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Electrowetting / Digital Microfluidics

IMA, December 6, 2009

Ali Nadim Keck Graduate Institute

& Claremont Graduate University Claremont, CA 91711 USA

Acknowledgments •  James Sterling •  Reza Miraghaie •  Anna Hickerson •  Christopher Cooney •  Chao-Yi “Richard” Chen •  Jie Dai •  Eve Fabrizio •  Robert Doebler •  Michael Emerling •  Maged Ismail •  Yousef Daneshbod •  Michael Franklin •  Alex Wu •  Peter Qu •  Anita Kalra

Funding: NIH SBIR I & II, DARPA, HSARPA, Tanner Research, Ionian Technologies, Northrop Grumman, SAIC, Tecan

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Surface Tension Dominates at Small Scales

Bond Number

Capillary Number

Weber Number

Scales:

Reynolds number Re = We / Ca = O(1)

θ Solid

Liquid

Vapor/Gas Young’s eqn:

Electrowetting on Dielectric (EWOD)

When potential V is applied (Young-Lippmann Equation):

R.B. Fair, Microfluid Nanofluid, 3, 245-281 (2007).

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Experimental Data

Figure from: Mugele & Baret, J. Phys.: Condens. Matter, 17, R705-R774 (2005)

Thomas Young Gabriel Lippmann

(1773-1829) (1845-1921)

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Young-Lippmann I

!sl !" !sl !12cV 2 c =

!o!r

d

cos(!) ="sv ! "sl

"lv+

cV 2

2"lv= cos(!o) +

cV 2

2"lv

When V applied, imagine the solid-liquid energy to be reduced:

V

d Dielectric Layer

Electrode

d Young’s Equation:

Young-Lippmann II: The “Wedge” Vallet, Vallade & Berge, Eur. Phys. J. B., 11, 583 (1999)

Kang, Langmuir, 18, 10318 (2002) 2-D, via Schwarz-Christoffel transformation

Singular charge density at the contact line

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The Wedge Solution

Fex =!V 2

2d

Horizontal component is independent of θ

Calculate the force by integration of Maxwell stress along the liquid-gas interface.

Fe =!V 2

2dcsc(")

Force localized near the contact line and normal to interface:

200µm

Examples of Masks for electrode patterning:

Discrete Drop Control by EWOD

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•  200 µm gap between top and bottom plates

•  100 mM KCl with blue or yellow dye

•  0.5 µL drop volumes

•  0.2 second electrode pulse duration

•  60 V (rms) AC

•  8 kHz AC frequency

Combine and Mix Two Drops

Grounding from Below Cooney, Chen, Emerling, Nadim & Sterling, Microfluidics & Nanofluidics, 2, 435 (2006).

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Single-Plate EWOD with ground lines

Electrodes

Ground lines

Three Simultaneous Actuations

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Drop Trajectory w/ and w/o Grounding Grounded

Floating

Young-Lippmann III [cf. Shapiro et al, J Appl Phys, 93, 5794 (2003)]

V Dielectric

Parallel plate capacitor

Minimize E to obtain the Young-Lippmann Eqn: P.E. of external charging source

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Minimize E ↔ Maximize C

Note negative sign!

Lumped Model : Drop of Fixed Shape

V1 V2

Vdrop=0

C1 C2

Grounding electrode Capacitor 1

(C1) area

Cooney, Chen, Emerling, Nadim & Sterling, Microfluidic Nanofluidic, 2, 435 (2006). Jones, “More about the electromechanics of electrowetting,” Mech Res Comm, 36, 2 (2009).

!

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Lumped Model: Floating Drop

V1 V2 Vdrop

C1 C2

C1 and C2 proportional to wetted areas

Maximum C at x = 1/2

Lumped Model: Grounded Drop

V1 V2 Vdrop=0

C1 C2

C1 and C2 proportional to wetted areas

Minimum E at x = 1 when |V1| > |V2|

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Lumped Model Summary Force

(Grounded: linear in x)

(Floating: quadratic in x)

Grounded

Floating

x = Area Fraction

!

!

Eflt = !Atot

2!o!r

d[x(1! x)](V1 ! V2)2

Field Model: Maxwell Stress Tensor Force on a point charge

Force on a point dipole

Maxwell Stress

qE p ·!E

fe = !eE + P ·!E

! · (!o!rE) = "e P = !o(!r ! 1)E

fe = !"pe +" · T

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James Clerk Maxwell

(1831-1879)

DC Case: Conducting Drop

For a (perfectly) conducting drop, the electric field vanishes within the drop. Continuity of the tangential E field at the interface implies a normal E field only. Hence:

Potential field outside the drop:

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DC Case: The Mesh (COMSOL)

3 µm

1 mm

0.866 mm

!2! = 0

! = 120!!r = 1

!r = 2.7

DC, Grounded Drop (AF=0.4)

BC:

Also see: Vallet, Vallade & Berge, Eur Phys J B, 11, 583 (1999) Kang, Langmuir, 18, 10318 (2002) Baird, Young & Mohseni, Microfluidic Nanofluidic, 3, 635 (2007)

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EW Force vs Distance

AC ElectroMechanics [cf. Hong, Ko, Kang & Kang, Microfluidics & Nanofluidics, 5, 263 (2008)]

Conductivity

Time harmonic

BC at interfaces:

Time-average of quadratic quantities:

! · (!o!rE) = "e

J = !E

!2!̃ = 0

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Critical Frequency

Water:

Water + Dielectric [cf. Jones, Langmuir, 18, 4437 (2002)]:

AC, Grounded, 1MHz

Air:

Dielectric Layer:

Drop: AF = 0.2

AF = 0.8

Edge of Electrode

!r = 1 , " = 0

!r = 2.7 , " = 0

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1MHz vs 1Hz

1 Hz

1 MHz

Ground line

Edge of Electrode

Results, AC+DC, Grounded+Floating

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Hydrodynamics: Drag on Sessile Translating Drop (spherical cap, lubrication)

Fh = !6!µUR [g(", 1! #)! g(", 0)]

g(!, ") =!cot(!)!

"csc2(!)! "2 ! cot(!) ln

#"csc2(!)! "2 ! cot(!)

$%

! = "slip/R 10!7 < ! < 10!1

Subramanian, Moumen, McLaughlin, Langmuir, 21, 11844 (2005)

Molecular scale cut-off near CL:

R is the radius of the base of the drop θ is the contact angle

Recent Reviews

•  F Mugele & JC Baret, “Electrowetting: From Basics to Applications,” J Phys Condens Matter, 17, R705 (2005).

•  RB Fair, “Digital Microfluidics: Is a True Lab-on-a-Chip Possible?” Microfluid Nanofluid, 3, 245 (2007).

•  SY Teh, R Lin, LH Hung, AP Lee, “Droplet Microfluidics,” Lab Chip, 8, 198 (2008).