Electrowetting From statics to dynamics

1. Introduction . . . . . . . . . . . . .2. Wetting fundamentals . . . . . . . .

2.1. Contact angle and contact angle hys2.1.1. Contact angle . . . . .2.1.2. Contact angle hysteresis

. . .

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. . .tion .. . .eresis

3.3.1. Why AC? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Advances in Colloid and Interface Science 210 (2014) 212

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Advances in Colloid and Interface Science

j ourna l homepage: www.e lsev ie r .com/ locate /c i sAbbreviations:AC, alternating current; DC, direct current; EWOD, electrowetting ondielectric; HD, hydrodynamic (model);MK,molecular kinetic (theory);A, area (m2); C, capacitanceper unit area (F/m2); E, electric eld strength (V/m); F, force (N); H, drop height (m); H, characteristic drop height (m); L, characteristic length (m); LC, capillary length (m); R, dropwetting radius (m); R, characteristic drop radius (m); R0, initial drop radius; T, absolute temperature (K); U, contact line velocity (m/s); U, characteristic contact line velocity (m/s);3.3.2. Frequency dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.3.3. Hydrodynamic ow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.4. Contact angle saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6V, voltage, applied potential (V); VS, saturation voltage (Vfrequency (Hz); fC, critical frequency (Hz); g, gravitationLS, liquidsolid interfacial tension (N/m); SV, solidvap(Pa s); eq, equilibrium contact angle; , contact angle; A, Corresponding author at: Experimental Interface Phys

615116 2282; fax: +49 615116 2048.E-mail address: bonaccurso@csi.tu-darmstadt.de (E. B

0001-8686/$ see front matter 2013 Elsevier B.V. All rihttp://dx.doi.org/10.1016/j.cis.2013.09.007. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

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3.2.2. Polarity effects . . . .

3.3. AC electrowetting . . . . . . .3.2. DC electrowetting . . . .3.2.1. Contact angle hyst2.2. Wetting dynamics . . . .2.2.1. Fast wetting stage2.2.2. Slow wetting stage

3. Static electrowetting . . . . . .3.1. The YoungLippmann equa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3teresis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5ContentsLongquan Chen, Elmar Bonaccurso Experimental Interface Physics, Center of Smart Interfaces, Technische Universitt Darmstadt, Alarich-Weiss-Str. 10, 64287 Darmstadt, Germany

a b s t r a c ta r t i c l e i n f o

Available online 10 October 2013

Keywords:WettingElectrowettingStatic & dynamic capillary phenomenaElectrocapillarity

More than one century ago, Lippmann found that capillary forces can be effectively controlled by externalelectrostatic forces. As a simple example, by applying a voltage between a conducting liquid droplet and thesurface it is sitting on we are able to adjust the wetting angle of the drop. Since Lippmann's ndings,electrocapillary phenomena or electrowetting have developed into a series of tools for manipulatingmicrodroplets on solid surfaces, or small amounts of liquids in capillaries for microuidic applications. In thisarticle, we briey review some recent progress of fundamental understanding of electrowetting and addresssome still unsolved issues. Specically, we focus on static and dynamic electrowetting. In static electrowetting,we discuss some basic phenomena found in DC and AC electrowetting, and some theories about the origin ofcontact angle saturation. In dynamic electrowetting, we introduce some studies about this rather recent area.At last, we address some other capillary phenomena governed by electrostatics and we give an outlook thatmight stimulate further investigations on electrowetting.

2013 Elsevier B.V. All rights reserved.); Vth, threshold voltage (V); Veff, effective voltage (V); c, coefcient; d, thickness (m); f, frequency (Hz); f0, molecular jumpal acceleration (m/s2); kB, Boltzmann constant; l, slip length (m); t, time (s); , wetting exponent; , surface tension (N/m);or interfacial tension (N/m); , relative permittivity; 0, free space permittivity; , molecular displacement (m); , viscosityadvancing contact angle; R, receding contact angle; , contact angle hysteresis; , density (kg/m3); , conductivity (S).ics, Center of Smart Interfaces, Technische Universitt Darmstadt, Alarich-Weiss-Str. 10, 64287 Darmstadt, Germany. Tel.: +49

onaccurso).

ghts reserved.

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[23,24]. In principle, electrowetting can be applied to drops sitting Natural surfaces are decorated with physical roughness or chemical

3L. Chen, E. Bonaccurso / Advances in Colloid and Interface Science 210 (2014) 212on a bare electrode, or on thin dielectric layer on top of an electrode.However, most of the recent electrowetting studies and applicationsare carried out on dielectric, giving rise to the denition ofelectrowetting-on-dielectric (EWOD).

In this review, we focus on the latest progress on somefundamental aspects of electrowetting. In Section 2, we give a shortdescription of the basics of static and dynamic wetting. Section 3 isdevoted to static electrowetting. We will discuss the basicphenomena in DC and AC electrowetting, as well as the contactangle saturation (CAS) phenomenon. In Section 4, recent resultsabout fast and low speed electrowetting will be presented. Finally,we briey address some other interesting capillary phenomena

moieties. The physical or chemical heterogeneity of surfaces leads todeviations of the contact angle from the one predicted by Young'sequation. Pinning of the contact line of a wetting/dewetting drop due4. Dynamic electrowetting . . . . . . . . . . . . . . . . . . . . .4.1. Fast dynamics of electrowetting . . . . . . . . . . . . . .4.2. Slow dynamics of electrowetting . . . . . . . . . . . . .

5. Other capillary phenomena governed by electrostatics . . . . . . . .5.1. Electro-coalescence . . . . . . . . . . . . . . . . . . . .5.2. Electrically assisted capillary wrapping . . . . . . . . . . .5.3. Electrostatic control of interfacial ow . . . . . . . . . . . .5.4. Electric enhancement of heat and mass transfer . . . . . . .

6. Conclusion and outlook . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction

Wettability is a key parameter to describe the chemicalphysicalproperties of a surface and is usually characterized by a very simplemethod: measuring the angle of contact or wetting angle of adroplet of a test liquid with the surface. Triggered by many industrialapplications, such as coating, printing, cleaning, or friction and wearcontrol, many chemical or physical methods have been developed tocontrol the wettability of surfaces [13]. Eventually, lyophilic,superlyophilic, lyophobic and superlyophobic surfaces can befabricated in laboratory by modifying the surface chemistry andintroducing multiscale physical roughness [13]. Such surfacesmaintain their wetting properties over some time, but do not allowfor an active control of their wettability after being manufactured.In practical applications, however, active control of the wettabilityis more attractive. Indeed, smart approaches such as thermal tuning[4,5], optical switching [6], as well as electrostatic controlling ofcontact angles [7,8] have been developed. Among them, theelectrostatic method is the most popular one due to its real-timeactuation, fast response, long term reliability, and good stability ofthe actuation.

During his works, Lippmann found that applying a voltagebetween mercury and aqueous electrolytes allowed for controllingthe position of the mercury meniscus in a capillary. In 1875, he wasprobably the rst to report this electrocapillary phenomenon, whichis at the foundations of electrowetting [9]. He further proposed aphysical model and developed a number of applications. Later,Mller [10], Frumkin et al. [11], Gorodetskaya and Kabanov [12],Smolders [13], and Nakamura et al. [14] conducted contact anglemeasurements at the mercury/metal-electrolyte interfaces. Theyfound that the contact angle decreased with applied potential, andargued that the decrease of contact angle was due to the change ofinterfacial energy [1015]. However, Lippmann's discovery and theother works did not attract much attention until the 1980s, whenthe term electrowetting was coined and proposed for designingdisplay devices [16,17]. Since then, electrowetting started to developrapidly and nowadays it has been successfully applied in areas likelab-on-chip systems [1820], adaptive optical lenses [21], electronicdisplay technology [17,22], or mixing in microuidic channelsgoverned by electrostatics.2. Wetting fundamentals

2.1. Contact angle and contact angle hysteresis

2.1.1. Contact angleWhen a liquid drop is brought into contact with a solid surface, the

drop spreads on the surface to minimize the free energy of the system.Eventually, the drop comes to rest on the surface in a minimum energystate. If the drop size, R0, is smaller than the capillary length, LC, e.g.R0LC

g

q, with and respectively the surface tension and the density

of the liquid and g the acceleration due to gravity, the gravity does notdistort the spherical drop shape and can thus be neglected [25]. Thiscondition is usually satised in all published electrowetting studies.For chemically and physically homogenous surfaces, the drop inequilibrium adopts a spherical cap shape, as shown in Fig. 1. Theequilibrium contact angle, eq, near the contact line is determined bythe interfacial tensions, LV, LS, and SV at the liquidsolidvaporinterfaces.

coseq SVLS

1

Usually, LV is denoted as for brevity. The above equation iscalled Young's equation, in honor of Thomas Young who expressedit with words in his work published in 1805 [26]. Young's equationcan be derived either from a mechanical perspective [1,3] or froma thermodynamic perspective [27]. eq is a useful parameter tocharacterize the wettability of surfaces, as one can easily relate thecontact radius R to eq with

R R0 sineq4

1 coseq 2

2 coseq

264

3751=3

: 2

Taking the limit as eq 0, we nd R which means the liquidtends to wet the surface completely. While if eq 180, we obtainR0, which reects that the surface repels the liquid extremely.

2.1.2. Contact angle hysteresisFig. 1. Sketch of a drop sitting on a solid substrate in equilibrium.

L is amacroscopic characteristic length and is typically of the order ofthe drop size. l denotes a microscopic slip length of the order of amolecular size. If the surface is very lyophilic, e.g. eq 1, one obtainsthe growth of the spreading radius as a function of time [28,29,39].

R e t1=10 6The above equation is sometimes referred to as Tanner's law [40].

4 L. Chen, E. Bonaccurso / Advances in Colloid and Interface Science 210 (2014) 212to surface heterogeneity causes an advancing contact angle A/areceding angle R. The difference between A and R is dened as thecontact angle hysteresis [1,3,28,29]

AR: 3

The contact angle hysteresis characterizes the homogeneity ofsurfaces. Larger values of correspond to more pronounced surfaceheterogeneities.

2.2. Wetting dynamics

When a drop touches a surface, the initial contact angle is largestand close to 180. Contact leads to a net horizontal capillary force of(cos eq cos ). This force drives drop wetting until equilibrium isattained. Three sources resist drop wetting: (i) the kinetic energy ofthe spreading drop, (ii) viscous dissipation within the liquid, and(iii) contact line dissipation at the drop rim. In recent years, benetingfrom the development of high speed imaging techniques, dynamicwetting has received considerable attention. Many studies showedthat the wetting proceeds in two stages, a fast early stage followedby a slow later stage.

2.2.1. Fast wetting stageFor low viscosity liquids, the spreading velocity is very high just

after a drop touches a solid surface. The Reynolds number incharacteristic (*) experiments, Re 2 UR , compares the balanceof inertial and viscous forces and is larger than unity. is the ratioof the characteristic drop height H and the characteristic dropradius R, and is approximately unity.U is the characteristic velocityof themoving contact line and is of order 1m/s [3034]. is the liquidviscosity. Thus, capillarity drives and inertia resists the fast wettingstage. The change (release) of surface energy is transformed intokinetic energy of the moving drop. Based on this energy balance,Bird et al. found that the spreading radius R grows with time taccording to a power law [31,35].

R ct 4

c is a coefcient, while the exponent is only related to thewettability of the surface. It was experimentally found that takesvalues between 0.5 and 0.25 when eq changes from ~0 to ~110[3133,35,36]. Biance et al. carried out a scaling analysis based ondrop coalescence theory. They obtained a power law dynamics with=0.5 for complete wetting [30], which was also observed byWinkelset al. in molecular dynamics (MD) simulations [34]. Shanahan et al.alternatively derived an inertial drop spreading model and found that takes values between 0.5 and 0.2 [33] depending on eq. However,all these models are at most semi-quantitative and do not capture alldetails of the wetting dynamics.

2.2.2. Slow wetting stageThe inertial wetting stage lasts several milliseconds only, depending

on drop size. After this fast stage wetting crosses into a slow stage inwhich drop spreading is resisted by viscous friction within the liquidand by molecular friction near the contact line. Two types of modelswere proposed, accounting for differentmechanisms. The hydrodynamic(HD) model considers viscous dissipation as the main resisting force.Based on the introduction of a cutoff or slip length near the contactline by Huh and Scriven [37] to get rid of the shear stress singularity,Voinov derived a relationship between the dynamic contact angle and the spreading velocity U [38].

3 3eq 9U ln

Ll

5The spreading could also be dominated by microscopic friction nearthe contact line. In the molecular kinetic (MK) theory, the drop rimmoves via individual molecular jumps activated by thermal energy,with an equilibrium frequency f0 and a displacement distance . Therelation between the spreading velocity and the dynamic contact angleis given by [27,41]

U 2 f 0 sinh2 coseq cos

2kBT

24

35: 7

kB is the Boltzmann constant and T is the absolute temperature. If theterm of sinh in Eq. (7) is small and the surface is very lyophilic, thespreading radius can be simplied to [42]

R e t1=7: 8Blake et al. also combined both the effects of hydrodynamic stress

and molecular friction in the modied molecular kinetic theory [43].Details about these wetting models can be found in a recent review byRalston et al. [44].

3. Static electrowetting

3.1. The YoungLippmann equation

Fig. 2a shows the sketch of a typical electrowetting setup in which athin dielectric layer with thickness d is deposited between a conductivedrop and a at electrode. The insulating layer is few micrometers thickand is mainly used to prevent electrolytic processes at the interfacebetween drop and electrode. When a direct current (DC) voltage isapplied between the drop and the electrode, the contact angle decreaseswith voltage V according to the so-called YoungLippmann equation

cos coseq C2

V2 9

eq is the equilibrium contact angle with zero applied voltage and isdetermined by Young's equation. C is the capacitance per unit area. Ifwe treat the capacitor between the drop and the electrode as a platecapacitor, C = 0d/d. d and 0 are the permittivities of the dielectriclayer and of vacuum, respectively. For alternating current (AC) voltage,the root mean square (rms) value of the voltage or effective voltage Veff2 , is used instead of V2. The YoungLippmann equation can be derived

by several approaches, as summarized, e.g., by Mugele and Baret [7]. Arigorous thermodynamic derivation of Eq. (9) was also presented byBormashenko recently [45]. These theories can be understood from twoperspectives:Fig. 2. (a) Standard electrowetting setup. (b) Schematic plot of electrowetting curve.

5L. Chen, E. Bonaccurso / Advances in Colloid and Interface Science 210 (2014) 212 Thermodynamic or electrochemical perspective. The classic model forelectrowetting was proposed by Lippmann [9]. In his experiments, avoltage was directly applied between the electrode (mercury) and theaqueous electrolyte. An electric double layer builds up spontaneouslyat the liquidsolid interface, with charges of opposite polarity beingrepelled from the interface. Thus, the liquidsolid interfacial energy,LS, decreases along with the new equilibrium contact angle, i.e. thesurface becomes more hydrophilic [46]. In EWOD, the thickness of thedielectric layer is signicantly larger than that of the electric doublelayer [16,47], and hence electrostatic energy stored in it is the mainsource to decrease LS.

Electromechanical perspective. Electrowetting could also be understoodconsidering the forces exerted on the liquid near the contact line, asproposed by Jones et al. [48,49]. When a voltage is applied, the electriceld near the contact line attracts the free charges as well as thepolarized dipoles, which gives rise to a Maxwell stress on the liquidair interface. In order to balance this stress, the liquidair interfacemust decrease its curvature to reduce the Laplace pressure. Eventually,a smaller apparent contact angle depending on the magnitude of theapplied voltage is attained.

A large amount of experimental studies showed that the YoungLippmann equation can well predict the contact angle when the voltageis smaller than a critical value VS [7,8,23,47]. When V VS, theelectrowetting contact angle does not increase with applied voltage(Fig. 2b), which is the effect known as contact angle saturation (CAS).The physics underlying CAS is not fully clear yet. A detailed descriptionof the recent progress on theories about CAS is presented in Section 3.4.

3.2. DC electrowetting

3.2.1. Contact angle hysteresisThe phenomenon of contact angle hysteresis also plays a role in

electrowetting [5052]. Typically, the contact angle hysteresis has twomain effects: rst, electrowetting can start only when the appliedvoltage is larger than a threshold value Vth [5356]; second, the contactangle hysteresis leads to different contact angles with the same appliedvoltage, depending if the voltage is increasing or decreasing. This isreferred as irreversibility or hysteresis of electrowetting [50,57].

The existence of the threshold voltage Vth can be explained byaccounting for contact line pinning. Due to the natural heterogeneitiesof real surfaces, the equilibrium contact angle has a value betweenthe receding and the advancing contact angle, e.g. R b eq b A.When electrowetting is initiated, the electrostatic force wants toreduce the contact angle. However, the contact line will move onlyif the electrostatic force exceeds the pinning force [50,51,5860].Balancing these two forces, Frchette et al. predicted the thresholdvoltage by [50]

Vth 2C

coseq cosA r

: 10

Thus, the threshold voltage can be decreased by using, e.g., lowcontact angle hysteresis surfaces. Until then, the lowest thresholdvoltages in electrowetting were reported in the range of 1520 V [19].In their paper, Frchette et al. showed that nearly no threshold voltageexisted on an oil-impregnated polydimethylsiloxane (PDMS) surfacewith only 1 contact angle hysteresis [50]. Eq. (10) also indicates thatVth can be reduced by decreasing the interfacial tension . This wasachieved by changing the uid around the drop from air to a liquid, asliquidliquid interfacial tensions are usually smaller than liquidairinterfacial tensions [55,57,61]. Moreover, the contact angle hysteresisin liquid/liquid/solid systems is also smaller than in liquid/solid/airsystems, as liquidliquid friction is much smaller than liquidsolid

friction [61].Similarly, the advancing/receding contact angle as the dropspreads/recedes with increasing/decreasing applied voltage can bemodied by considering the effects of the contact line pinning force[50,58]

cosA or R cosV0A or R CV2

211

where A or RV = 0 is the advancing/receding contact angle measured withzero voltage applied. As the contact angle hysteresis is independent ofthe applied voltage [5052], reversible electrowetting could be achievedwith low contact angle hysteresis systems such as in the liquid/liquid/solid system [57,61] or on superhydrophobic/superlyophobic surfaces[62].

3.2.2. Polarity effectsAccording to the YoungLippmann equation in Section 3.1, the

contact angle decreases with the applied voltage following the sameparabolic curve regardless of the polarity of the voltage. However,early studies showed different polarity effects of electrowetting ondifferent materials. On one side, when Parylene was used as aninsulating layer, the change of contact angle was independent ofpolarity [6365]. On the other side, when Teon was used severalgroups reported a strong deviation from the theory with a positiveapplied voltage [6668]. Since the liquids (water or aqueous electrolytesolutions) used in experiments were similar, authors attributed thepolarity effects to material properties [6668]. Werner and co-workersinvestigated the interfacial charge on Teon in aqueous electrolytesolutions [69]. They found that hydroxyl ions (OH) have strongerinteraction to the Teon surface than the hydronium ions (H3O+) dueto the presence of oxygen atoms in Teon [66,70]. As a result, thecapacitance of the liquidsolid interface is better described by both adielectric layer and an electric double layer, rather than by only adielectric layer, as done in the YoungLippmann model [68,71], and itcan explain the polarity effects of electrowetting on Teon surfaces.

In standard electrowetting experiments or applications, water andaqueous electrolyte solutions were normally used [18,19,5068,70,71].Although water has useful solvent properties, its poor thermal stability,it tendency to evaporate, and its corrosion ability lead to signicantlimitations in microuidic applications. Ionic liquids, as rst pointedout by Ralston et al., are more promising for robust applications due totheir unique properties: high thermal stability, non-ammability, andno signicant vapor pressure [72]. In the same paper, Ralston et al.showed polarity effects and related them to the different properties/sizes of cations and anions [72]. A systematic study was carried outlater by Armstrong and coworkers. They found that anions or cationswith smaller size have stronger inuence on the asymmetry of theelectrowetting curve since they interact more strongly with the Teonsurface than larger anions or cations do [73].

As discussed above, polarity effects in electrowetting are recognizedto be most probably due to molecular processes near the liquidsolidinterface, which cannot be captured by simple optical instruments.Thus, MD simulations could help in understanding the physicalmechanisms. Luzar and co-workers studied the electrowetting ofwater nanodrops on apolar hydrophobic surfaces, such as grapheneor parafn [7477]. They observed that the electrowetting contactangle is sensitive to the polarity of an electric eld directedperpendicular to the surface. The explanation was that water iseasier to be polarized along the outgoing, rather than along theincoming, electric eld to the surface [7476]. However, in thepresence of any salt ions, the strong afnities of them towards thesurface increase the screening of the electric eld, and eventuallysuppress the polarity effects caused by different electric responses

of hydrogen bonding [78].

3.3. AC electrowetting

3.3.1. Why AC?Inmostmicrouidic electrowetting systems [19], alternating current

(AC) voltage is applied because of following benets:

Reduction of contact angle hysteresis. As discussed above, the contactangle hysteresis exists in DC electrowetting due to pinning effects[5052]. In contrast, using AC voltage electrowetting continuouslyperturbs the force balance at the contact line and essentially leads tothe depinning of the contact line from the surface [51,58]. Eventually,the contact angle hysteresis is smaller in AC than in DC electrowetting[51,58,79].

6 L. Chen, E. Bonaccurso / Advances in Colloid and Interface Science 210 (2014) 212 Delay of contact angle saturation. Many experimental results showedthat the contact angle saturation occurs at a smaller contact angleand at a higher effective voltage for AC rather than DC electrowetting,in both liquid/solid/air [80,81] and liquid/liquid/solid systems [8284].Hong et al. provided the explanation that the effective electric eldstrength is reduced by increasing the frequency, and that this canlead to a delay of the dielectric breakdown [85]. The underlyingphysics of delayed saturation in AC electrowetting is still not fullyunderstood.

Reduction of ion adsorption. Another possible reason leading toirreversibility or a large contact angle hysteresis in DC electrowettingis ion adsorption at the liquidsolid interface. It was reported that theion adsorption at the liquidsolid interface was reduced by applyingAC instead of DC voltage [86,87].

3.3.2. Frequency dependenceThe YoungLippmann equation is only valid for AC electrowetting

when the liquid can be treated as a perfect conductor. This holds if theAC frequency is larger than the resonance frequency of sessile drops(typically of few hundreds hertz) and is far smaller than a criticalfrequency fC (typically of 10100kHz) [7]. The electrowetting efciencydiminisheswith frequency increasing beyond the upper limit, while it isdependent on the frequency between the two limits [48,49,58,85]. Thegeneral AC electrowetting behavior can be captured by the analogywith an equivalent electric circuit, as shown by Mugele and Baret [7](Fig. 3). The drop is represented as a resistor and a capacitor, and thedielectric layer is treated as another capacitor. The electric double layersformed at the liquid-dielectric layer or at the liquid-counter electrodeinterfaces are not considered. At low frequency ( fC), thedrop behavesmore like a conductor rather than an insulator, which satises theassumption for YoungLippmann's equation. However, at very highfrequency (fC), the drop behaves more like an insulator, whichleads to the breakdown of electrowetting. The critical frequency isrelated to the physical properties of the drop as well as to its geometry[7].

f C e d lk0 d lk 12Fig. 3. The equivalent circuit for AC electrowetting.d, l and l are the conductivities of the dielectric layer and liquidand the permittivity of the liquid, respectively. k ~ d/R is the size ratioof the dielectric layer and the drop. For deionized water, fC is typicallyfew kHz, which matches with experimental observations [48,49,58].

The above discussion qualitatively introduces the frequencydependence of AC electrowetting, while a quantitative understanding isstill missing. Hong et al. carried out a numerical investigation of ACelectrowetting [85]. They found that the electric eld strength wasremarkably reduced in the dielectric layer near the contact line, whichmay lead to a decrease of the electrostatic contribution to the wettingtension. Their numerical results were consistent with experiments. Mostrecently, Klarmanet al. proposed amodel based on a similar congurationas shown in Fig. 3 [88]. They also accounted for the effects of the electricdouble layer at the immersed counter-electrode and discussed this effecton AC and DC electrowetting. Among others, they concluded that theeffect of the polarization of the counter-electrode could be neglected inmost practical cases, since the area of the counter-electrode is usuallymuch smaller than the contact area between the drop and the solid.

3.3.3. Hydrodynamic owIn recent years, researchers have reported hydrodynamic ows

inside drops in AC electrowetting [24,8993]. The ow patterns aredependent on the frequency of the applied voltage as well as on theconductivity of the liquid (Fig. 4a). In the low frequency range (typicallyup to 1kHz), the ow forms two axisymmetric toroidal vortexes whosecenter is not visible [90,93] (Fig. 4b). The low frequency ow is ratherunstable and is very sensitive to the counter-electrode position. Incontrast, in the high frequency range (larger than few tens of kHz),the ow is highly stable and the vortex center is always located aroundthe counter-electrode [90]. Also, the vortex direction of the lowfrequency and high frequency ows are different (Fig. 4b & d), whichindicates that the ow generation mechanisms are different. Forintermediate frequencies, no ow is observed in the drop (Fig. 4c).

The low frequency ow is mainly driven by the oscillations of thedrop [90]. The oscillation of the contact line caused by AC potential canresult in a hydrodynamic viscous streaming inside the drop. However,the low frequency ow observed is not as steady as the viscous ow.Moreover, the direction of the low frequency ow in air [90] is oppositeto the one observed in mixing experiments of water/glycerol drops insilicone oil ambient [24,93]. Both phenomena point out that someadditional mechanisms may inuence the hydrodynamics. Based onthese experiments in oil, Mugele et al. suggested that the capillaryStokes drift induced by the capillary wave drives the internal ow inthe drop [93,94]. These studies pointed to more open questions, likehow do the viscosity or the density of the atmosphere surrounding thedrop inuence ow pattern and ow stability inside the drop.

The high frequency ow is induced by the so-called electrothermaleffects [89,91]. With high frequency AC voltage applied, the liquidbehaves like an insulator as there is not sufcient time to completelycharge the capacitor of the dielectric layer [7,88]. As a result, the electriceld inside the drop leads to Joule heating of the liquid, giving rise toa gradient in conductivity and permittivity [89,91]. Eventually, thevoltage applied on the electrically inhomogeneous drop generates anelectric body force resulting in an internal ow.

3.4. Contact angle saturation

In the past years,manymodels or hypotheses have been proposed toexplain the contact angle saturation, as reviewed by Mugele [7,23], andrecently by Chevalliot et al. [80], Koopal [95] and Sedev [96]. Here, webriey recap the latest progress:

(1) Zero interfacial tension. According to the classical thermodynamicmodel of electrowetting, the change of the contact angle isentirely ascribed to the reduction of the liquidsolid interfacial

tension (LS). Ralston and coworkers suggested that LS should

ic

7L. Chen, E. Bonaccurso / Advances in Colloid and Interface Science 210 (2014) 212not be less than zero to keep thermodynamic stability [47,97].Thus, the thermodynamic limit with LS=0 causes the contactangle saturation. They showed a consistence between theirmodel and experimental results [47,97]. Berry and coworkersconrmed this model by low voltage electrowetting in bothliquid/liquid/solid systems and liquid/solid/air systems [98,99].One big challenge to verify this model is that it is hardly possibleto directly measure liquidsolid interfacial tensions. However,recent measurements of thin lms [100] and adhesion force[101] showed no major change of the liquidsolid interfacialtension upon applying an external potential. Other groups alsonoticed that the zero interfacial tension theory does not predictreliably the saturation contact angle, e.g. with cos S = SV/[80,82,83]. Moreover, Mugele and co-workers numericallyfound that the electrostatic force does not affect the interfacialtensions force balance at the contact line [102], and they furtherexperimentally observed that the microscopic contact anglealways equals Young's angle [103]. This was later conrmedby MD simulation by Liu et al. [104]. Till now, no studiesconsidered the possibility of a signicant change of theliquidvapor or solidvapor interfacial tensions uponapplying an electric potential. Recent work, however, showedthat the surface tension of water decreased remarkably byapprox. 50% upon electrically charging the water surface[105] even if the external potential was in the kV range; or

Fig. 4. (a) The inuence of electrolyte concentration on the frequency range of hydrodynam(c) and 128 kHz (d). The electrolyte concentration in (b)(d) is 103M.Reproduced with permission from Ref. [90].that the solidvapor and solidliquid interfacial energy canbe reduced upon weak electron irradiation [106] causing areversed electrowetting effect, i.e. increasing the contactangle upon irradiation. These results suggest that electriccharges can affect either of the interfacial tensions playing arole in electrowetting or in contact angle saturation.

(2) Dielectric breakdown. Near the contact line, the electric elddiverges as the interface curvature is extremely small. The electriceld may locally become so strong that it exceeds the dielectricbreakdown strength of the insulating layer [64]. As a result, thedielectric layer locally breaks down [107,108]. The chargestransferred to the dielectric layer lead to screen the electric eld,which eventually reduces the electrostatic contribution andcauses electrowetting saturation. This hypothesis was proposedby Drygiannakis et al. who showed a good match between theirexperimental results and theory [107]. Similar conclusions werealso drawn by Berry et al. based on their experiments on thinamorphous uoropolymer lms [98,109]. However, Chevalliotet al. recently reported experimental results on DC electrowettingshowing that the saturation contact angle is invariant withrespect to a number experimental parameters, among which arethe electric eld strength, the interfacial curvature near thecontact line, or the type of dielectric used [80].

(3) Contact line instability. In early AC electrowetting studies, Valletet al. observed an instability of the contact line close to thecritical (saturation) voltage for low conductivity liquids such aswater [110]. They found that microdrops spontaneously ejectedfrom the contact line as the voltage was larger than a criticalvalue. This phenomenon was reproduced later by Mugele andHerminghaus with various liquids [111] and was attributed tothe diverging of charge density around the contact line. Whilethe applied voltage is larger than a critical value, the Maxwellforce exceeds the capillary force near the contact line, whichleads to emission of (charged) satellite droplets. This instabilityat the contact line was identied as a possible cause for contactangle saturation [110,111]. Park et al. also suggested that theinstability with droplet ejection is preceded by a contact anglereduction and the extrusion of a thin layer from the edge of thedroplet [112,113]. However, these models cannot explain thesuppression of the instability by increasing the conductivity ofthe liquids, e.g. with salts [110,111]. As contact line instabilitydoes not arise in DC electrowetting, it hence may not capturethe actual physics of contact angle saturation.

(4) Gas ionization or insulating uid charging.Vallet et al. also reportedair ionization around the contact line for voltages larger than thesaturation voltage and suggested that it could be responsible for

ows with V=80V and the three typical ow patterns with frequency of 1 kHz (b), 18kHzcontact angle saturation [110]. Indeed, it was experimentallyfound that the contact angle of a drop can be controlled bycharging its surface via a corona discharge [114,115] or byelectrons [106]. As corona discharge or air ionization is dependenton relative humidity [115], one possible way to validate thishypothesis would be to check whether the relative humidity ofthe surrounding air inuences contact angle saturation. On theother hand, corona discharge is not applicable to liquidliquidsolid electrowetting systems. In such systems, Chevalliot et al.suggested that it could be possible that the insulating uid ischarged due to ejection of charges or satellite drops from theconducting drop [80]. However, this hypothesis calls for furtherexperimental evidence.

(5) Minimization of the electrostatic energy. Lin et al. proposed atheoretical model based on an energy balance [116] instead of aforce balance, as is used in the derivation of the YoungLippmannequation. In AC electrowetting, especially at higher voltages and ina well-dened frequency range, a strong hydrodynamic owdevelops inside the drop [24,8993]. The ow causes additionalenergy dissipation and the dissipated energy increases with theapplied potential. Eventually, this leads to aminimumelectrostatic

contribution to the total energy of the system when VVS [116].However, this model fails to explain the contact angle saturationof DC electrowetting, as no internal ow develops there, anddoes not reproduce the correct dependence cos V2 for V b VS.Klarman and Andelman also developed a model based on energydissipation [88], and accounted for the electrostatic energy of theelectric double layer around the counter-electrode. This is areasonable approach, as the electric eld is always stronger nearthe electrode than that in the bulk drop [89,91]. They found aminimumof the electrostatic energy contribution to the saturationvoltage for bothDC andAC electrowetting systems. Thiswas basedon the assumption that the capacitance C is not constant butfunction of and has a minimum at VS. However, this assumptionis not based on rst principles and would require a rigorous proof.

(6) Tailor cone. Most recently, Chevalliot et al. carried out a systematicstudy of all physical and chemical parameters which may lead tocontact angle saturation according to the above models [80].Based on their experimental results, they state that there areparallels between the phenomena of Tailor cone formation andcontact angle saturation. This, if conrmed, could provide a newdirection for a universal theory of the saturation problem inelectrowetting.

4. Dynamic electrowetting

4.1. Fast dynamics of electrowetting

The early wetting stage after a drop touches a surface runs very fast,as discussed in Section 2.2. This type of electrowetting is ubiquitous asmost surfaces are naturally charged, which is the reason except forwell controlled conditions that there is always difference of potentialbetween drops and surfaces before theywet each other. These naturallyarising excess surface charges need to be redistributed between dropand surface upon meeting, and thus play a role in most spontaneouswetting processes like rain drops hitting the soil or ink drops wettingpaper. Stone and co-workers were the rst to investigate the fastdynamic wetting of sessile drops just after contact with a surfaceunder an applied electric potential [35]. They found that the dropspreading radius grows with a power law with a larger exponent, 2/3. Without applied potential = 1/2 on completely wettingsurfaces. The effect of the applied potential was to deform the sphericaldrop into a conical shape close to the point of contact. The authors set upan energy balance accounting for this new contact geometry andderived a power law with an exponent of 2/3. Exponents larger than1/2 were also observed by Chen et al. [117] in experiments. However,exponents were not constant, but a function of the applied potential,of surface wettability, and of electrolyte concentration. Similar to staticelectrowetting, where the contact angle saturates when the appliedvoltage is larger than VS, they found a saturation of the wettingexponent for aqueous electrolyte drops with low salt concentration.For high electrolyte concentrations, no saturation was observed at the

ic

8 L. Chen, E. Bonaccurso / Advances in Colloid and Interface Science 210 (2014) 212Fig. 5. Typical experimental congurations for dynamic electrowetting setups. (a) DynamIn many applications, such as lab-on-chip, electrowetting dynamics isof great interest as it controls the response timeof the devices [19]. Duringthe wetting process, the dynamics is determined by the energy balancebetween the driving and the resisting forces [28,29,39]. The drivingforce of the spreading drop is always the change of surface energy,which is related to the difference between the initial and equilibriumcontact angle. The resisting force could be the kinetic energy of themoving drop [3033], the viscous dissipation in the vicinity of themovingcontact line [28], or the microscopic dissipation of the molecular jumps[67]. In electrowetting systems it is thus expected that the addition ofelectrostatic energy to the energy balance will modify the dynamics ofspreading. In literature, many experimental congurations have beenapplied to study the dynamics of electrowetting, as shown in Figs. 2a & 5.capillary rise experiments.voltages applied (up to V 1000 V). Chen et al. modied Stone's earlymodel for partial wetting [31] by adding the contribution of theelectrostatic energy stored in the electrostatic double layer near theliquidsolid interface as a driving force. The proposed model can explainthe experimental observations. MD simulations conrmed that theelectric double layer is formed in a time scale of fewhundred picoseconds[117], which satises the assumption that the electrostatic double layerexists during the fast wetting process (typically, ~10ms). However, thesaturation of the wetting exponent in dependence of salt concentrationand applied potential is still an open question.

The inertial wetting stage was also observed in the MD simulationsof the early wetting of nanodrops [117]. However, the electrostaticenergy did not enhance the wetting exponent here. One plausible

wetting experiments with a spreading sessile drop. (b) Wilhelmy plate method and (c)

9L. Chen, E. Bonaccurso / Advances in Colloid and Interface Science 210 (2014) 212explanation is that the electrostatic double layer is not yet fully formedin this short period. In fact, the ion migration time needed to form theelectrostatic double layer near the liquidsolid interface by applying apotential was ~500 ps, which is two times longer than the inertialwetting time [117]. Thus electrostatics does not inuence the earlyspreading of nanodrops, but it does for their later (viscous) wettingand for their equilibrium contact angle.

4.2. Slow dynamics of electrowetting

The electrostatic effects on the viscous stage of dynamic wetting aredifcult to investigate experimentally with a conguration as in Fig. 5a,since the drop detaches from the needle during this stage. Losing contactwith the needle (which also acts as counter-electrode) leads to an opencircuit conguration. Alternatively, MD simulations can be applied toinvestigate the slow electrowetting. It was found that wetting follows apower law R ~ t0.1 without applied electric eld [117] which isconsistent with the HD model [28,29,39]. With an applied electric eldof 0.1 V/nm the wetting exponent was larger and the wetting law wasR ~ t0.15 [117]. Similar wetting exponents from MD simulations werealso obtained by Yuan and Zhao [118]. Despite these preliminaryndings,there is still a lack of knowledge on the effect of an applied electricpotential on slow electrowetting dynamics. Another unsolved issue isthe inuence of the electrolyte concentration on slow electrowettingdynamics.

Most studies of dynamic electrowetting in literature were carried outwith the standard conguration shown in Fig. 2a, with the needle(counter-electrode) permanently inserted in the drop for applying theelectric potential. The driving force due to the electrostatic contribution is

F cosEeq coseq

: 14

eqE is the new equilibrium electrowetting contact angle that is afunction of the applied voltage. This force is compensated by viscousdissipation or contact line friction during the spreading. Decamps andDe Coninck modied the MK theory with this electrocapillary force andapplied it to spontaneous spreading experiments of glycerol drops onTeon [119]. They found that the contact line friction was constant overa large range of applied potentials. Ralston and co-workers studied thedynamic electrowetting of various ionic liquids in liquid/liquid/solidsystems [82,83] and liquid/solid/air systems [120]. They used both HDmodel and MK theory to interpret their data. They found that viscousdissipation dominates the dynamics when the contact angle and contactline velocity are small, while the MK theory was more suitable to explainthe dynamics at high contact angles and with high contact line velocity[83,120]. They also showed that the equilibrium frequency of molecularjumps decreased with liquid viscosity, which indicates that it is moredifcult for liquid molecules with higher viscosities to move from oneadsorption site to another since the cohesion force between themoleculesis much stronger. Very recently, Hong et al. reported that liquid viscosityhas a weak effect on electrowetting velocity over a broad range ofviscosities (from approx. 1 to 200mPa s) [121]. McHale and co-workersinvestigated the dynamic dielectrowetting of dielectric liquids[122,123]. In their paper, they modied the HD model and found thatwhen the applied voltage was larger than a threshold value the wettingexponent increased with the voltage [123]. Yuan and Zhao studied thedynamic electrowetting of cylindrical water nanodrops with MDsimulations [118]. They observed a power-law growth of thespreading radius with time and an increase of the wetting exponentwith the electric eld. When a critical value of the eld strength wasreached, the exponent saturated similarly to the saturation found instatic electrowetting [7,23].

Dynamic electrowetting studies were also carried out with theWilhelmy plate conguration (Fig. 5b). Schneemilch et al. studied the

electrowetting of a Teon-covered rod and applied the MK theory tot their data. They showed that the applied potential controlled thewettability of the surface and that average molecular displacement, ,decreased with the applied potential [124]. Puah et al. applied a similarmethod to investigate the inuence of the electric surface charge onwetting dynamics [125]. Also there, MK theory was applied. This timeit was found that the equilibriumdisplacement frequency, k0, dependedon the applied potential and was determined by the charges at theliquidsolid interface, while did not show a signicant relation tosurface charge density. The values of were determined mainly by thespacing of the adsorption sites on the solid surface. This was consistentwith previous work of the group using a standard electrowettingconguration [82,83,120]. Blake et al. modied the MK theory byintroducing the actual capillary force in Eq. (14) [126]. However, theyfound that both k0 and were independent of the applied voltage.This brief presentation of experimental results is just to show that alsoexperiments performed with different congurations and materialsare not always in agreement, and that the cause of disagreement is notyet clear. On the other hand, it becomes increasingly clear that MDsimulations are now at a level that they can well capture the processesat the scale of the contact line [127]. They represent thus a promisingtool for exploring the inuence of external potentials on moleculardisplacements of the contact line in particular and of the electrowettingprocess in general.

In recent years, electrostatic assisted ow in capillaries ormicrochannels attracted quite some attention because of envisionedapplications in microuidics and lab-on-chip applications (Fig. 5c).Wang and Jones proposed a hydrodynamic model to describe theelectrowetting-induced capillary rise in a millimeter-sized plane-parallel channel [128]. According to this model, there is a criticalpotential below which contact line friction dominates over viscousdissipation, and above which these effects are reversed. However,when the channel size shrinks to several tens of micrometers,Herminghaus and co-workers showed that viscous dissipation alwaysdominates the electrowetting dynamics [129131].

5. Other capillary phenomena governed by electrostatics

5.1. Electro-coalescence

When two drops of the same liquid come into contact, they mergewith each other to minimize the surface energy. Drop surface chargesor externally applied potentials can favor or in some cases delay coalescence [132,133]. If the drops are oppositely charged, non-coalescence was observed when the electric eld was larger than acritical value EC (Fig. 6). The failing of coalescence can be explained byconsidering the local pressure at the drop apex during coalescence[132,134]. Exposed to an electric eld, the drop deformed into a conicalshape upon approaching the oppositely charged interface. The apertureangle of the cone depends on the eld strength. If the cone angle islarger than 31, the local curvature in the liquid thread results in sucha high pressure that prevents coalescence. A similar phenomenon wasalso observed in the coalescence of a drop with a at solid surface[117]. When the electric eld was below the critical value EC, theimpinging drop partially coalesced with the interface [135138]. Thecoalescence was only partial, since a daughter drop was ejected andmoved away from the interface, as it acquired an opposite charge duringcontact. The size of the daughter drop is determined by electrostatic andcapillary forces [136].

5.2. Electrically assisted capillary wrapping

It was recently demonstrated by several authors that capillary forcescan be used to fold thin lms and to wrap them around droplets[139141]. In order to achieve a reversible wrapping, an additional forceis needed to oppose the capillary folding force. One way is using the

electrostatic force. Pineirua et al. controlled the folding and unfolding of

the

10 L. Chen, E. Bonaccurso / Advances in Colloid and Interface Science 210 (2014) 212capillary origami by varying the unfolding torques with an external DCvoltage [142]. The authors showed that this technique can be used toassemble small scale three dimensional soft structures. Zhao and co-workers reported a similar effect using low frequency AC voltages [143].

5.3. Electrostatic control of interfacial ow

The electrostatic force can also be used to control interfacial ows, asit deforms the shape of a drop or a rivulet. Lee et al. transferred theelectrostatic energy into the surface energy by applying a voltage tospherical drops sitting on superhydrophobic surfaces [144]. If theincreased surface energy overcomes a critical barrier, the drop can beinduced to jump off the surface. The voltage for making a 5 l waterdrop jumpoff is approx. 100V. The authors also showed that it is possibleto transfer drops between two parallel plates, which is envisioned to ndapplications in three-dimensional digital microuidics. Bormashenkoet al. investigated the deformation of liquid marbles under electric eldand found that liquid properties inuence the deformation [145].When a composite liquid marble was exposed to a sufciently highelectric eld, the highly polarizable drop climbed on top of the lowpolarizable drop to minimize the total energy of the system. Noblinand Celestini proposed a newmethod for controllingwater jet dynamics.Applying an AC voltage between the metallic nozzle generating the jetand a metallic electrode below a dielectric polymer layer, they showedthat they could control the reection angle of the jet, or even to

Fig. 6. Inuence of an electric eld on drop coalescence: below a critical eld strength ECinterface. The scale bar is 0.5mm.Reproduced with permission from Ref. [132].completely prevent bouncing. For water, the authors determined amaximum threshold frequency of approx. 1.5 kHz above which theeffects disappear, since the liquid starts behaving like a dielectric [146].Very recently, Yun et al. presented an experimental and numericalstudy about the prevention of drop rebound from solid surfaces byelectrostatic charging of the drops. Electric charges were transferred towater droplets while they fell through variously shaped ring electrodes.Such an electrostatic charging affected drop oscillations and thusinduced a kinetic energy dissipation, which in turn reduced or evensuppressed drop rebounding [147]. Most recently, the electrostaticforces were also applied to suppress the Leidenfrost effect [148]. Byapplying an electric eld between a Leidenfrost droplet and the heatedsubstrate onwhich it was levitating, the vapor layer thickness decreased.Eventually, a millimeter-sized drop contacted the heated substrate withan applied voltage of approx. 40V.

5.4. Electric enhancement of heat and mass transfer

Many authors also reported that the heat and mass transfer can becontrolled by applying an external electric eld. Takano et al.experimentally studied the evaporation of various drops of liquids attemperatures exceeding the Leidenfrost temperature [149151]. Theyfound that the evaporation was enhanced under an applied eld, as theeld induced interfacial instability leading to direct contact between thelevitating drop and the heated substrate [150]. They concluded that theenhancement was more remarkable for polar liquids than for non-polarliquids, as charge relaxation time on them was much shorter [150,152].Recently, Butt and co-workers calculated that the presence of an electriceld can reduce the saturation vapor pressure and lead to a eld-induced condensation of, e.g., water [153]. This explains the anodicoxidation at the nanoscale in dependence of relative humidity [154,155].

6. Conclusion and outlook

In the last 10years the topic of electrowetting spawned an increasingnumber of theoretical, numerical, and experimental works. A good dealof fundamental and especially technological issues has been addressedand solved. The YoungLippmann equation, despite its simplicity, isable to quantitatively describe the physical processes and to predictthe wetting behavior of most systems most of the time. The unboundcreativity of researchers, however, continuously nds new ways ofcombining capillary and electric forces with new material propertiesand system geometries. The YoungLippmann equation can thus notaccount for all new observed phenomena. Some issues remain to besolved, most important being the understanding of the saturationpotentials in static and in dynamic electrowetting, of the molecular

drop coalesces with the interface, and above EC the impinging drop rebounds from thetransport processes in the bulk and at the interfaces associated withapplying electric potentials to various liquids, and of the ionic andelectrochemical processes taking place at the surface of the electrodes.

The natural contact angle hysteresis inherent to real surfaces leadsto poor controllability and sometimes to the irreversibility of theelectrowetting process. Controllability could be improved either usingliquid/liquid/solid systems, by applying AC instead of DC potentials, orby using superhydrophobic/superlyophobic surfaces. Polarity effects inDC electrowetting, generating a non-symmetric wetting behavior forpositive and negative voltages, have been found to be most probablycaused by molecular processes in the liquids. So the use of special ad-hoc liquids is recommended in certain applications. AC voltage is appliedmore andmore in electrowetting, as it can overcomemany disadvantagesof DC electrowetting. However, additional phenomena arise and setlimitations for the applicability, such as the frequency dependence ofthe conductivity of the liquid, or the generation of hydrodynamic owsinside the liquid. Such side effects need also to be considered in designinglab-on-chip devices. Saturation, referring to the existence of a criticalthreshold voltage above which the electrowetting effectiveness does notfurther increase, remains a challenge for all electrowetting theories.Since saturation is most probably dominated by microscopic interfacial

11L. Chen, E. Bonaccurso / Advances in Colloid and Interface Science 210 (2014) 212processes, molecular dynamics simulations could represent a useful toolfor triggering novel investigations. First papers in this areas appeared,but more are required.

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Electrowetting From statics to dynamics1. Introduction2. Wetting fundamentals2.1. Contact angle and contact angle hysteresis2.1.1. Contact angle2.1.2. Contact angle hysteresis

2.2. Wetting dynamics2.2.1. Fast wetting stage2.2.2. Slow wetting stage

3. Static electrowetting3.1. The YoungLippmann equation3.2. DC electrowetting3.2.1. Contact angle hysteresis3.2.2. Polarity effects

3.3. AC electrowetting3.3.1. Why AC?3.3.2. Frequency dependence3.3.3. Hydrodynamic flow

3.4. Contact angle saturation

4. Dynamic electrowetting4.1. Fast dynamics of electrowetting4.2. Slow dynamics of electrowetting

5. Other capillary phenomena governed by electrostatics5.1. Electro-coalescence5.2. Electrically assisted capillary wrapping5.3. Electrostatic control of interfacial flow5.4. Electric enhancement of heat and mass transfer

6. Conclusion and outlookReferences