T. B. Jones / University of Rochester 1jones/electromech_of_EWOD.pdf · T. B. Jones / University of Rochester 9 9 Quincke bubble method (1883) (for insulating liquid) air bubble trapped

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T. B. Jones / University of Rochester 1

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Electromechanical interpretation ofelectrowetting & relationship to

liquid dielectrophoresis

18 July 2007

T. B. JonesUniversity of Rochester

Rochester, NY (USA)

The purpose of this lecture is to present a generalelectromechanical model that encompasses electrowetting(EWOD) & DEP actuation of aqueous liquids. I willreview briefly the frequency-based relationship of the twomechanisms & then show how classical electromechanicscaptures all the important dynamics. The connection ofEWOD (& DEP) actuation to contact angle will bediscussed. A case will be made that contact angle effects& translational electromechanics are best regarded asdistinct observable phenomena. New results showing theeffect of saturation on both static equilibria & dynamicswill be presented. In particular, the dynamics resultsprovide new physical insights.

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TerminologyEWOD: electrowetting phenomena ondielectric-coated electrodes -- lowfrequency/high conductivity, origin isqE force acting near meniscus

Liquid DEP: dielectrophoresis of liquidmedia -- high frequency/lowconductivity, origin is ponderomotiveforce on dielectrics

related by frequency

This terminology is used throughout the remainder of thelecture.

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EWOD/DEP is revealed using“modified” Pellat experiment

grounded Al channelwith glass sidewalls

spacing ~ 1 mmcoating thickness ~ 4 mm

haqueousliquid

+V-

Gravity provides a calibrated force!

H

To investigate the effect of frequency on aqueous liquidactuation, one can modify the classic Pellat experiment(1895) by coating the electrodes with a uniform dielectriclayer of the order of ~1 micron in thickness. Typicalelectrode spacing is ~1 mm & the electrodes are ~5 cm inheight. An Al metal channel with glass side walls containsthe liquid & is grounded during all experiments.

To avoid potential variation along the length of theelectrodes, bipolar AC voltage supplied by a transformerwith a grounded center tap is preferred. Particularly at lowfrequencies, this arrangement helps to defeats parasiticresistances that would otherwise disturb the symmetry ofthe voltage drop across the dielectric layers on the twoelectrodes.

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Classic textbook example ofponderomotive (DEP) force

Fxe =

∂ ¢ W e∂ x V =constant

where ¢ W e = 12 C(x)V 2

Lumped parameter (energy) method

k slabxV D Fxe

†

Fxe = -

(k slab -1)eo wV 2

2 D

Most texts on electrodynamics exemplify the ponderomotive forceby using the classic example of a solid dielectric slab betweenparallel electrodes. This simple geometry nicely illustrates thepower of lumped parameter electromechanics & Maxwell stresstensor methods in determining electrical forces. Here, we employthese methods to gain insight into the relationship of EWOD &DEP liquid microactuation.While the E field must be non-uniform somewhere, seeminglyparadoxically, the lumped parameter method determines the forcewithout detailed information about the E field non-uniformity.Electromechanics gives the correct answer for the observable effectwhile not revealing where the force “acts”. In fact, the matter offorce distribution is irrelevant with respect to translationalmotions and, in the case of liquid or solid dielectrics, it isunmeasurable.Over the past 150 years, several different force density distributionshave been formulated. While each of them seems to distribute theforce differently, all give the correct answer to the ONLY testablequestion, i.e., the net measurable force on the ponderable body.

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Alternate formulation

T e = - 12k eo Eo

2

where Eo = V / D

Stress tensor method

Fxe = [Tslab

e - Taire ]WD

SAME AS LUMPEDPARAMETER METHOD!

k slabV D Fxe

S

T aire Tslab

e

Because the Maxwell stress tensor is extracted from a forcedensity expression derived from Maxwell’s equations, it isinherently consistent with energy conservation. This iswhy it can be employed with no information about theelectric field non-uniformity in evaluating the net electricalforce, both for this geometry and for certain others wherethe E field solution can be expressed analytically atdielectric interfaces, i.e., in regions where the dielectricconstant gradient is strong. Such an approach is possibleonly when using the Korteweg/Helmholtz force densityformulation.This formation, presented in Landau and Lifshitz (andother classic texts), was favored by J. R. Melcher for thesimple reason that it is easiest to use.

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Replace solid slab by liquid:Pellat's experiment (1895)

Tze = [Tair

e -Tliquide ]

Tze = - 1

2 (k liquid -k air )eo Eo2

where Eo = V / D

Force balance:

Maxwell stress:

Tze = [ pair - pliquid ]

h

gravity g

k liquid

Tair

epair

Tliquid

e pliquid

V

Eo

z

The ideas covered previously are wholly relevant tothe electrohydrostatics of dielectric & conductiveliquids.It is natural to consider the geometry of two verticalparallel electrodes dipped into a liquid. Thisgeometry is known as Pellat's experiment (1895),and it serves as a very convenient experimentalplatform to study force effects important to themicrofluidic systems of interest to day.Initially, we constrain the liquid interface to be flat,but this restriction is removed later; in fact, we findthat the shape of the surface is immaterial to theobservable, upward-directed electromechanicaleffect.

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Solving for h:

pliquid - pair =

(rliquid - rair )gh

hydrostatics:

PELLAT'S RESULT FORDIELECTRIC HEAD

h =(k liquid -k air )eo Eo

2

2(rliquid - rair )g

= 1

h

gravity g

k liquid

Tair

epair

Tliquid

e pliquid

V

Eo

z

The problem is most easily treated using the Korteweg-Helmholtz force density formulation, found in all theclassic texts (Landau & Lifshitz, Stratton, Becker, etc.).For homogeneous, incompressible dielectric liquids, the K-H force density places all electrical forces at interfaces &allows us to treat pressure as the familiar hydrostaticquantity, in fact, an extra variable.The Kelvin formulation, , does not have thisadvantage & must be used with caution.Usually, the density of air may be neglected compared tothat of the liquid. But, if the experiment is conducted in animmiscible dielectric liquid bath, the other terms must beretained.

(P ⋅—) E

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Quincke bubble method (1883)(for insulating liquid)

air bubble trappedbetween 2 parallelelectrodes

manometer

dielectric oil bath

The Quincke experiment, even older than the Pellatexperiment, measures the static "excess" pressure in an airbubble between two parallel & horizontal electrodes in aninsulating oil bath. Just like the Pellat experiment, thisapparatus can be modified for measurements relevant toEWOD and DEP microfluidics by coating the electrodeswith a uniform dielectric layer.Refer to: TB Jones, JD Fowler, YS Chang, and C-J Kim“Frequency-based relationship of electrowetting anddielectrophoretic liquid microactuation,” Langmuir, vol.19, pp. 7646-7651, 2003.

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Conductive slab & coated electrodes

Fxe ª Td

e 2wd

T e = - 12k d eo Ed

2

where Ed = V / 2 d

xV

Fxe =

∂ ¢ W e∂ x V =constant

where ¢ W e = 12 C(x)V 2

conductive slab(at potential midpoint)

S dielectric layer : d , k d

D

Energy method Stress tensor method

Lumped parameter electromechanics & Maxwellstress methods are both applicable to the case of aconductive slab between dielectric-coated electrodesas long as d << D << x & w. We only need beassured that the interface is far from the fringingfield region.To use the Maxwell stress, we employ a few tricksin choosing the closed surface S.The correctness of this approach is verified bycomparison to lumped parameter method (based oncapacitance), which is unassailably accurate. Thisconfidence is based on the fact that a correctlyformulated electrical terminal relation fully accountsfor energy flow.

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Conductive slab & coated electrodes

xV


D

Both methods yield same force expression:

Fxe ª -

k d eo W V 2

4d if d << D,W

EWOD force is stronger than DEP!

conductive slab(at potential midpoint)

These two methods yield the same result becauseboth stem from the identical energy conservationrule.

Note that, if the left edge of the conductive slab isnot perpendicular to the electrodes, or in fact hasany moderately irregular profile that does notintersect the fringing field region, the net force isunchanged.

This observation tells us that the local details of theelectric field, and therefore the apparentdistribution of the electrical force, do notinfluence the net force.

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What about slab contour inside electrodes?

V


D >> d

Maxwell stress tensor predicts thatelectric force is independent of slab

profile between electrodes!

conductive slab(at midpoint)

Lumped parameter electromechanics is based on energyconservation. It isolates the force of electrical origin.The Maxwell stress tensor, also inherently consistent withenergy conservation, is in fact equivalent to lumpedparameter electromechanics. The only requirement is thatS must enclose all regions of ponderable object where thevolume force is non-zero. Each force density formulationhas its own associated Maxwell stress & its ownrequirements for the definition of S.Electromechanics makes no reference to the "true"distribution of electrical forces in the slab, whetherinsulative or conductive. For observable center-of-massmotions of electromechanical systems, such a question isnot relevant.

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Replace slab by conductive liquid

†

Fze ª -[Td

e ] 2wd

†

Tde = - 1

2kd eo Ed2

where Ed ª V /2d

Balance of forces on S:

gravity g

conductive liquid

h

Sd , k d

dielectric coating

Fze = (pliquid - pair ) wD

Assumed: H >> D >> d

The same analysis can be employed for the case of aconductive liquid between two vertical, dielectric-coated electrodes.The force expression is identical to that obtained forthe solid, conductive slab using the lumpedparameter method.One may already anticipate that the shape of theliquid meniscus cannot influence the net force ofelectrical origin, Fe. Thus, for the moment, weignore all capillary effects. These will be consideredlater in the presentation.

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Solve for height-of-rise h:

h =k d eo V 2

4(rliquid - rair )gd DÆ

k d eo V 2

4rliquid gd D

pliquid - pair = - (rliquid - rair )ghHydrostatics:

Agrees with Welters & Fokkink (1998)without any reference to contact angle.

Equilibrium is established by balancing theopposing electrical & gravitational forces. Theresulting expression for h agrees with that obtainedby Welters & Fokkink (Langmuir, 1998).As long as d << D, the EWOD effect seems to bemuch stronger than the DEP effect because of theintensification of the E field within the dielectriclayer by the conductive liquid.

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“True” origin of electric force

hE

Locally intense E field actson induced surface charge.

+ + + +++++++ + + + + + +

- - - - - - - - - - - - - - - - -

conductiveliquid

insulativeliquid or air

insu

lativ

e la

yer

elec

trod

e

conductive liquid

If d << D & R , force isindependent of theliquid/solid contact angle.

Couloubic interpretation

One can legitimately seek a Coulombicinterpretation for the upward-directed force thatelevates the liquid. If we consider the stronglyintensified, nonuniform E field acting on theinduced surface charges at the free liquid surfacenear the contact line, we have such an interpretation.

Note that, based on what the Maxwell stress tensorteaches us, the net (integrated) force apparently doesnot depend on the local profile (curvature) of theconductive liquid.

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data of K-L. Wang

0 50 100 150 200 250 300 3500.0

0.2

0.4

0.6

0.8

1.0

f = 10

kHz

f = 2 kHz

DEP limitf > 20 kHz

EWOD limitf < 400 Hz

DI water :D=1.0 mmd = 4microns

Hei

ght-o

f-rise

h (c

m)

Applied voltage V (V-rms)

Unit: Hz DC 20 50 100 200 400 1k 2k 5k 10k 15k 20k

Frequency dependence of hSolid lines are derived from electromechanical model.

Typical height-of-rise data versus voltage: DI water fromDC to 20 kHz. The solid curves are predictions of thegeneral electromechanical model that uses (i) a simple RCckt model to determine the electric field distribution, (ii)the Maxwell stress tensor to evaluate the upward-directedelectrical force on the liquid, and (iii) the fluid hydrostaticequation. See Wang, Jones, Yao (Langmuir, 2004) fordetails.For voltage V below a frequency-dependent threshold, h ~V2, just as predicted by the model. Above this threshold, avery evident saturation effect manifests itself & restrictsthe attainable height-of-rise.Note that, as frequency is increased, the saturation-limitedheight-of-rise is actually increased, by as much as a factorof two for the DC value, at ~2 kHz.

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AC electromechanics:frequency-dependent field distribution

Finite conductivity ofliquid means thatvoltage distributionbetween dielectric layer& water depends on ACfrequency.

Finite conductive liquid

hE

+

-

+

-V/2

V/2

waterTo explain dependence uponAC frequency, there is no needto refer to contact angle.

The simple RC circuit shown superimposed on the figureexplains the origin of the frequency-dependentelectromechanical effect. It is the basis of the model thatsuccessfully predicts the h versus V data of the previousslide.

Experimental note: The ohmic current associated with thefinite conductivity of the water might become important ifthere is any asymmetry in the experimental setup, or if thesource resistances of any transformer setup used to createthe center-grounded AC voltage (not shown in the figure)are unbalanced.

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The coefficient K depends on the dielectric constant& thickness of the dielectric layer, the electrodespacing, plus the dielectric constant, conductivity &density of the liquid, as well as the electricalfrequency.This theory is remarkably successful in predictingthe height-of-rise up to the onset of saturation.

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Correlation below saturation

†

h = K Vrms2

†

K = f (w;k d ,kw ,s w ,rw , D,d)

where

H >> D >> d

is derived from ckt model with standardassumption that fringing field is negligible

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Excellent data correlationbelow saturation

Vol

tage

supp

lylim

it: 2

0 kH

z

h = KV2

DC 10 100 1k 10k 100k 1M0.0

0.5

1.0

1.5

2.0co

effic

ient

K (1

0-5 c

m2 /V

)

frequency f (Hz)

DI water 20mM Mannitol 1mM KCl

Data Key

data of K-L. Wang

For voltages below saturation, the data correlate well to thetheory for frequencies from DC to 20 kHz, liquid electricalconductivities from ~10-4 to ~10-3 S/m, & electrodespacings D from ~1 mm down to ~0.5 mm.As shown in this plot, we have tested the theory for sugar& salt solutions as well as DI water, covering more thanorder-of-magnitude range of liquid electricalconductivities.Each point plotted here is obtained from a least-squarescurve fit of h versus V2 data. The 95% confidence intervalsof these points (derived from Student's t statistics but notshown here) are not much larger than the sizes of the datasymbols themselves.

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EWOD & DEP actuationare related by frequency

• EWOD: the low-frequency or high-conductivity limit

• DEP microactuation: the high-frequency or perfectly insulating limit

E ~ 0 inside liquid

E ≠ 0 inside liquid

EWOD & DEP liquid actuation are, respectively, thelow- & high-frequency responses of a slightlyconducting liquid (usually aqueous) to a non-uniform electric field.The unified electromechanical model, which doesnot require any detailed knowledge of "where theforce acts," successfully correlates all the data belowsaturation.It may be pointed out in passing that changes in theliquid contact angle have NEVER been consideredor proposed as the mechanism responsible for theheight-of-rise of insulative liquids in the Pellatexperiment.

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Capillary risehg

hE

EWOD rise

Relationship to capillarityheight-of-rise & contact angle

coatedelectrodes

conductive liquidContact angle changeswith voltage: qE(V) < qo

qE

qo

initial profile

To this point, the matter of contact angle, electrowetting,and their effects on the electric-field-induced height-of-risehave been ignored. Let us now add these effects together,starting with a straightforward description of the expectedobserved phenomena.

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Classic example of electrowettingContact angle qE decreases whenvoltage is applied, causing droplet tospread.

dielectric coating

+

Metal electrode

qo

For reference, now consider the standardphenomenological demonstration of“electrowetting,” as observed on a plane, dielectric-coated metal electrode when a voltage is appliedbetween the electrode & a sessile droplet ofconductive liquid.This same effect was observed long ago byLippmann for sessile droplets of certain electrolytesolutions and Hg drops on bare metal electrodes. Itwas necessary to perform such experiments at muchlower voltages to avoid electrolysis.

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Classic example of electrowetting

Initial staticdroplet profile

Metal electrode

qE

+

These snapshots of the sessile liquid droplet showthe droplet profile before the voltage has beenapplied & then after voltage application, waitinglong enough for any transient motion to die away.The droplet achieves a new static equilibriumenforced by the altered contact angle & electricalpressure exerted on the liquid surface.Both droplet profiles are essentially spherical capsas long as Bo << 1, where Bo is the Bond number,comparing surface tension to gravity. This is alwaysthe case in terrestrial gravity for water droplets lessthan about 1 microliter in volume.

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Equation of B. Berge

†

cosqE -cosqo =kd eo V 2

8d g

based on electrostatic energy minimization:

where d << D is the thickness of the dielectric.

This practical equation, a special case of the more generalresult of Lippmann, is due to Bruno Berge. Berge derivedit using a straightforward electrostatic energy minimizationmethod.An alternate derivation, based on a capacitive(electromechanical) model is equally possible, if one usesthe spherical cap model for the liquid configuration.Deficiency of this model: it moves into strange territory atthe voltage value where the contact angle reaches zero, i.e.,qE = 0.Berge’s model can not deal with the phenomenon ofcontact angle saturation, but neither can any other energymethod. The decrease of the contact angle below somecritical value probably defines the voltage threshold forsaturation.

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Contact angle model for height-of-rise

hg =2g cosqo

rg DIf:

hE =2g cosqE - cosqo[ ]

r g D

Then, by extension:hg

hE

D

qE

qo

z

conductive liquid

The mechanistic model often invokes hypothesizesthat the additional, observed liquid rise, hE, is due tothe change in the contact angle.Questions: does this method correctly predict hEand, if it does, what does this prove?

good ref on phenomena of capillarity: Hendriksson U & Eriksson JC 2004 Thermodynamics of capillary rise: why is the meniscuscurved J. Chem. Educ. 81, 150–155.

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Using Berge’s equation

hE =2g cosqE - cosqo[ ]

r g D=

k d eo V 2

4 r g d D

The result is:

cosqE -cosqo =k d eo V 2

8dg

same as before

Thus, the contact angle model for the electric field coupledstatic height-of-rise predicts the same for hE(V).

The mechanistic model appears to break down at the voltage valuewhere the contact angle reaches zero, i.e., qE = 0. If one tries tokeep track of the value of cos qE, then this model would seem tosuggest that something goes haywire at qE = 0 and perhaps that hEwill be limited by this condition, despite further increase in thevoltage. However, there is no reason to accept any such predictionbased on the more fundamentally grounded principles ofelectromechanics.

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Significance of this correspondence

Does either model fix the force "location"?

Does the correspondence confirm contactangle model of liquid actuation?

No. Both theories are based onenergy methods & neither pinpointsthe force.

No. It confirms mutual consistencyof the models wrt observablebehavior, at least up to q E = 0° wherecontact angle model fails.

The correspondence referred to here is that between(i) the mechanistic theory, attributing the electricalcontribution to the upward force to the change in thecontact angle (actually the change in the cosine ofthe contact angle), and (ii) the electromechanicalformulation, treating the system as a variablecapacitor and then using a virtual work method todetermine the force.The two methods give consistent results becausethey are based in fact on mutually consistent energymethods; neither inherently tells us where the force“acts”. Such a question is not relevant if theobservable of interest is the height-of-rise or anyother center-of-mass displacement.

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Electromechanical formulation

Fze = 1

2 V 2 dC dzForce of electrical origin:

C(z)=k d weo z

2 d+ const.System capacitance:

Gravitational force on liquid: F g = r ghE w D

Equate these forces: hE =k d eo V 2

4r g d DAgain the same & again no referenceto contact angle or capillarity!

Using lumped parameter electromechanics, weagain get the same answer for the force and thus forthe height of rise hE! And we arrive at this answerhaving made NO reference to either contact angle orsurface curvature. This formulation depends onlyon capacitance.

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Gedanken experiment

gravity

conductive liquid

Predicted height-of-riseis unchanged, despitefixed contact angle.

h

Membrane constrainsmeniscus to be flat.

V

Consider a Gedanken experiment with a thin, rigidmembrane placed atop the liquid surface, whichfloats up & down as the liquid level rises or falls,constraining the surface to be flat.Electromechanics gives the identical upward forceas predicted for the solid slab.The liquid rises upward without any change incontact angle. Contact angle changes are notrequired for a rise of the liquid to occur.No details of E field non-uniformity are needed.

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Major contentions forelectromechanical model

• Electromechanical model provides unifieddescription of liquid actuation in non-uniformelectric field at all frequencies.

• Contact angle modulation does not drive liquiddisplacement; the two effects are distinctobservables.

• Contact angle modulation does lead tosaturation, which influences electromechanics.

The frequency-based relationship of EWOD and DEP is nowwell-established. Across the range of frequencies from theconductive (EWOD) limit to the insulative (DEP) limit, andbelow the onset of saturation, a large volume of data fromtwo entirely different experiments (modified Pellatexperiment and Quincke bubble method) conform well to theunified electromechanical theory: Jones, Wang, and Yao, “Frequency-dependent electromechanics of aqueous liquids: electrowetting anddielectrophoresis,” Langmuir, vol. 20, pp. 2813-2818, 2004.Jones, Fowler, Chang, and Kim “Frequency-based relationship of electrowettingand dielectrophoretic liquid microactuation,” Langmuir, vol. 19, pp. 7646-7651,2003

Basic theoretical considerations (along with dynamicexperiments) support the view that liquid actuation(observable translational motions) do not depend on changesin the contact angle.

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Electrical & capillary effects are additive

†

h = ho + hE (V )

hg

hE

D

qE

qo

z

conductive liquid

hExplanation of hE as achange in the contact angleis less compelling thaninterpretation as Coulombicforce effect (qE).

The mechanistic model (due to Berge) hypothesizesthat the additional, observed liquid rise, hE, is due tothe change in the contact angle.

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If d << D & R: thechange in systemcapacitance due todisplacement of contactline, Dz, dominates asthe energy storagemechanism.

Why does virtual energy methodwork as it does?

R

conductive liquid: E = 0

Dz

The contact angle of the conductive liquid at thecontact line will not influence the capacitancesignificantly, if d << D, R.

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Recommendation #1Identify two independent electric-fieldmediated observables:

• STATIC CONTACT ANGLE EFFECTS DUE TO APPLIEDVOLTAGE

• STATIC DISPLACEMENT & MOTION OF LIQUIDS DUE TO

NONUNIFORM E FIELD

The previous arguments point to the physicalinterpretation that contact angle reduction is NOTnecessary for existence of an observabletranslational force & that therefore the surfacetension is not the mechanism of EWOD.This conclusion leads to the suggestion that wedistinguish between two observable phenomena:• Static contact angle effects.• Translational (electromechanical) force effects.It seems unwise to attribute bulk liquid motion tocontact angle effects. These are two distinct aspectsof the effect of the electric field on a liquid.

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Recommendation #2

Do not attribute translationaldisplacements & motions tocontact angle changes.

Many papers wrongly suggestthis, if not claiming it outright.Some authors even suggest thatsurface tension is changed.


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Recommendation #3

Exploit electromechanicalformulations* to predict thebehavior of dynamic EWOD &DEP microfluidic schemes.

*… Use capacitance (or Maxwellstress tensor)


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Capacitance modeling

When possible, formulate model interms of capacitance as a functionof appropriate mechanicalvariable, i.e., C = C(z):

NB: Identification of themechanical variable is difficult incase of liquid lens.

†

Fze = 1

2 V 2 dC dz


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Possible definition of mech. variable

qE

r

C(r)

†

C(r) ªeo k d p r 2

d

d

Even the classic “electrowetting” demonstrationexperiment can be formulated as an electromechanicsproblem, by making appropriate assumptions about theliquid droplet profile (spherical cap) and definingcapacitance in terms of some arbitrary mechanical variable.Here, the radius r is used, but others such as contact angleor the height of the spherical cap will work just as well.

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Maxwell stress tensor method

Tde = - 1

2k d eo Ed2

where Ed = V / 2d

This method gives thesame expression for theelectrical force, alsowithout pin-pointinglocation of force.

conductive liquid: E = 0

SFz = 2 ¥Td

e wd

E = Ed

The lumped parameter result is easily confirmedusing the Maxwell stress tensor, again with noreference made to contact angle & no need to knowthe messy details of the electric field.Note that stress tensor integration along theelectrodes provide no vertically directedcontribution to the force because the shear stress isproportional to the tangential electric field, which isalways zero at perfectly conducting surfaces.

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Why?• Liquid motions & displacements do not

depend on contact angle changes.• DEP & EWOD actuation are high- & low-

frequency RC ckt limits of electromechanicalresponse.

• Electromechanics (+ circuit theory) provides apowerful & convenient way to predictphenomena not readily explainable usingcontact angle interpretation.

The previous arguments suggest that it is best toavoid implying any causative link between contactangle changes & the electromechanically inducedmotions exploited in microfluidic schemes.Translational motions & changes to static surfaceconfiguration are caused resp. by non-uniformity of& perturbations to the existing E field.On the other hand, there is no reason to abandon theterm electrowetting (& acronym EWOD). Its useis well-established in microfluidics literature.When voltage is turned on, liquid does "wet" thesurface. The nature of this wetting - while complex- is not so different as to preclude calling itelectrowetting.

Documents

T. B. Jones / University of Rochester 1jones/electromech_of_EWOD.pdf · T. B. Jones / University of Rochester 9 9 Quincke bubble method (1883) (for insulating liquid) air bubble trapped