HIGHLIGHT www.rsc.org/softmatter | Soft Matter

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Fundamental challenges in electrowetting:from equilibrium shapes to contact anglesaturation and drop dynamicsFrieder Mugele*

DOI: 10.1039/b904493k

Electrowetting is a versatile tool for manipulating typically submillimetre-sized drops in variousmicrofluidic applications. In recent years the microscopic understanding of the electrowettingeffect has substantially improved leading to a detailed description of the drop shape and the(singular) distribution of the electric field in the vicinity of the contact line. Based on thesefindings, novel quantitative models of contact angle saturation, the most important andlongstanding fundamental problem in the field, have recently been developed. Futurechallenges arise in the context of dynamic electrowetting: neither the translational motion ofdrops nor the generation of internal flow patterns are currently well understood.

Introduction

Electrowetting is arguably the most flex-

ible method to actively control the wetting

behavior of conductive liquids on

partially wetting surfaces. By applying

a voltage between the drop and an elec-

trode submerged in the substrate, contact

reductions in excess of 90� can be ach-

ieved with actuation speeds on the milli-

second timescale, determined solely by

hydrodynamic response times. Hundreds

of thousands of actuation cycles can be

applied without any appreciable sign of

degradation. The rapidly growing appli-

cations of electrowetting (EW) include the

areas of optics (e.g. liquid lenses,1–3

various beam steering devices,4 reflec-

Frieder Mugele

Prof. Frieder

PhD in physi

Paul Leidere

employments

Laboratory a

pointed Cha

University of

focuses on

mechanical s

Forces Appa

microfluidics

wetting on s

soft matter m

colloids to liv

University of Twente, Physics of ComplexFluids, Enschede, The Netherlands

This journal is ª The Royal Society of Chemistry

tors), displays,5–7 reserve batteries,8,9 as

well as lab-on-a-chip systems.10–12 In the

latter area, EW has become the most

popular platform for so-called ‘digital’

microfluidic systems that are based on the

manipulation of discrete drops in a mi-

crofluidic chip. Using a large number of

individually addressable electrodes, EW

allows for generating, moving, merging,

splitting, mixing, etc. of individual drops.

Each application area has its own chal-

lenges, which are discussed in various

specifically targeted review articles in

recent years.5,10,11 For a general review on

electrowetting, see ref. 13.

In this article, I highlight the recent

progress on selected fundamental aspects

relevant to all applications of EW. I

discuss how EW arises from the interac-

tion of conductive liquid drops with

externally applied electric fields. Numer-

Mugele studied physics and obtained his

cs at the University of Konstanz with Prof.

r. After postdoc and research assistant

at the Lawrence Berkeley National

nd at the University of Ulm he was ap-

ir of Physics of Complex Fluids at the

Twente in 2004. In his current research he

three main directions: i) nanofluidics:

tudies (Atomic Force Microscopy, Surface

ratus) of confined molecular fluids. ii)

and (electro)wetting: two-phase flows and

tructured and functionalized surfaces. iii)

echanics: rheology of complex fluids from

ing cells.

2009

ical calculations of equilibrium drop

shapes will be presented describing the

distribution of the electric field and its

divergence in the vicinity of the contact

line. Based on these findings, progress

with respect to the longstanding problem

of contact angle saturation will be dis-

cussed. Finally, I briefly address a few

open problems and challenges for the near

future: drop dynamics and contact line

motion, mixing and internal flow

patterns, and novel configurations for

electrowetting.

Basic electrowetting and itsinterpretation

The electrowetting equation

The generic configuration of an electro-

wetting setup consists of a sessile drop of

a partially wetting conductive liquid on

an electrically insulating dielectric layer

covering a flat electrode, as shown in

Fig. 1. In typical experiments, the drop

size ranges from a 0.1 to 1 mm and the

dielectric layer has a thickness d between

a fraction of a micrometre and a few

micrometres. Since electrowetting can

only reduce contact angles, one chooses

dielectric layers (e.g. fluoropolymers) that

display a high contact angle at zero

voltage. Upon applying a (not too high)

voltage between the electrode on the

substrate and the drop the contact angle

decreases following the so-called electro-

wetting equation

Soft Matter, 2009, 5, 3377–3384 | 3377

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cosq ¼ cosqY + cU2/2s ¼ cosqY + h (1)

in which q and qY are the voltage-depen-

dent contact angle in EW and Young’s

angle of the system at zero voltage,

respectively. s is the interfacial tension

between the drop and the ambient

medium—typically either air or inert oil.

c ¼ 330/d is the capacitance per unit area

between the drop and the electrode on the

substrate (3: dielectric constant of insu-

lator; 30: permittivity of vacuum). The

dimensionless EW number h ¼ cU2/2s

measures the relative strength of electro-

static and surface tension forces in the

system. Fig. 2 illustrates the linear rela-

tion between cosq and h for a series of

drops with variable surface tension. The

collapse of the data shown in the main

panel demonstrates that EW also

provides a convenient way to measure

interfacial tensions for a wide range of

materials, as shown in ref. 14.

Fig. 1 Generic electrowetting setup showing a dro

voltage (solid). The zoomed view shows the bent su

the vicinity of the contact line. Arrows indicate the

Fig. 2 Electrowetting curves. Inset: cosq vs. U2 f

proteins) in ambient oil with increasing interfacial t

Main panel: master curve cosq demonstrating the co

from ref. 14.)

3378 | Soft Matter, 2009, 5, 3377–3384

The EW equation is frequently denoted

as the Young–Lippmann equation

because it can be obtained by combining

Young’s equation, cosqY ¼ (ssv � ssl)/s,

relating the contact angle to the inter-

facial tensions of the system (sv: solid–

vapor; sl: solid–liquid) and Lippmann’s

equation rsl ¼ �vssl/vU (rsl: interfacial

charge density), which yields an effec-

tive reduction of the solid–liquid inter-

facial tension with increasing voltage

according to seffsl (U) ¼ ssl � cU2/2.

Inserting the latter into Young’s equa-

tion leads to eqn (1). This ‘electro-

chemical’ picture of EW is appropriate

on macroscopic scales and provides

correct answers in many practical

considerations on EW. However, when

local properties near the three-phase

contact line matter, as for instance in

the context of contact angle saturation

and contact line motion, a more

detailed description is required.

p at zero voltage (dashed) and with an applied

rface profile and the diverging charge density in

electric field.

or a series of aqueous solutions (surfactants,

ension from 5 to 38 mN/m from top to bottom.

llapse of the data when plotted vs. h. (Adapted

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Equilibrium surface profiles and

electromechanical model of EW

A series of numerical and theoretical

studies15–22 recently addressed this issue. It

was shown that the reduction of the

contact angle in EW can be understood

completely in terms of an electrome-

chanical force balance at the drop surface

while keeping all interfacial tensions

constant. All of these studies follow the

same basic reasoning: the voltage applied

in EW gives rise to electric fringe fields

close to the contact line and thus results in

a Maxwell stress, which pulls on the liquid

surface (see Fig. 1 top). In order to

balance this stress, the shape of the drop

surface has to be curved in such a way that

the Laplace pressure DPL balances the

Maxwell stress pel everywhere along the

surface:

pel ¼3a30

2~Eð~r Þ2¼ 2skð~r Þ ¼ DPL (2)

Here 3a is the dielectric constant of the

ambient medium and k is the local mean

curvature of the drop surface. The calcu-

lations yield the following main results:

(i) the Maxwell stress (and hence the

curvature of the surface) diverges alge-

braically upon approaching the contact

line. This divergence arises from the

‘sharp edge’ or ‘lightning rod’ effect well-

known from basic electrostatics.24 In the

EW geometry, these fields are localized

within a distance of order d from the

contact line. Beyond that, the Maxwell

stress is negligible and the curvature

approaches the asymptotic value corre-

sponding to the global shape of the drop.

(ii) The divergence is sufficiently weak

such that the net force acting on the

contact line vanishes. (iii) Integrating the

horizontal component of the Maxwell

stress over a distance $d yields a net

horizontal force fel ¼ cU2/2. (This result

has in fact been obtained earlier by Jones

using either the stress tensor formalism or

a lumped parameter model.25)

These results imply (i) that the local

contact angle at the contact line is not

affected by the electric fields in EW and

(ii) that the contact angle that does follow

the EW equation is the apparent contact

angle q measured at a distance zd away

from the contact line. This is in contrast

to the electrochemical approach, which

implies a decrease of the local contact

angle because it assumes a voltage-

dependent solid–liquid interfacial

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tension. The controversy between the two

competing models can thus be settled by

simultaneously measuring both the local

and the apparent contact angle as a func-

tion of the applied voltage. The length

scale separating local from apparent

behavior is given by d/3, which can be

chosen according to the experimental

needs. Using insulators with a thickness

between 10 and 150 mm, Buehrle and

Mugele23 could visualize the drop surface

down to a scale smaller that d. As shown

in Fig. 3, the global shape of the drop

remains spherical and the apparent

contact angle indeed decreases for all

insulator thicknesses as expected from the

EW equation. For sufficiently thick insu-

lators, however, a clear cross over is

visible from the apparent behavior at

large scales to the local behavior on

a scale <d. As predicted by the numerical

calculations, the drop shape was found to

be consistent with a voltage-independent

local contact angle: the ‘true’ interfacial

tensions is thus indeed independent of the

applied voltage within the experimental

resolution. The contact angle reduction

can thus be explained exclusively in terms

of the electrostatic forces pulling on the

drop surface.

Relation between electromechanical

and electrochemical picture of EW

In order to appreciate the differences

between the two different models of EW,

it is useful to recapitulate the basic steps

Fig. 3 Video snapshots of sessile drops of an aque

lator thickness is d¼ 10, 50, and 150 mm from top to

to right: h¼ 0, 0.5, and 1. Note in particular the diff

the right hand column. (Reproduced with permissio

This journal is ª The Royal Society of Chemistry

of the electrochemical approach. (A very

useful derivation can be found in ref. 26.)

In this approach, one equates the change

in Helmholtz free energy released upon

charging the drop-substrate interface with

the reduction of interfacial tension. For

simple metal–electrolyte interfaces, this

variation is given by the electrostatic

energy involved in charging the electric

double layer. In the typical EW configu-

ration, however, the electrolyte is sepa-

rated from the electrode on the substrate

by the insulating layer (see Fig. 1). In that

case, most of the electrostatic energy

involved in charging the drop-substrate

interface is stored in the insulating layer,

since the capacitance of the latter is typi-

cally three to four orders of magnitude

smaller than the one of the electric double

layer.27 This implies that the ‘true’ (e.g.

water–teflon) solid–liquid interfacial

tension consisting of the chemical contri-

butions and the electrostatic energy

stored in the electric double layer is

constant up to a correction factor of order

3lD/3l d (lD: Debye length; 3l: dielectric

constant of liquid). This automatically

leads to the observed invariance of the

local contact angle. Within the electro-

chemical approach, the total electrostatic

energy is nevertheless incorporated into

an ‘effective’ solid–liquid interfacial

tension, which would more appropriately

be denoted as effective drop-substrate

interfacial tension. Treating the insulating

layer as a part of the composite drop-

substrate interface, the electrochemical

ous salt solution in ambient silicone. The insu-

bottom and the EW number increases from left

erences in drop shape close to the contact line in

n from ref. 23.)

2009

approach describes the physics of the

systems only on scales large compared to

its thickness d. In contrast, the electro-

mechanical picture treats the electrostatic

energy in this layer (or equivalently: the

resulting forces) explicitly. Therefore it

describes the physics of the system both

on scales larger and smaller than d.

The electromechanical picture is thus

the more advanced model: it contains the

predictions of the electrochemical picture

as a limiting case (d / 0) and in addition

it provides predictions about the local

properties in the vicinity of the contact

line, which have been verified experi-

mentally (see Fig. 3). As we will see, these

predictions are crucial for understanding

important practical problems such as

contact angle saturation at high voltage

and contact line dynamics.

Another interesting aspect of the elec-

tromechanical approach has been pointed

out explicitly by Jones:25,28 the total force

fel per unit length of the contact line

experienced by the drop is independent of

the surface profile. The reduction of the

(apparent) contact angle is therefore

‘merely’ a characteristic of the response of

conductive liquids to such forces. This

observation implies that contact angle

saturation does not necessarily limit the

maximum force that can be applied to

a drop.

Contact angle saturation inelectrowetting

The EW equation is generally found to be

fairly well obeyed at low voltage. Above

some system-dependent threshold

voltage, however, contact angle satura-

tion sets in and q eventually becomes

independent of the applied voltage (see

Fig. 4a). For generic materials such as

oxide-covered Si with a (nanometre) thin

hydrophobic top coating the saturation

value of q can be as high as 70–80�, which

is a serious limitation in various applica-

tions. Early observations and tentative

explanations of contact angle saturation

have been discussed in ref. 13. A generally

accepted picture of the phenomenon of

contact angle saturation is still lacking,

yet the recent advances discussed in the

previous section provide important clues.

At first glance, one might suspect that

the divergence of the electric field at the

contact line alone would cause deviations

from the EW equation. Yet, the numerical

Soft Matter, 2009, 5, 3377–3384 | 3379

Fig. 4 (a) Contact angle versus applied voltage for a sample 1 mm SiO2 insulator covered by 20 nm

Teflon hydrophobic top coating. Electric breakdown strength Ebd¼ 109 V/m. Symbols: experimental

data; solid line: model curve based on local dielectric breakdown; dashed line: EW equations. (b) and

(c) potential distribution and electric field distribution close to contact line, respectively, at points

indicated by 1 to 4 (left to right) in (a) (reproduced with permission from ref. 18).

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calculations discussed above do not

display any sign of contact angle satura-

tion and the EW equation is obeyed down

to the lowest apparent contact angle

investigated of 5�.15,29 All calculations

done so far are based on two basic

assumptions: first they are limited to two

spatial dimensions (including circular

symmetry) and second they assume

perfect linear dielectric properties of both

the insulating layer and the ambient

medium up to the highest field strength.

Neither of these assumptions is likely to

hold in the presence of diverging electric

fields.

Adding the third geometric dimension

to the problem gives the additional

possibility of transverse instabilities of the

contact line. Early experiments using

rather thick insulating layers showed

a contact angle saturation mechanism

that involved the ejection of satellite

droplets from the contact line.30,31 Berge

and coworkers30 suggested that the

diverging charge density at the three

phase contact line leads to the excitation

of transverse modulations of the contact

line, which eventually become unstable

beyond a certain critical voltage. The

3380 | Soft Matter, 2009, 5, 3377–3384

effect bears similarities with sessile drops

that are vigorously mechanically shaken

until azimuthal oscillatory modes of the

contact line become unstable and emit

satellite droplets.32 In the EW case,

however, a quantitative analysis is still

lacking largely due to the complexity

involved in analyzing the electric field

distribution in a three-dimensional

geometry. Fontelos and Kindelan33

recently presented a mathematical anal-

ysis that led to symmetry-breaking insta-

bilities, however, their model does not

correctly represent the field geometry in

EW. The effect is comparable to the well-

known Taylor cone instability of electri-

fied liquid jets,34 albeit with a reduced

symmetry. Apart from the fundamental

interest, possible applications, e.g. in the

context of microfluidic drop generation,35

make it worthwhile to study the problem

in more detail.

The second (and in practice probably

more relevant) option, the breakdown of

dielectric layers due to the diverging fields

in the vicinity of the contact line, has been

investigated in more detail in a series of

publications by Papathanasiou and

coworkers.16–18 Starting from the

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(numerical) observation of diverging

electric fields close to the contact line,

these authors measured leakage currents

and implemented various approaches of

a strongly non-linear constitutive equa-

tion of the insulating layer leading to local

dielectric breakdown and charge trapping

in the vicinity of the contact line. Volume

elements of dielectric are turned conduc-

tive if the local field exceeds the material’s

breakdown field strength.18 Upon

increasing the voltage, a finger-like

structure of conductive material appears

at the insulator surface ahead of the

contact line. Charge injected into the

structure screens the electric field and

thereby limits the force acting on the

contact line (see Fig. 4). The details of this

procedure depend on the specific consti-

tutive equation and to some extent prob-

ably also to the refinement of the

numerical grid. While there is certainly

room for improvements, the essential

physics of the process seems to be

captured correctly by the model and the

current implementation already allows

for calculating electrowetting curves from

zero voltage up to the saturation regime in

remarkable agreement with experimental

data for a wide range of materials.

It is also interesting to discuss the

contact angle saturation model proposed

by Ralston and coworkers.36,37 The model

acquired considerable popularity because

it is easy to apply and because it produces

saturation angles and voltages in reason-

able agreement with many experimental

data.37–40 Starting from the electro-

chemical picture of EW, the model

predicts that contact angle saturation

should occur when the effective solid–

liquid interfacial energy vanishes at

a certain critical voltage. This idea is

based on the general thermodynamic

consideration that systems with a negative

interfacial tension gain energy upon

forming additional interface and should

therefore not be stable. For liquid–liquid

interfaces, negative interfacial tensions

indeed lead to spontaneous emulsifica-

tion. Yet, the apparent success of the cri-

teron in EW seems fortuitous for several

reasons: (i) absolute values of solid–liquid

interfacial tensions are generally poorly

understood in physical chemistry.41 Using

Zisman’s critical surface tension (as in ref.

36) as a substitute is a widely spread

practice but does not provide a reliable

absolute values for ssl. (ii) Applying the

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criterion to the effective interfacial

tension requires a mechanism destabiliz-

ing the solid–liquid interface. So far no

such mechanism has been proposed for

rigid solid surfaces. Effects like the

contact line instability discussed above

may be cast into a negative effective (line)

tension. However, the corresponding

critical voltage will probably be deter-

mined by other criteria than the vanishing

of Lippmann’s effective solid–liquid

interfacial tension. (iii) Finally, and most

importantly, the discussion in the

preceding section showed that the true

solid–liquid interfacial tension does not

change at all in EW.

Overall, the calculations of the micro-

scopic field distributions have improved

our understanding of the EW effect

tremendously. Approaches based on non-

linearities due to the divergence of electric

fields at the contact line such as the one by

Drygiannakis et al.18 seem to capture the

relevant physics of contact angle satura-

tion and are likely to ultimately resolve

this long standing mystery of electro-

wetting. Improving the dielectric strength

and the chemical inertness of the insu-

lating layers will remain the key approach

for achieving better devices. Yet, the

current models also provide some other

clues of how contact angle saturation can

be postponed. The divergence of the

electric field is weaker the larger qY and

ultimately vanishes for qY / p.15 The use

of (very) thick insulators—which is of

course often undesirable for other

reasons—allows for distributing the elec-

tric field over a wider region and should

thereby also postpone contact angle

saturation. The particularly low satura-

tion angle observed on 50 mm thick

Teflon18,30 supports this idea. Petrin22

recently pointed out that the use of

dielectric fluids instead of electrically

conductive ones removes the singularity

for certain values of qY. In view of the

wide variety of (partially non-conductive)

solvents used in lab-on-a-chip devices,42

this option may be of interest in certain

cases. Similarly, the finite penetration

depth of AC electric fields at either high

frequency or low conductivity, which

have been analyzed extensively in the

context of ‘apparent’ contact angle satu-

ration,43–46 also leads to a distribution of

the electric fields over a wider range,

which should help to alleviate the detri-

mental effects of the local fields. Finally,

This journal is ª The Royal Society of Chemistry

the distinction between the contact angle

saturation and maximum electrostatic

force raised by Jones28 opens up another

possible pathway: voltage pulses with an

amplitude beyond the static saturation

voltage but with a duration shorter that

the typical time required for some non-

linear process to develop may allow for

applying higher average forces than the

maximum continuous voltage.

Open frontiers in electrowetting

Drop and contact line dynamics

A quantitative description of the

dynamics of drop motion and the various

other drop manipulation operations such

as drop splitting and merging has been

a long standing concern in EW research.

The dynamics are controlled by the

balance between the driving electrostatic

forces and viscous dissipation. The latter

includes contributions arising from the

bulk and from the moving contact line.

Depending on the ambient conditions,

dynamic EW is either a problem of two-

phase fluid dynamics (ambient oil) or

a problem of motion of a three-phase

contact line (ambient air).

In the former case, several studies

reported that the ambient oil can

become entrapped underneath the

moving drop48–51 leading to smooth,

lubricated contact line motion. Experi-

ments by Staicu and Mugele52 revealed

that the phenomenon can be understood

along the lines of the classical lubrication

flow problems of Landau-Levich and

Bretherton53 The thickness of the

entrapped oil layer was found to be

hzðdffiffiffi

RpÞ2=3ðCa=hÞ2=3, where R is the

three dimensional radius of curvature of

the drop and Ca ¼ mv/s is the capillary

number (m: oil viscosity; v: contact line

velocity). The experiments also showed

that the entrapped oil layers subsequently

break up into drops under the destabiliz-

ing influence of the electric field following

a spinodal dewetting scenario.52

For the problem of EW-driven drop

motion in ambient air, estimates indicate

that the dissipation from the bulk and

from the moving contact line are of the

same order of magnitude.54,55 EW

dynamics is therefore directly related to

the general problem of contact line

motion, which has been a major challenge

in fluid dynamics since the 1970s.56–58

2009

According to classical hydrodynamics the

viscous dissipation diverges in the vicinity

of the moving contact line. This diver-

gence can only be resolved by some

molecular scale process, such as slip at the

solid–liquid interface, disjoining pressure

effects, or local shear thinning. Alterna-

tively, molecular scale hopping processes

such as evaporation and condensation of

liquid have been invoked to explain the

dynamics and dissipation of moving

contact lines.59,60 In addition to these

intrinsic problems, contact angle hyster-

esis and contact line pinning due to

surface heterogeneity poses additional

challenges (see ref. 61 for a review).

Independent of these fundamental prob-

lems, various computational fluid

dynamics studies investigated the basic

processes of drop motion, splitting, and

control.47,62–66 Qualitatively, these studies

typically reproduce the experimentally

observed behavior, as shown in Fig. 5.

Quantitative agreement, however, relies

on empirical correction factors

accounting for the unknown contact line

friction.

Experimentally, it was recently found

that AC voltage dramatically reduces the

effective hysteresis experienced by a drop

in electrowetting.67 Alternating local

electric fields help to detach the contact

line from pinning sites and thereby

mobilize the drop in the same spirit as

mechanical shaking.68 To the extent that

increasingly complex fluids are being

manipulated on increasingly complex

surfaces, a better understanding of

pinning and depinning on heterogeneous

surfaces will become increasingly impor-

tant.

Internal flows and mixing

Efficient mixing is a general concern in

microfluidics.69 In the typical sandwich

configuration of EW-driven lab-on-a-

chip devices, the no-slip boundary

condition on the top and bottom surfaces

produce a parabolic flow profile deep

inside the drop, which leads to mixing due

to Taylor-Aris dispersion.69 To prevent

the time-reversal symmetry of Stokes

flow from cancelling this effect, it has been

suggested to move drops along e.g.

squared or figure eight-shaped closed

paths rather than linearly translating

them back and forth.70,71 Only

recently, the first PIV based analyses of

Soft Matter, 2009, 5, 3377–3384 | 3381

Fig. 5 Drop splitting process in EW device. (a) Experimental data. (b)–(d) Numerical simulation

for decreasing electric driving force (top to bottom). Note the discrepancy in either the absolute

time scale or the drop morphology between simulation and experiment, which is attributed to

contact line friction. (Reproduced with permission from ref. 47.)

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three-dimensional flow fields have been

presented.72,73 In particular for the

increasingly popular configurations of

sessile drops on a single substrate40,76–80

with a large free surface even the origins

of the internal flow patterns are only

poorly understood. In the case of AC-

EW, Ko et al.73 concluded from the

dependence of the observed flow patterns

on the AC frequency and on the salt

concentration that electrokinetic effects

play an important role at high frequency,

whereas low frequency flows were attrib-

uted to hydrodynamic viscous streaming.

Interestingly, however, the low frequency

flow patterns of Ko et al. display the

opposite orientation compared to earlier

dye visualization experiments77 (see

Fig. 6). While these specific differences

may be resolved within the picture of

hydrodynamic streaming, additional

driving mechanisms for internal flows

such as surface tension gradients arising

from either local heating or from

3382 | Soft Matter, 2009, 5, 3377–3384

concentration gradients of surface-active

species81 as well as tangential electrical

stresses82 deserve more attention in the

future.

Alternative approaches in

electrowetting

Two variants of the classical EW config-

uration have attracted some—primarily

theoretical—attention in recent years.

First, Jones et al.83 reported some time

ago the ejection of a liquid finger from

a liquid drop deposited by two parallel

insulator-covered electrodes separated by

a thin slit upon applying high frequency

AC voltage. They explained this

phenomenon in terms of dielectrophoretic

forces. In a series of recent publications,

Yeo et al.84,85 provided a detailed theo-

retical analysis of this phenomenon.

Coupling the electrostatic and the fluid

dynamic problem in lubrication approxi-

mation, they derived scaling relations

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describing the ejection of the liquid finger.

They point out that the high speed of this

actuation method is related to a body

force due to gradients of the electric fields

parallel to the drop surface. In contrast to

the normal electric fields in the standard

EW geometry, these fields do not diverge

upon approaching the contact line, which

might allow for high speed actuation

without dielectric breakdown.

Second, Monroe et al.86–88 theoretically

explored the use of interfaces between two

immiscible electrolytic solutions (ITIES)

for manipulating wetting properties. In

contrast to conventional EW systems, this

approach is based on two conductive

liquids with different dielectric properties

and conductivity. The drop is in direct

contact with a metal electrode and the

electric potential of the ambient fluid is

also externally controlled. The system is

characterized by two back-to-back elec-

tric double layers at the liquid–liquid

interface. The properties of these double

layers can be controlled by varying the

applied potentials. Substantial variations

of the interfacial energies and hence the

contact angles can be achieved upon

applying as little as a few hundred milli-

volts.89 As a consequence of the complex

behavior of the electrolyte solutions, the

contact angle can either increase or

decrease upon applying a voltage and

extremely low contact angles may—at

least in theory—be achieved.

More experimental research to test the

practical usefulness of these two

approaches as well as the predictions of

the models would be desirable.

Conclusions

In summary, detailed analyses of the

electric field distribution in the vicinity of

the three phase contact line in recent years

greatly improved our understanding of

the equilibrium electrowetting effect. The

invariance of the local contact angle upon

applying a voltage as well as the algebraic

divergence of the electric field close to the

contact line have become widely accepted.

Promising approaches to solve the long

standing problem of contact angle satu-

ration have been formulated based on the

non-linear response of the materials

exposed to these high local fields.

With respect to dynamics, important

open issues remain. In particular, the

dynamics of three phase contact lines and

al is ª The Royal Society of Chemistry 2009

Fig. 6 Visualization of internal flow patterns. (a) Motion of tracer particles inside a sessile drop

under AC voltage at low and high AC frequency. Arrows indicate the flow direction, which reverses

from low to high AC frequency. At intermediate frequencies, no internal flow is observed.

(Reproduced with permission from ref. 73.) (b) Distribution of fluorescent dye due to hydrodynamic

flows in a drop performing electrowetting-driven oscillations at z80 Hz (Reproduced from ref. 74.

For an explanation of the oscillation mechanism, see ref. 75.)

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their interaction with surface heteroge-

neity pose significant challenges reaching

far beyond the realm of electrowetting.

Possible driving mechanisms of internal

flows, such as viscous streaming, Mar-

angoni and electrohydrodynamic flows,

require additional research in the future.

Acknowledgements

I thank Dirk van den Ende, Michel Duits,

Benjamin Cross, Jung Min Oh, Arun

Banpurkar, Siva Vanapalli, Florent Mal-

loggi, Adrian Staicu, Gor Manukyan, and

Hao Gu for their various contributions to

the EW work in Twente, as well as the

MESA+ and Impact research institutes at

Twente University for financial support.

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al is ª The Royal Society of Chemistry 2009