 5mm diameter) • Very good optical quality • Reduced electrical consumption Applications • Medical optics • Autofocus lenses for CCD cameras • Bar code readers

http://www.varioptic.com/

6

Why electromechanical approach?

Development of Electromechanical Theory

Why electromechanical approach? • Limited validity of Lippmann–Young equation due to contact-angle saturation.

Contact angle saturation

• Some MEs are unfamiliar with the energy method.

Why electromechanical approach? • Increase of contact angle by electrowetting?

0kV

1kV

2kV

3kV

LippmannYoung eqn.

Why electromechanical approach?

Why electromechanical approach?

• Mechanism of the contact line instability?

• Mechanism of the contact line instability?

1mm

M. Vallet et al. Eur. Phys. J. B, 1999.

7

Why electromechanical approach?

Essence of the electromechanical theory • Use of Gauss theorem and the Maxwell stress tensor.

• Limited validity of Lippmann–Young equation due to contact-angle saturation. • Mechanism of the contact line instability? • An alternative approach is necessary to analyze the complex phenomena.

F = ∫ f dV = ∫ T ⋅ n dS Ω

Σ2 Ω2

(Korteweg–Helmholtz force density)

Σ1

T = − 12 εE 2 I + εEE

(Maxwell stress tensor)

Σ3

Wel = −F ⋅ e x

(wetting tension)

Ω1

n Ω3

Direct integration of Maxwell stress

dielectric solid electrode

∇ 2ϕ = 0 F=

∫ T ⋅ n dS

S12 + S13

θ

T = − 12 εE 2 I + εEE Se

w

u=∞ S12

w = u + iπ

Z = ∫ (e w ' + 1)α dw' + iπ

y

iπ

Z = x + iy

π  w = u + iv = u + i ϕ V 

l

ϕ =V

θ

S13

u = −∞

=

ϕ = 0, v = 0

Charge distribution at the surface 5

10

1

10 1

5

1

1

3

3

1

5

σ/σo

3

i σ = ε | E x − iE y |= e dZ / dw

o

1

σ 1 /(e − 1) , on S12 , = σ o 1 /(1 − e u ) a , on S13 .

10

10

θ= 30o o 60 90o 120o o 150

8

0

10 0

10

u

σ2 n 2ε

o

θ = 30 60o o 90 o 120 o 150

εV

60

2

n=

Maxwell stress acting on surface

l/d

σ /σo

εE 2

ε substrate = ε air

Important assumption:

Note: Effect of electrical double layer is neglected.

droplet edge region

T ⋅ n = ( − 12 εE 2 I + εEE ) ⋅ n

x

Maxwell stress tensor

6

2

V

S13 Sd

(modified Young’s equation)

γ

(σ/σo) × sinθ

liquid Perfect conductor droplet

F

S∞

(σ/σo)2 × sinθ

S12

Wel

Schwarz-Christoffel transformation Ω

fluid

cos θ = cos θ o +

Analysis of potential problem

Σ Sa

Σ

f = ρ f E − 12 E 2∇ε

4 2 0

-1

0

2

4

6 y /d -1

8

10

a

10 -1 -2 10

10

-1

l /d

10

0

10

1

10 -2

0

2

4

y / d -1

6

8

10

3 5

Charge distribution

Maxwell stress

8

Surface force and wetting tension σ2 εV 2 F= ∫ dl = 2ε 2d 2 S 12

• Conventional electrowetting equation is recovered.

εV 2 1 ∫S (eu − 1) 2α dl = 2d cosecθ 12

fluid

γ 12

liquid droplet

fluid

γ 12

liquid droplet

Derivation of Lippmann–Young eqn.

F=

2d

Fx =

cosecθ

θ

γ 13

εV

2

2d

Fex =

cosecθ

γ 23

Fx

γ 12 cos θ = γ 23 − γ 13 +

εV 2 2d

εV 2

2d εV 2 Fey = cot θ 2d

Fy

dielectric solid

γ 23

Fx

dielectric solid

εV 2

2d εV 2 cot θ Fy = 2d

Fy

θ

γ 13

εV

2

F=

; Lippmann–Young eqn. (Langmuir 2002, 18, 10318)

Origin of electrowetting phenomena

Generalization of Theory

• Electrowetting originates from wetting tension, rather than from change of surface energy. • Roll of the vertical force should be explained. fluid

Fx =

εV 2 2d

, Fy =

εV 2 2d

cot θ

liquid droplet

γ 13

γ 12

θ

F=

εV

2

2d

cosecθ

--------

++++

Fy

Fx

dielectric solid

γ 23

--------

++++

--------

+++++ ++++

(a)

++++

++++

(c)

(b)

Note: Effect of interfacial shape is not considered.

Surface force and wetting tension

Electromagnetic momentum conservation • Force on a volume Ω:

FΩ =

∫

Ω

f dV =

∫

Σ

T ⋅ n dS

Ftot = F + f y' e y = − f y' e y − ∫

• Maxwell stress with osmotic pressure:

T = −(Π + 12 εE 2 )I + εEE; • A vector identity: Σ2 Ω2 Ω1

∫

Σ

Π = 2n ∞ kT [cosh βϕ − 1] Ω

κ2 ∇ ⋅ E = −∇ ϕ = 2 sinh βϕ β

Σ3 Ω3

Σ

1 2

εE 2 ] I − εEE}⋅ n dS = 0

Σ tot

T ⋅ n dS

Σ2

Ω1

2

∫ {[Π +

T ⋅ n dS = ∫

Ω2

(n ⋅ E ) E dS = ∫ [E (∇ ⋅ E ) + E ⋅ ∇ E ]dΩ

(Poisson–Boltzmann equation)

Σ1

n

Σ tot

S12 + S 21

Σ1

S12

fx =

S 21

n Σ3

ε 3 (V − ϕ13 ) 2

βϕ 12  4ε 1κ 1  cosh − 1 β 2  2  2 ε (V − ϕ 23 ) 4ε 2κ 2  βϕ 23  − 3 − cosh − 1 2  β  2d 2  2d

+

(Langmuir 2003, 19, 5407)

Ω3

9

Surface force and wetting tension

--------

++++

Note:

n n  Wel( I ) = 8kT  1b − 2b [cosh β2V − 1]  κ1 κ 2 

cos θ = cos θ o +

Benefits of the electromechanical theory • Familiar to MEs

Wel

γ

• Easy and clear; requires understanding only on the Maxwell stress tensor.

++++

 8n kT   8n kT  Wel( II ) =  1b [cosh βϕ21∞ − 1] − σ 1ϕ1∞  −  2b [cosh βϕ22 ∞ − 1] − σ 2ϕ 2 ∞    κ1   κ2 + (σ 1 − σ 2 )ϕ o Geometry dependent term.

--------

+++++ ++++

• Suitable for numerical calculations for complex situations.

(Langmuir 2003, 19, 6881)

Wel( III ) = -------++++

ε3 2d

• Can handle dynamic problems. [(V − ϕ1∞ ) 2 − (V − ϕ 2∞ ) 2 ]

+8

++++

n1b kT

κ1

[cosh βϕ21∞ − 1] − 8

n2b kT

κ2

[cosh βϕ22 ∞ − 1]

Validity of the Derjaguin approximation … Frumkine–Derjaguin approach (base on the DLVO theory)

Usefulness

droplet

Validity of the Derjaguin approximation on the Frumkin–Derjaguin approach

a b

−∞

+∞

h

a b

original profile

a' b'

h

film

n Ω'

surrounding fluid

S5

θ∞

Ω

S6 S1

ho O

droplet

S4

cosθ ∞ = 1 +

Wel

γ

Velϕ (ho ) =

S2

Wel

S8

S7

S9

cos θ = cos θ o + Wel = −F ⋅ e x S3

x

S1

∫

∞

ho

π t (h) dh = 1 +

[2ϕ ϕ cschκh 1

2

o

2

Vt (ho )

γ

− (ϕ12 + ϕ 22 )(coth κho − 1)

]

[2ϕ 2

2 2 1∞ϕ 2 ∞ cschκho + (ϕ1∞ + ϕ 2 ∞ )(coth κho − 1)]

εκ

εκ 2

1

γ∫

∞

ho

π t (h) dh = 1 +

[2ϕ ϕ cschκh 1 2

o

Electromechanical approach cos θ = cos θ o +

Vt (ho )

γ

− (ϕ12 + ϕ 22 )(coth κho − 1)

Velσ (ho ) =

εκ 2

[2ϕ

]

ϕ 2∞ cschκho + (ϕ12∞ + ϕ 22∞ )(coth κho − 1)]

1∞

droplet

S6

Welϕ =

εκ 2

Welσ =

[2ϕ ϕ cschκh 1 2

εκ 2

εκ 2

o

θ∞

+∞ a b

a' b' film

h

ho a' b'

S7

droplet

S5

substrate

n Ω'

surrounding fluid

original profile

εκ 2

ϕ12∞ (cos θ ∞ − 1)

S9

θ∞ S2

Wel

S8

Ω

S6 S1

ho O

]

electrocapillary term

(ϕ12∞ − ϕ 22∞ )(coth κho − 1) + y

a b

h

γ

− (ϕ12 + ϕ 22 )(coth κho − 1)

ϕ 22 (cos θ ∞ − 1)

substrate −∞

Wel

Wel = −F ⋅ e x

+

F = − ∫ T ⋅ n dS − ∫ T ⋅ n dS

γ

Validity of the Derjaguin approximation … Frumkine–Derjaguin approach (base on the DLVO theory)

Electromechanical approach y

Velσ (ho ) =

εκ

substrate

a' b'

Validity of the Derjaguin approximation …

Velϕ (ho ) =

droplet

ho

1

cosθ ∞ = 1 +

θ∞

droplet

S4

S3

x

substrate

10

Validity of the Derjaguin approximation … • For constant potential (CP) case, valid for all the contact angles with minor correction. • For constant charge (CC) case, significant error due to existence of tangential stress. liquid surface

E

E ds

• Reduction of actuation voltage: now, normally ~30V • Delay of saturation angle by AC voltage (dielectrophoresis, Prof. Jones in U. Rochester) • Mechanism of contact angle saturation. • Contact line instability (droplet ejection) • Minimization of protein adsorption by additives.

En

t

n

Some of current issues on electrowetting

dh

θ

EEt t

dx

CP case

CC case

Concluding remarks • Electrowetting has many advantages for microfluidic actuation of liquids such as 9 fast 9 low energy consumption 9 digitized operations • An electromechanical framework on electrowetting is established.

11