Electrowetting -- from statics to dynamics.

CIS-01314; No of Pages 11 Advances in Colloid and Interface Science xxx (2013) xxx–xxx

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Electrowetting — From statics to dynamics Longquan Chen, Elmar Bonaccurso ⁎ Experimental Interface Physics, Center of Smart Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Str. 10, 64287 Darmstadt, Germany

a r t i c l e

i n f o

Available online xxxx Keywords: Wetting Electrowetting Static & dynamic capillary phenomena Electrocapillarity

a b s t r a c t More than one century ago, Lippmann found that capillary forces can be effectively controlled by external electrostatic forces. As a simple example, by applying a voltage between a conducting liquid droplet and the surface it is sitting on we are able to adjust the wetting angle of the drop. Since Lippmann's findings, electrocapillary phenomena – or electrowetting – have developed into a series of tools for manipulating microdroplets on solid surfaces, or small amounts of liquids in capillaries for microfluidic applications. In this article, we briefly review some recent progress of fundamental understanding of electrowetting and address some still unsolved issues. Specifically, 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 of contact 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 that might stimulate further investigations on electrowetting. © 2013 Elsevier B.V. All rights reserved.

Contents 1. 2.

3.

Introduction . . . . . . . . . . . . . . . . . Wetting fundamentals . . . . . . . . . . . . 2.1. Contact angle and contact angle hysteresis 2.1.1. Contact angle . . . . . . . . . 2.1.2. Contact angle hysteresis . . . . 2.2. Wetting dynamics . . . . . . . . . . . 2.2.1. Fast wetting stage . . . . . . . 2.2.2. Slow wetting stage . . . . . . Static electrowetting . . . . . . . . . . . . . 3.1. The Young–Lippmann equation . . . . . 3.2. DC electrowetting . . . . . . . . . . . 3.2.1. Contact angle hysteresis . . . . 3.2.2. Polarity effects . . . . . . . . 3.3. AC electrowetting . . . . . . . . . . . 3.3.1. Why AC? . . . . . . . . . . . 3.3.2. Frequency dependence . . . . 3.3.3. Hydrodynamic flow . . . . . . 3.4. Contact angle saturation . . . . . . . .

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Abbreviations: AC, alternating current; DC, direct current; EWOD, electrowetting on dielectric; HD, hydrodynamic (model); MK, molecular kinetic (theory); A, area (m2); C, capacitance per unit area (F/m2); E, electric field strength (V/m); F, force (N); H, drop height (m); H⁎, characteristic drop height (m); L, characteristic length (m); LC, capillary length (m); R, drop wetting 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); V, voltage, applied potential (V); VS, saturation voltage (V); Vth, threshold voltage (V); Veff, effective voltage (V); c, coefficient; d, thickness (m); f, frequency (Hz); f0, molecular jump frequency (Hz); fC, critical frequency (Hz); g, gravitational acceleration (m/s2); kB, Boltzmann constant; l, slip length (m); t, time (s); α, wetting exponent; γ, surface tension (N/m); γLS, liquid–solid interfacial tension (N/m); γSV, solid–vapor interfacial tension (N/m); ε, relative permittivity; ε0, free space permittivity; λ, molecular displacement (m); μ, viscosity (Pa s); θeq, equilibrium contact angle; θ, contact angle; θA, advancing contact angle; θR, receding contact angle; Δθ, contact angle hysteresis; ρ, density (kg/m3); σ, conductivity (S). ⁎ Corresponding author at: Experimental Interface Physics, Center of Smart Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Str. 10, 64287 Darmstadt, Germany. Tel.: +49 615116 2282; fax: +49 615116 2048. E-mail address: [email protected] (E. Bonaccurso). 0001-8686/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cis.2013.09.007

Please cite this article as: Chen L, Bonaccurso E, Electrowetting — From statics to dynamics, Adv Colloid Interface Sci (2013), http://dx.doi.org/ 10.1016/j.cis.2013.09.007

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L. Chen, E. Bonaccurso / Advances in Colloid and Interface Science xxx (2013) xxx–xxx

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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 flow . . . . 5.4. Electric enhancement of heat and mass transfer 6. Conclusion and outlook . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . .

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1. Introduction

2. Wetting fundamentals

Wettability is a key parameter to describe the chemical–physical properties of a surface and is usually characterized by a very simple method: measuring the angle of contact – or wetting angle – of a droplet of a test liquid with the surface. Triggered by many industrial applications, such as coating, printing, cleaning, or friction and wear control, many chemical or physical methods have been developed to control the wettability of surfaces [1–3]. Eventually, lyophilic, superlyophilic, lyophobic and superlyophobic surfaces can be fabricated in laboratory by modifying the surface chemistry and introducing multiscale physical roughness [1–3]. Such surfaces maintain their wetting properties over some time, but do not allow for an active control of their wettability after being manufactured. In practical applications, however, active control of the wettability is more attractive. Indeed, smart approaches such as thermal tuning [4,5], optical switching [6], as well as electrostatic controlling of contact angles [7,8] have been developed. Among them, the electrostatic method is the most popular one due to its real-time actuation, fast response, long term reliability, and good stability of the actuation. During his works, Lippmann found that applying a voltage between mercury and aqueous electrolytes allowed for controlling the position of the mercury meniscus in a capillary. In 1875, he was probably the first to report this electrocapillary phenomenon, which is at the foundations of electrowetting [9]. He further proposed a physical model and developed a number of applications. Later, Möller [10], Frumkin et al. [11], Gorodetskaya and Kabanov [12], Smolders [13], and Nakamura et al. [14] conducted contact angle measurements at the mercury/metal-electrolyte interfaces. They found that the contact angle decreased with applied potential, and argued that the decrease of contact angle was due to the change of interfacial energy [10–15]. However, Lippmann's discovery and the other works did not attract much attention until the 1980s, when the term electrowetting was coined and proposed for designing display devices [16,17]. Since then, electrowetting started to develop rapidly and nowadays it has been successfully applied in areas like lab-on-chip systems [18–20], adaptive optical lenses [21], electronic display technology [17,22], or mixing in microfluidic channels [23,24]. In principle, electrowetting can be applied to drops sitting on a bare electrode, or on thin dielectric layer on top of an electrode. However, most of the recent electrowetting studies and applications are carried out on dielectric, giving rise to the definition of electrowetting-on-dielectric (EWOD). In this review, we focus on the latest progress on some fundamental aspects of electrowetting. In Section 2, we give a short description of the basics of static and dynamic wetting. Section 3 is devoted to static electrowetting. We will discuss the basic phenomena in DC and AC electrowetting, as well as the contact angle saturation (CAS) phenomenon. In Section 4, recent results about fast and low speed electrowetting will be presented. Finally, we briefly address some other interesting capillary phenomena governed by electrostatics.

2.1. Contact angle and contact angle hysteresis

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2.1.1. Contact angle When 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 energy state.q If ffiffiffiffi the drop size, R0, is smaller than the capillary length, LC, e.g. R0 ≪ γ LC ¼ ρg , with γ and ρ respectively the surface tension and the density of the liquid and g the acceleration due to gravity, the gravity does not distort the spherical drop shape and can thus be neglected [25]. This condition is usually satisfied in all published electrowetting studies. For chemically and physically homogenous surfaces, the drop in equilibrium adopts a spherical cap shape, as shown in Fig. 1. The equilibrium contact angle, θeq, near the contact line is determined by the interfacial tensions, γLV, γLS, and γSV at the liquid–solid–vapor interfaces. cosθeq ¼

γ SV −γLS γ

ð1Þ

Usually, γLV is denoted as γ for brevity. The above equation is called Young's equation, in honor of Thomas Young who expressed it with words in his work published in 1805 [26]. Young's equation can be derived either from a mechanical perspective [1,3] or from a thermodynamic perspective [27]. θeq is a useful parameter to characterize the wettability of surfaces, as one can easily relate the contact radius R to θeq with 2

31=3

4 6 7 R ¼ R0 sinθeq 4 2 5 1− cosθeq 2 þ cosθeq

:

ð2Þ

Taking the limit as θeq → 0°, we find R → ∞ which means the liquid tends to wet the surface completely. While if θeq → 180°, we obtain R → 0, which reflects that the surface repels the liquid extremely. 2.1.2. Contact angle hysteresis Natural surfaces are decorated with physical roughness or chemical moieties. The physical or chemical heterogeneity of surfaces leads to deviations of the contact angle from the one predicted by Young's equation. Pinning of the contact line of a wetting/dewetting drop due

Fig. 1. Sketch of a drop sitting on a solid substrate in equilibrium.



to surface heterogeneity causes an advancing contact angle θA/a receding angle θR. The difference between θA and θR is defined as the contact angle hysteresis Δθ [1,3,28,29] Δθ ¼ θA −θR :

L is a macroscopic characteristic length and is typically of the order of the drop size. l denotes a microscopic slip length of the order of a molecular size. If the surface is very lyophilic, e.g. θeq ≪ 1, one obtains the growth of the spreading radius as a function of time [28,29,39].

ð3Þ Ret

The contact angle hysteresis characterizes the homogeneity of surfaces. Larger values of Δθ correspond to more pronounced surface heterogeneities. 2.2. Wetting dynamics When a drop touches a surface, the initial contact angle θ is largest and close to 180°. Contact leads to a net horizontal capillary force of γ(cos θeq − cos θ). This force drives drop wetting until equilibrium is attained. Three sources resist drop wetting: (i) the kinetic energy of the spreading drop, (ii) viscous dissipation within the liquid, and (iii) contact line dissipation at the drop rim. In recent years, benefiting from the development of high speed imaging techniques, dynamic wetting has received considerable attention. Many studies showed that the wetting proceeds in two stages, a “fast” early stage followed by a “slow” later stage. 2.2.1. Fast wetting stage For low viscosity liquids, the spreading velocity is very high just after a drop touches a solid surface. The Reynolds number in characteristic (*) experiments, Re ¼ 2 ρUμ R , compares the balance of inertial and viscous forces and is larger than unity. is the ratio of the characteristic drop height H⁎ and the characteristic drop radius R⁎, and is approximately unity. U⁎ is the characteristic velocity of the moving contact line and is of order 1m/s [30–34]. μ is the liquid viscosity. Thus, capillarity drives and inertia resists the fast wetting stage. The change (release) of surface energy is transformed into kinetic energy of the moving drop. Based on this energy balance, Bird et al. found that the spreading radius R grows with time t according to a power law [31,35]. R ¼ ct

α

ð4Þ

c is a coefficient, while the exponent α is only related to the wettability of the surface. It was experimentally found that α takes values between 0.5 and 0.25 when θeq changes from ~0° to ~110° [31–33,35,36]. Biance et al. carried out a scaling analysis based on drop coalescence theory. They obtained a power law dynamics with α = 0.5 for complete wetting [30], which was also observed by Winkels et al. in molecular dynamics (MD) simulations [34]. Shanahan et al. alternatively derived an inertial drop spreading model and found that α takes values between 0.5 and 0.2 [33] depending on θeq. However, all these models are at most semi-quantitative and do not capture all details of the wetting dynamics. 2.2.2. Slow wetting stage The inertial wetting stage lasts several milliseconds only, depending on drop size. After this fast stage wetting crosses into a slow stage in which drop spreading is resisted by viscous friction within the liquid and by molecular friction near the contact line. Two types of models were proposed, accounting for different mechanisms. The hydrodynamic (HD) model considers viscous dissipation as the main resisting force. Based on the introduction of a cutoff or slip length near the contact line by Huh and Scriven [37] to get rid of the shear stress singularity, Voinov derived a relationship between the dynamic contact angle θ and the spreading velocity U [38]. μ L 3 3 θ ¼ θeq þ 9 U ln γ l

ð5Þ

3

1=10

ð6Þ

The above equation is sometimes referred to as Tanner's law [40]. The spreading could also be dominated by microscopic friction near the contact line. In the molecular kinetic (MK) theory, the drop rim moves via individual molecular jumps activated by thermal energy, with an equilibrium frequency f0 and a displacement distance λ. The relation between the spreading velocity and the dynamic contact angle is given by [27,41] 3 2 2 γλ cosθeq − cosθ 4 5: U ¼ 2 f 0 λ sinh 2kB T

ð7Þ

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

1=7

:

ð8Þ

Blake et al. also combined both the effects of hydrodynamic stress and molecular friction in the modified molecular kinetic theory [43]. Details about these wetting models can be found in a recent review by Ralston et al. [44]. 3. Static electrowetting 3.1. The Young–Lippmann equation Fig. 2a shows the sketch of a typical electrowetting setup in which a thin dielectric layer with thickness d is deposited between a conductive drop and a flat electrode. The insulating layer is few micrometers thick and is mainly used to prevent electrolytic processes at the interface between drop and electrode. When a direct current (DC) voltage is applied between the drop and the electrode, the contact angle θ decreases with voltage V according to the so-called Young–Lippmann equation cosθ ¼ cosθeq þ

C 2 V 2γ

ð9Þ

θeq is the equilibrium contact angle with zero applied voltage and is determined by Young's equation. C is the capacitance per unit area. If we treat the capacitor between the drop and the electrode as a plate capacitor, C = ε0εd/d. εd and ε0 are the permittivities of the dielectric layer and of vacuum, respectively. For alternating current (AC) voltage, the root mean square (rms) value of the voltage – or effective voltage – V2eff, is used instead of V2. The Young–Lippmann equation can be derived by several approaches, as summarized, e.g., by Mugele and Baret [7]. A rigorous thermodynamic derivation of Eq. (9) was also presented by Bormashenko recently [45]. These theories can be understood from two perspectives:

Fig. 2. (a) Standard electrowetting setup. (b) Schematic plot of electrowetting curve.


4


• Thermodynamic or electrochemical perspective. The classic model for electrowetting was proposed by Lippmann [9]. In his experiments, a voltage was directly applied between the electrode (mercury) and the aqueous electrolyte. An electric double layer builds up spontaneously at the liquid–solid interface, with charges of opposite polarity being repelled from the interface. Thus, the liquid–solid interfacial energy, γLS, decreases along with the new equilibrium contact angle, i.e. the surface becomes more hydrophilic [46]. In EWOD, the thickness of the dielectric layer is significantly larger than that of the electric double layer [16,47], and hence electrostatic energy stored in it is the main source to decrease γLS. • Electromechanical perspective. Electrowetting could also be understood considering the forces exerted on the liquid near the contact line, as proposed by Jones et al. [48,49]. When a voltage is applied, the electric field near the contact line attracts the free charges as well as the polarized dipoles, which gives rise to a Maxwell stress on the liquid– air interface. In order to balance this stress, the liquid–air interface must decrease its curvature to reduce the Laplace pressure. Eventually, a smaller apparent contact angle depending on the magnitude of the applied voltage is attained. A large amount of experimental studies showed that the Young– Lippmann equation can well predict the contact angle when the voltage is smaller than a critical value VS [7,8,23,47]. When V ≥ VS, the electrowetting 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 description of the recent progress on theories about CAS is presented in Section 3.4. 3.2. DC electrowetting 3.2.1. Contact angle hysteresis The phenomenon of contact angle hysteresis also plays a role in electrowetting [50–52]. Typically, the contact angle hysteresis has two main effects: first, electrowetting can start only when the applied voltage is larger than a threshold value Vth [53–56]; second, the contact angle hysteresis leads to different contact angles with the same applied voltage, depending if the voltage is increasing or decreasing. This is referred as irreversibility or hysteresis of electrowetting [50,57]. The existence of the threshold voltage Vth can be explained by accounting for contact line pinning. Due to the natural heterogeneities of real surfaces, the equilibrium contact angle has a value between the receding and the advancing contact angle, e.g. θR b θeq b θA. When electrowetting is initiated, the electrostatic force wants to reduce the contact angle. However, the contact line will move only if the electrostatic force exceeds the pinning force [50,51,58–60]. Balancing these two forces, Fréchette et al. predicted the threshold voltage by [50]

V th

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2γ cosθeq − cosθA : ¼ C

ð10Þ

Thus, the threshold voltage can be decreased by using, e.g., low contact angle hysteresis surfaces. Until then, the lowest threshold voltages in electrowetting were reported in the range of 15–20 V [19]. In their paper, Fréchette et al. showed that nearly no threshold voltage existed on an oil-impregnated polydimethylsiloxane (PDMS) surface with only 1° contact angle hysteresis [50]. Eq. (10) also indicates that Vth can be reduced by decreasing the interfacial tension γ. This was achieved by changing the fluid around the drop from air to a liquid, as liquid–liquid interfacial tensions are usually smaller than liquid–air interfacial tensions [55,57,61]. Moreover, the contact angle hysteresis in liquid/liquid/solid systems is also smaller than in liquid/solid/air systems, as liquid–liquid friction is much smaller than liquid–solid friction [61].

Similarly, the advancing/receding contact angle as the drop spreads/recedes with increasing/decreasing applied voltage can be modified by considering the effects of the contact line pinning force [50,58]

cosθA

or R

V¼0 or R

¼ cosθA

2

þ

CV 2γ

ð11Þ

0 where θVA = or R is the advancing/receding contact angle measured with zero voltage applied. As the contact angle hysteresis is independent of the applied voltage [50–52], reversible electrowetting could be achieved with 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 effects According to the Young–Lippmann equation in Section 3.1, the contact angle decreases with the applied voltage following the same parabolic curve regardless of the polarity of the voltage. However, early studies showed different polarity effects of electrowetting on different materials. On one side, when Parylene was used as an insulating layer, the change of contact angle was independent of polarity [63–65]. On the other side, when Teflon was used several groups reported a strong deviation from the theory with a positive applied voltage [66–68]. Since the liquids (water or aqueous electrolyte solutions) used in experiments were similar, authors attributed the polarity effects to material properties [66–68]. Werner and co-workers investigated the interfacial charge on Teflon in aqueous electrolyte solutions [69]. They found that hydroxyl ions (OH−) have stronger interaction to the Teflon surface than the hydronium ions (H3O+) due to the presence of oxygen atoms in Teflon [66,70]. As a result, the capacitance of the liquid–solid interface is better described by both a dielectric layer and an electric double layer, rather than by only a dielectric layer, as done in the Young–Lippmann model [68,71], and it can explain the polarity effects of electrowetting on Teflon surfaces. In standard electrowetting experiments or applications, water and aqueous electrolyte solutions were normally used [18,19,50–68,70,71]. Although water has useful solvent properties, its poor thermal stability, it tendency to evaporate, and its corrosion ability lead to significant limitations in microfluidic applications. Ionic liquids, as first pointed out by Ralston et al., are more promising for robust applications due to their unique properties: high thermal stability, non-flammability, and no significant 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 out later by Armstrong and coworkers. They found that anions or cations with smaller size have stronger influence on the asymmetry of the electrowetting curve since they interact more strongly with the Teflon surface than larger anions or cations do [73]. As discussed above, polarity effects in electrowetting are recognized to be most probably due to molecular processes near the liquid–solid interface, which cannot be captured by simple optical instruments. Thus, MD simulations could help in understanding the physical mechanisms. Luzar and co-workers studied the electrowetting of water nanodrops on apolar hydrophobic surfaces, such as graphene or paraffin [74–77]. They observed that the electrowetting contact angle is sensitive to the polarity of an electric field directed perpendicular to the surface. The explanation was that water is easier to be polarized along the outgoing, rather than along the incoming, electric field to the surface [74–76]. However, in the presence of any salt ions, the strong affinities of them towards the surface increase the screening of the electric field, and eventually suppress the polarity effects caused by different electric responses of hydrogen bonding [78].



3.3. AC electrowetting 3.3.1. Why AC? In most microfluidic electrowetting systems [19], alternating current (AC) voltage is applied because of following benefits: • Reduction of contact angle hysteresis. As discussed above, the contact angle hysteresis exists in DC electrowetting due to pinning effects [50–52]. In contrast, using AC voltage electrowetting continuously perturbs the force balance at the contact line and essentially leads to the 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]. • Delay of contact angle saturation. Many experimental results showed that the contact angle saturation occurs at a smaller contact angle and at a higher effective voltage for AC rather than DC electrowetting, in both liquid/solid/air [80,81] and liquid/liquid/solid systems [82–84]. Hong et al. provided the explanation that the effective electric field strength is reduced by increasing the frequency, and that this can lead to a delay of the dielectric breakdown [85]. The underlying physics of delayed saturation in AC electrowetting is still not fully understood. • Reduction of ion adsorption. Another possible reason leading to irreversibility or a large contact angle hysteresis in DC electrowetting is ion adsorption at the liquid–solid interface. It was reported that the ion adsorption at the liquid–solid interface was reduced by applying AC instead of DC voltage [86,87]. 3.3.2. Frequency dependence The Young–Lippmann equation is only valid for AC electrowetting when the liquid can be treated as a perfect conductor. This holds if the AC frequency is larger than the resonance frequency of sessile drops (typically of few hundreds hertz) and is far smaller than a critical frequency fC (typically of 10–100 kHz) [7]. The electrowetting efficiency diminishes with frequency increasing beyond the upper limit, while it is dependent on the frequency between the two limits [48,49,58,85]. The general AC electrowetting behavior can be captured by the analogy with an equivalent electric circuit, as shown by Mugele and Baret [7] (Fig. 3). The drop is represented as a resistor and a capacitor, and the dielectric layer is treated as another capacitor. The electric double layers formed at the liquid-dielectric layer or at the liquid-counter electrode interfaces are not considered. At low frequency (≪fC), the drop behaves more like a conductor rather than an insulator, which satisfies the assumption for Young–Lippmann's equation. However, at very high frequency (≫fC), the drop behaves more like an insulator, which leads to the breakdown of electrowetting. The critical frequency is related to the physical properties of the drop as well as to its geometry [7]. fCe

σ d þ σ lk ε0 ðεd þ εl kÞ

ð12Þ

5

σd, σl and εl are the conductivities of the dielectric layer and liquid and the permittivity of the liquid, respectively. k ~ d/R is the size ratio of the dielectric layer and the drop. For deionized water, fC is typically few kHz, which matches with experimental observations [48,49,58]. The above discussion qualitatively introduces the frequency dependence of AC electrowetting, while a quantitative understanding is still missing. Hong et al. carried out a numerical investigation of AC electrowetting [85]. They found that the electric field strength was remarkably reduced in the dielectric layer near the contact line, which may lead to a decrease of the electrostatic contribution to the wetting tension. Their numerical results were consistent with experiments. Most recently, Klarman et al. proposed a model based on a similar configuration as shown in Fig. 3 [88]. They also accounted for the effects of the electric double layer at the immersed counter-electrode and discussed this effect on AC and DC electrowetting. Among others, they concluded that the effect of the polarization of the counter-electrode could be neglected in most practical cases, since the area of the counter-electrode is usually much smaller than the contact area between the drop and the solid. 3.3.3. Hydrodynamic flow In recent years, researchers have reported hydrodynamic flows inside drops in AC electrowetting [24,89–93]. The flow patterns are dependent on the frequency of the applied voltage as well as on the conductivity of the liquid (Fig. 4a). In the low frequency range (typically up to 1 kHz), the flow forms two axisymmetric toroidal vortexes whose center is not visible [90,93] (Fig. 4b). The low frequency flow is rather unstable and is very sensitive to the counter-electrode position. In contrast, in the high frequency range (larger than few tens of kHz), the flow is highly stable and the vortex center is always located around the counter-electrode [90]. Also, the vortex direction of the low frequency and high frequency flows are different (Fig. 4b & d), which indicates that the flow generation mechanisms are different. For intermediate frequencies, no flow is observed in the drop (Fig. 4c). The low frequency flow is mainly driven by the oscillations of the drop [90]. The oscillation of the contact line caused by AC potential can result in a hydrodynamic viscous streaming inside the drop. However, the low frequency flow observed is not as steady as the viscous flow. Moreover, the direction of the low frequency flow in air [90] is opposite to the one observed in mixing experiments of water/glycerol drops in silicone oil ambient [24,93]. Both phenomena point out that some additional mechanisms may influence the hydrodynamics. Based on these experiments in oil, Mugele et al. suggested that the capillary Stokes drift induced by the capillary wave drives the internal flow in the drop [93,94]. These studies pointed to more open questions, like how do the viscosity or the density of the atmosphere surrounding the drop influence flow pattern and flow stability inside the drop. The high frequency flow is induced by the so-called electrothermal effects [89,91]. With high frequency AC voltage applied, the liquid behaves like an insulator as there is not sufficient time to completely charge the capacitor of the dielectric layer [7,88]. As a result, the electric field inside the drop leads to Joule heating of the liquid, giving rise to a gradient in conductivity and permittivity [89,91]. Eventually, the voltage applied on the electrically inhomogeneous drop generates an electric body force resulting in an internal flow. 3.4. Contact angle saturation In the past years, many models or hypotheses have been proposed to explain the contact angle saturation, as reviewed by Mugele [7,23], and recently by Chevalliot et al. [80], Koopal [95] and Sedev [96]. Here, we briefly recap the latest progress:

Fig. 3. The equivalent circuit for AC electrowetting.

(1) Zero interfacial tension. According to the classical thermodynamic model of electrowetting, the change of the contact angle is entirely ascribed to the reduction of the liquid–solid interfacial tension (γLS). Ralston and coworkers suggested that γLS should


6


Fig. 4. (a) The influence of electrolyte concentration on the frequency range of hydrodynamic flows with V = 80 V and the three typical flow patterns with frequency of 1 kHz (b), 18 kHz (c) and 128 kHz (d). The electrolyte concentration in (b)–(d) is 10−3 M. Reproduced with permission from Ref. [90].

not be less than zero to keep thermodynamic stability [47,97]. Thus, the thermodynamic limit with γLS = 0 causes the contact angle saturation. They showed a consistence between their model and experimental results [47,97]. Berry and coworkers confirmed this model by low voltage electrowetting in both liquid/liquid/solid systems and liquid/solid/air systems [98,99]. One big challenge to verify this model is that it is hardly possible to directly measure liquid–solid interfacial tensions. However, recent measurements of thin films [100] and adhesion force [101] showed no major change of the liquid–solid interfacial tension upon applying an external potential. Other groups also noticed that the zero interfacial tension theory does not predict reliably the saturation contact angle, e.g. with cos θS = γSV/γ [80,82,83]. Moreover, Mugele and co-workers numerically found that the electrostatic force does not affect the interfacial tensions force balance at the contact line [102], and they further experimentally observed that the microscopic contact angle always equals Young's angle [103]. This was later confirmed by MD simulation by Liu et al. [104]. Till now, no studies considered the possibility of a significant change of the liquid–vapor or solid–vapor interfacial tensions upon applying an electric potential. Recent work, however, showed that the surface tension of water decreased remarkably by approx. 50% upon electrically charging the water surface [105] – even if the external potential was in the kV range; or that the solid–vapor and solid–liquid interfacial energy can be reduced upon weak electron irradiation [106] – causing a reversed electrowetting effect, i.e. increasing the contact angle upon irradiation. These results suggest that electric charges can affect either of the interfacial tensions playing a role in electrowetting or in contact angle saturation. (2) Dielectric breakdown. Near the contact line, the electric field diverges as the interface curvature is extremely small. The electric field may locally become so strong that it exceeds the dielectric breakdown strength of the insulating layer [64]. As a result, the dielectric layer locally breaks down [107,108]. The charges transferred to the dielectric layer lead to screen the electric field, which eventually reduces the electrostatic contribution and causes electrowetting saturation. This hypothesis was proposed by Drygiannakis et al. who showed a good match between their experimental results and theory [107]. Similar conclusions were also drawn by Berry et al. based on their experiments on thin amorphous fluoropolymer films [98,109]. However, Chevalliot et al. recently reported experimental results on DC electrowetting showing that the saturation contact angle is invariant with respect to a number experimental parameters, among which are

the electric field strength, the interfacial curvature near the contact line, or the type of dielectric used [80]. (3) Contact line instability. In early AC electrowetting studies, Vallet et al. observed an instability of the contact line close to the critical (saturation) voltage for low conductivity liquids such as water [110]. They found that microdrops spontaneously ejected from the contact line as the voltage was larger than a critical value. This phenomenon was reproduced later by Mugele and Herminghaus with various liquids [111] and was attributed to the diverging of charge density around the contact line. While the applied voltage is larger than a critical value, the Maxwell force exceeds the capillary force near the contact line, which leads to emission of (charged) satellite droplets. This instability at the contact line was identified as a possible cause for contact angle saturation [110,111]. Park et al. also suggested that the instability with droplet ejection is preceded by a contact angle reduction and the extrusion of a thin layer from the edge of the droplet [112,113]. However, these models cannot explain the suppression of the instability by increasing the conductivity of the liquids, e.g. with salts [110,111]. As contact line instability does not arise in DC electrowetting, it hence may not capture the actual physics of contact angle saturation. (4) Gas ionization or insulating fluid charging. Vallet et al. also reported air ionization around the contact line for voltages larger than the saturation voltage and suggested that it could be responsible for contact angle saturation [110]. Indeed, it was experimentally found that the contact angle of a drop can be controlled by charging its surface via a corona discharge [114,115] or by electrons [106]. As corona discharge or air ionization is dependent on relative humidity [115], one possible way to validate this hypothesis would be to check whether the relative humidity of the surrounding air influences contact angle saturation. On the other hand, corona discharge is not applicable to liquid–liquid– solid electrowetting systems. In such systems, Chevalliot et al. suggested that it could be possible that the insulating fluid is charged due to ejection of charges or satellite drops from the conducting drop [80]. However, this hypothesis calls for further experimental evidence. (5) Minimization of the electrostatic energy. Lin et al. proposed a theoretical model based on an energy balance [116] instead of a force balance, as is used in the derivation of the Young–Lippmann equation. In AC electrowetting, especially at higher voltages and in a well-defined frequency range, a strong hydrodynamic flow develops inside the drop [24,89–93]. The flow causes additional energy dissipation and the dissipated energy increases with the applied potential. Eventually, this leads to a minimum electrostatic



contribution to the total energy of the system when V ≥ VS [116]. However, this model fails to explain the contact angle saturation of DC electrowetting, as no internal flow develops there, and does not reproduce the correct dependence cos θ ∝ V2 for V b VS. Klarman and Andelman also developed a model based on energy dissipation [88], and accounted for the electrostatic energy of the electric double layer around the counter-electrode. This is a reasonable approach, as the electric field is always stronger near the electrode than that in the bulk drop [89,91]. They found a minimum of the electrostatic energy contribution to the saturation voltage for both DC and AC electrowetting systems. This was based on the assumption that the capacitance C is not constant but function of θ and has a minimum at VS. However, this assumption is not based on first principles and would require a rigorous proof. (6) Tailor cone. Most recently, Chevalliot et al. carried out a systematic study of all physical and chemical parameters which may lead to contact angle saturation according to the above models [80]. Based on their experimental results, they state that there are parallels between the phenomena of Tailor cone formation and contact angle saturation. This, if confirmed, could provide a new direction for a universal theory of the saturation problem in electrowetting.

4. Dynamic electrowetting In many applications, such as lab-on-chip, electrowetting dynamics is of great interest as it controls the response time of the devices [19]. During the wetting process, the dynamics is determined by the energy balance between the driving and the resisting forces [28,29,39]. The driving force of the spreading drop is always the change of surface energy, which is related to the difference between the initial and equilibrium contact angle. The resisting force could be the kinetic energy of the moving drop [30–33], the viscous dissipation in the vicinity of the moving contact line [28], or the microscopic dissipation of the molecular jumps [67]. In electrowetting systems it is thus expected that the addition of electrostatic energy to the energy balance will modify the dynamics of spreading. In literature, many experimental configurations have been applied to study the dynamics of electrowetting, as shown in Figs. 2a & 5.

7

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 as most surfaces are naturally charged, which is the reason – except for well controlled conditions – that there is always difference of potential between drops and surfaces before they wet each other. These naturally arising excess surface charges need to be redistributed between drop and surface upon meeting, and thus play a role in most spontaneous wetting processes like rain drops hitting the soil or ink drops wetting paper. Stone and co-workers were the first to investigate the fast dynamic wetting of sessile drops just after contact with a surface under an applied electric potential [35]. They found that the drop spreading radius grows with a power law with a larger exponent, α′ ≈ 2/3. Without applied potential α = 1/2 on completely wetting surfaces. The effect of the applied potential was to deform the spherical drop into a conical shape close to the point of contact. The authors set up an energy balance accounting for this new contact geometry and derived a power law with an exponent of 2/3. Exponents larger than 1/2 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 static electrowetting, where the contact angle saturates when the applied voltage is larger than VS, they found a saturation of the wetting exponent α′ for aqueous electrolyte drops with low salt concentration. For high electrolyte concentrations, no saturation was observed at the voltages applied (up to V ≈ 1000 V). Chen et al. modified Stone's early model for partial wetting [31] by adding the contribution of the electrostatic energy stored in the electrostatic double layer near the liquid–solid interface as a driving force. The proposed model can explain the experimental observations. MD simulations confirmed that the electric double layer is formed in a time scale of few hundred picoseconds [117], which satisfies the assumption that the electrostatic double layer exists during the fast wetting process (typically, ~10 ms). However, the saturation of the wetting exponent in dependence of salt concentration and applied potential is still an open question. The inertial wetting stage was also observed in the MD simulations of the early wetting of nanodrops [117]. However, the electrostatic energy did not enhance the wetting exponent here. One plausible

Fig. 5. Typical experimental configurations for dynamic electrowetting setups. (a) Dynamic wetting experiments with a spreading sessile drop. (b) Wilhelmy plate method and (c) capillary rise experiments.


8


explanation is that the electrostatic double layer is not yet fully formed in this short period. In fact, the ion migration time needed to form the electrostatic double layer near the liquid–solid interface by applying a potential was ~500 ps, which is two times longer than the inertial wetting time [117]. Thus electrostatics does not influence the early spreading of nanodrops, but it does for their later (viscous) wetting and for their equilibrium contact angle. 4.2. “Slow” dynamics of electrowetting The electrostatic effects on the viscous stage of dynamic wetting are difficult to investigate experimentally with a configuration as in Fig. 5a, since the drop detaches from the needle during this stage. Losing contact with the needle (which also acts as counter-electrode) leads to an open circuit configuration. Alternatively, MD simulations can be applied to investigate the slow electrowetting. It was found that wetting follows a power law R ~ t0.1 without applied electric field [117] — which is consistent with the HD model [28,29,39]. With an applied electric field of 0.1 V/nm the wetting exponent was larger and the wetting law was R ~ t0.15 [117]. Similar wetting exponents from MD simulations were also obtained by Yuan and Zhao [118]. Despite these preliminary findings, there is still a lack of knowledge on the effect of an applied electric potential on slow electrowetting dynamics. Another unsolved issue is the influence of the electrolyte concentration on slow electrowetting dynamics. Most studies of dynamic electrowetting in literature were carried out with the standard configuration shown in Fig. 2a, with the needle (counter-electrode) permanently inserted in the drop for applying the electric potential. The driving force due to the electrostatic contribution is E F ¼ γ cosθeq − cosθeq :

ð14Þ

θEeq is the new equilibrium electrowetting contact angle that is a function of the applied voltage. This force is compensated by viscous dissipation or contact line friction during the spreading. Decamps and De Coninck modified the MK theory with this electrocapillary force and applied it to spontaneous spreading experiments of glycerol drops on Teflon [119]. They found that the contact line friction was constant over a large range of applied potentials. Ralston and co-workers studied the dynamic electrowetting of various ionic liquids in liquid/liquid/solid systems [82,83] and liquid/solid/air systems [120]. They used both HD model and MK theory to interpret their data. They found that viscous dissipation dominates the dynamics when the contact angle and contact line velocity are small, while the MK theory was more suitable to explain the dynamics at high contact angles and with high contact line velocity [83,120]. They also showed that the equilibrium frequency of molecular jumps decreased with liquid viscosity, which indicates that it is more difficult for liquid molecules with higher viscosities to move from one adsorption site to another since the cohesion force between the molecules is much stronger. Very recently, Hong et al. reported that liquid viscosity has a weak effect on electrowetting velocity over a broad range of viscosities (from approx. 1 to 200 mPa s) [121]. McHale and co-workers investigated the dynamic dielectrowetting of dielectric liquids [122,123]. In their paper, they modified the HD model and found that when the applied voltage was larger than a threshold value the wetting exponent increased with the voltage [123]. Yuan and Zhao studied the dynamic electrowetting of cylindrical water nanodrops with MD simulations [118]. They observed a power-law growth of the spreading radius with time and an increase of the wetting exponent with the electric field. When a critical value of the field strength was reached, the exponent saturated similarly to the saturation found in static electrowetting [7,23]. Dynamic electrowetting studies were also carried out with the Wilhelmy plate configuration (Fig. 5b). Schneemilch et al. studied the electrowetting of a Teflon-covered rod and applied the MK theory to

fit their data. They showed that the applied potential controlled the wettability of the surface and that average molecular displacement, λ, decreased with the applied potential [124]. Puah et al. applied a similar method to investigate the influence of the electric surface charge on wetting dynamics [125]. Also there, MK theory was applied. This time it was found that the equilibrium displacement frequency, k0, depended on the applied potential and was determined by the charges at the liquid–solid interface, while λ did not show a significant relation to surface charge density. The values of λ were determined mainly by the spacing of the adsorption sites on the solid surface. This was consistent with previous work of the group using a standard electrowetting configuration [82,83,120]. Blake et al. modified the MK theory by introducing the actual capillary force in Eq. (14) [126]. However, they found that both k0 and λ were independent of the applied voltage. This brief presentation of experimental results is just to show that also experiments performed with different configurations and materials are not always in agreement, and that the cause of disagreement is not yet clear. On the other hand, it becomes increasingly clear that MD simulations are now at a level that they can well capture the processes at the scale of the contact line [127]. They represent thus a promising tool for exploring the influence of external potentials on molecular displacements of the contact line in particular and of the electrowetting process in general. In recent years, electrostatic assisted flow in capillaries or microchannels attracted quite some attention because of envisioned applications in microfluidics and lab-on-chip applications (Fig. 5c). Wang and Jones proposed a hydrodynamic model to describe the electrowetting-induced capillary rise in a millimeter-sized planeparallel channel [128]. According to this model, there is a critical potential below which contact line friction dominates over viscous dissipation, 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 always dominates the electrowetting dynamics [129–131]. 5. Other capillary phenomena governed by electrostatics 5.1. Electro-coalescence When two drops of the same liquid come into contact, they merge with each other to minimize the surface energy. Drop surface charges or externally applied potentials can favor – or in some cases delay – coalescence [132,133]. If the drops are oppositely charged, noncoalescence was observed when the electric field was larger than a critical value EC (Fig. 6). The failing of coalescence can be explained by considering the local pressure at the drop apex during coalescence [132,134]. Exposed to an electric field, the drop deformed into a conical shape upon approaching the oppositely charged interface. The aperture angle of the cone depends on the field strength. If the cone angle is larger than 31°, the local curvature in the liquid thread results in such a high pressure that prevents coalescence. A similar phenomenon was also observed in the coalescence of a drop with a flat solid surface [117]. When the electric field was below the critical value EC, the impinging drop partially coalesced with the interface [135–138]. The coalescence was only partial, since a daughter drop was ejected and moved away from the interface, as it acquired an opposite charge during contact. The size of the daughter drop is determined by electrostatic and capillary forces [136]. 5.2. Electrically assisted capillary wrapping It was recently demonstrated by several authors that capillary forces can be used to fold thin films and to wrap them around droplets [139–141]. In order to achieve a reversible wrapping, an additional force is needed to oppose the capillary folding force. One way is using the electrostatic force. Pineirua et al. controlled the folding and unfolding of



9

Fig. 6. Influence of an electric field on drop coalescence: below a critical field strength EC the drop coalesces with the interface, and above EC the impinging drop rebounds from the interface. The scale bar is 0.5 mm. Reproduced with permission from Ref. [132].

capillary origami by varying the unfolding torques with an external DC voltage [142]. The authors showed that this technique can be used to assemble small scale three dimensional soft structures. Zhao and coworkers reported a similar effect using low frequency AC voltages [143]. 5.3. Electrostatic control of interfacial flow The electrostatic force can also be used to control interfacial flows, as it deforms the shape of a drop or a rivulet. Lee et al. transferred the electrostatic energy into the surface energy by applying a voltage to spherical drops sitting on superhydrophobic surfaces [144]. If the increased surface energy overcomes a critical barrier, the drop can be induced to jump off the surface. The voltage for making a 5 μl water drop jump off is approx. 100V. The authors also showed that it is possible to transfer drops between two parallel plates, which is envisioned to find applications in three-dimensional digital microfluidics. Bormashenko et al. investigated the deformation of liquid marbles under electric field and found that liquid properties influence the deformation [145]. When a composite liquid marble was exposed to a sufficiently high electric field, the highly polarizable drop climbed on top of the low polarizable drop to minimize the total energy of the system. Noblin and Celestini proposed a new method for controlling water jet dynamics. Applying an AC voltage between the metallic nozzle generating the jet and a metallic electrode below a dielectric polymer layer, they showed that they could control the reflection angle of the jet, or even to completely prevent bouncing. For water, the authors determined a maximum threshold frequency of approx. 1.5 kHz above which the effects disappear, since the liquid starts behaving like a dielectric [146]. Very recently, Yun et al. presented an experimental and numerical study about the prevention of drop rebound from solid surfaces by electrostatic charging of the drops. Electric charges were transferred to water droplets while they fell through variously shaped ring electrodes. Such an electrostatic charging affected drop oscillations and thus induced a kinetic energy dissipation, which in turn reduced – or even suppressed – drop rebounding [147]. Most recently, the electrostatic forces were also applied to suppress the Leidenfrost effect [148]. By applying an electric field between a Leidenfrost droplet and the heated substrate on which it was levitating, the vapor layer thickness decreased. Eventually, a millimeter-sized drop contacted the heated substrate with an applied voltage of approx. 40 V. 5.4. Electric enhancement of heat and mass transfer Many authors also reported that the heat and mass transfer can be controlled by applying an external electric field. Takano et al. experimentally studied the evaporation of various drops of liquids at

temperatures exceeding the Leidenfrost temperature [149–151]. They found that the evaporation was enhanced under an applied field, as the field induced interfacial instability leading to direct contact between the levitating drop and the heated substrate [150]. They concluded that the enhancement was more remarkable for polar liquids than for non-polar liquids, as charge relaxation time on them was much shorter [150,152]. Recently, Butt and co-workers calculated that the presence of an electric field can reduce the saturation vapor pressure and lead to a fieldinduced condensation of, e.g., water [153]. This explains the anodic oxidation at the nanoscale in dependence of relative humidity [154,155]. 6. Conclusion and outlook In the last 10years the topic of electrowetting spawned an increasing number of theoretical, numerical, and experimental works. A good deal of fundamental and especially technological issues has been addressed and solved. The Young–Lippmann equation, despite its simplicity, is able to quantitatively describe the physical processes and to predict the wetting behavior of most systems most of the time. The unbound creativity of researchers, however, continuously finds new ways of combining capillary and electric forces with new material properties and system geometries. The Young–Lippmann equation can thus not account for all new observed phenomena. Some issues remain to be solved, most important being the understanding of the saturation potentials in static and in dynamic electrowetting, of the molecular transport processes in the bulk and at the interfaces associated with applying electric potentials to various liquids, and of the ionic and electrochemical processes taking place at the surface of the electrodes. The natural contact angle hysteresis inherent to real surfaces leads to poor controllability and sometimes to the irreversibility of the electrowetting process. Controllability could be improved either using liquid/liquid/solid systems, by applying AC instead of DC potentials, or by using superhydrophobic/superlyophobic surfaces. Polarity effects in DC electrowetting, generating a non-symmetric wetting behavior for positive and negative voltages, have been found to be most probably caused by molecular processes in the liquids. So the use of special adhoc liquids is recommended in certain applications. AC voltage is applied more and more in electrowetting, as it can overcome many disadvantages of DC electrowetting. However, additional phenomena arise and set limitations for the applicability, such as the frequency dependence of the conductivity of the liquid, or the generation of hydrodynamic flows inside the liquid. Such side effects need also to be considered in designing lab-on-chip devices. Saturation, referring to the existence of a critical threshold voltage above which the electrowetting effectiveness does not further increase, remains a challenge for all electrowetting theories. Since saturation is most probably dominated by microscopic interfacial


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