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Electrowetting: A versatile tool for drop manipulation, generation, and characterization
Advances in Colloid and Interface Science 161 (2010) 115–123
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Advances in Colloid and Interface Science j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c i s
Electrowetting: A versatile tool for drop manipulation, generation, and characterization Frieder Mugele ⁎, Michel Duits, Dirk van den Ende Physics of Complex Fluids, Univ. of Twente, MESA+ Institute for Nanotechnology and Institute for Mechanics Processes and Control Twente, PO Box 217, 7500 AE Enschede, The Netherlands
a r t i c l e
i n f o
Available online 18 November 2009 Keywords: Microfluidics Electrowetting Two-phase flow Drop generation Wetting Interfacial tension
a b s t r a c t Electrowetting is arguably the most flexible tool to control and vary the wettability of solid surfaces by an external control parameter. In this article we briefly discuss the physical origin of the electrowetting effect and subsequently present a number of approaches for selected novel applications. Specifically, we will discuss the use of EW as a tool to extract materials properties such as interfacial tensions and elastic properties of drops. We will describe some modifications of the EW equation that apply at finite AC voltage for low conductivity fluids when the electric field can partially penetrate into the drops. We will discuss two examples where finite conductivity effects have important consequences, namely electrowetting of topographically structured surfaces as well as the generation of drops in AC electric fields. Finally, we review recent attempts to incorporate electrowetting into conventional channel-based microfluidic devices in order to enhance the flexibility of controlling the generation of drops. © 2009 Elsevier B.V. All rights reserved.
Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Electrowetting basics . . . . . . . . . . . . . . . . . . . . . . . 3. Electrowetting-based microdrop tensiometry . . . . . . . . . . . 4. Beyond Newtonian fluids: electrowetting response of complex fluids 5. Electrowetting with AC voltage . . . . . . . . . . . . . . . . . . 6. Controlling drop generation in two-phase flow in microchannels . . 7. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction On small scales the behavior of liquid drops is dominated by surface tension and wetting forces. By controlling the interaction between liquid and solid we can qualitatively alter the behavior of drops on surfaces. Chemically patterned surfaces give rise to complex drop morphologies, topographically structured hydrophobic surfaces display superhydrophobicity, and surfaces with a gradient in wettability give rise to drop motion [1,2]. From a practical perspective, active means of controlling the wettability of surfaces are very attractive. Many approaches such as thermocapillarity [2] and chemically switchable molecular layers are very attractive. Yet ⁎ Corresponding author. E-mail address: [email protected] (F. Mugele). 0001-8686/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cis.2009.11.002
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limitations regarding the range, speed, flexibility, and long term reliability of the actuation have so far prevented the broad application of these effects. In contrast, electrowetting (EW) [3,4] allows for contact angle variations in excess of 90° at speeds that are only limited by the intrinsic hydrodynamic response time of the fluid for any kind of conductive fluid (and even some strongly polarizable nonconductive ones) for hundreds of thousands of actuation cycles without any sign of degradation. As a consequence, EW has become the most popular platform for ‘digital’ microfluidic systems that are based on the manipulation of discrete drops in a microfluidic chip [4–6]. Using a large number of individually addressable electrodes, EW allows for generating, moving, merging, splitting, and mixing of individual drops. While these basic drop manipulation operations were initially demonstrated with simple liquids (aqueous salt solutions), recent biotechnological applications make use of a large
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variety of fluids with an increasingly complex ‘cocktail’ of solutes as required for instance for immunoassays and DNA replication using polymerase chain reaction (PCR) [5,7]. In these applications, EW makes use of discrete drops as individual (bio)chemical microreactors with well-defined and/or well-controlled chemical composition — an approach that is shared with microchannel-based two-phase flow systems [8]. Compared to EW devices, the latter offer the advantage of high throughput capability, which makes them suitable for combinatorial screening applications and for the synthesis of novel materials, such as micrometer-sized colloidal particles, functional microparticles, capsules, emulsions, etc. with a high degree of monodispersity. Both in EW and in channel-based microfluidic systems, the generation and manipulation of drops depend crucially on the materials properties of the liquid, including in particular interfacial tensions and rheological properties. The desire to generate and manipulate drops of liquids with increasingly complex composition therefore asks for tools to characterize these properties on chip. For continuous flow systems a variety of approaches have been proposed based either on the hydrodynamically induced deformation of flowing drops in channels of variable geometry [9,10] or on the comparator principle, which makes use of the excess hydraulic resistance generated by a ‘drop’ (which can be as complex as living cells) inside a microfluidic channel with respect to a droplet-free reference channel [11]. In this article, we review briefly the basic principle of the electrowetting effect and its derivation from the minimization of interfacial and electrostatic energies. A more detailed review can be found in [4]. Subsequently, we present a number of applications of EW focusing on recent work in our laboratory. First, we demonstrate that materials properties such as the interfacial tension and elasticity can be extracted with remarkable accuracy from the EW response of submillimeter sessile drops. Second, we discuss modifications of the EW due to effects of finite conductivity in the case of electrowetting with AC voltage. Finally, we present several proof-of-principle experiments demonstrating the capability of EW to manipulate two-phase flows inside microchannels. 2. Electrowetting basics Fig. 1 shows the generic configuration of an electrowetting setup. It consists of a sessile drop of a partially wetting conductive liquid on an electrically insulating dielectric layer covering a flat electrode. Typically the drop size is of order 0.1 to 1 mm and is much larger than the thickness d of the dielectric layer, which mostly lies between 0.1 µm and a few micrometers. Since electrowetting can only reduce the contact angle of conductive liquids, which are typically used as the droplet phase, one usually chooses dielectric layers (e.g. fluoropolymers) that display a high contact angle at zero voltage. Upon applying a voltage U between the electrode on the substrate and the drop — in the generic configuration via the immersed wire — the contact angle is reduced as shown in Fig. 2. The contact angle reduction displays two regimes. At low
Fig. 2. Typical electrowetting response of an aqueous drop in ambient silicone oil displaying a parabolic increase of cosθ up to a voltage of approximately 250 V and contact angle saturation at higher voltages.
voltage, the contact angle reduction is characterized by a quadratic increase of cosθ with increasing U. At higher voltage, this dependence becomes weaker and eventually the contact angle saturates at some finite value, which depends on the specific system. The low voltage regime can be understood by minimizing at fixed volume the interfacial energies and electrostatic energies assuming that the drop phase is perfectly conductive and that the ambient phase and the dielectric layer behave as perfect dielectrics. Since one fixes the electrical potentials of the drop and of the electrode on the substrate, the electrostatic contribution enters with a negative sign in the Gibbs free energy G 1 → → ! G = ∑ σi Ai − ∫ D E dV = min : 2 i
ð1Þ
Here σi and Ai are the interfacial tensions and the interfacial areas of the interfaces i between the substrate and the drop, the substrate and the ambient phase, and the drop and the ambient phase. For convenience, we denote these as solid–liquid (sl), solid–vapor (sv), and liquid–vapor (lv) interfaces, respectively, noting that the ambient → phase may consist of a second immiscible liquid rather than vapor. E → and D are the electric field and the electric displacement, respectively, and the volume integral extends over the entire system. For perfectly conductive drops the electric field assumes non-zero values only within the dielectric layer below the drop and in a small region of order d around the three-phase contact line. If the drop size is large compared to d, the latter line contribution can be neglected and the electrostatic volume integral reduces to the energy of a parallel plate capacitor cU2 Asl/2, where c = ε0ε/d is the capacitance per unit area (ε0ε: dielectric permittivity of the insulating layer). Hence, the Gibbs free energy reduces to 2
G≈σlv Alv + ðσsl −cU = 2ÞAsl + σsv Asv ;
ð2Þ
which shows that σsl and the electric contribution can be combined to 2 an effective solid–liquid interfacial tension σeff sl = σsl − cU /2. The electrocapillarity relation has first been derived by Gabriel Lippmann, who investigated the capillary depression of mercury in electrolytefilled glass capillaries at variable applied voltage [12]. Upon minimizing Eq. (2) at constant volume or upon simply inserting Lippmann's effective interfacial tension into Young's equation cosθy = (σsv − σsl) / σlv, one obtains the electrowetting equation 2
Fig. 1. Schematic setup of a generic electrowetting experiment involving a sessile drop with a high Young angle at zero volt (dashed drop) on an insulating substrate of thickness d and dielectric constant ε covering a metal electrode (thick black line). Upon applying a voltage U via the immersed wire to the drop, the contact angle decreases.
cos θ = cos θY + cU =2σlv = cos θY + η
ð3Þ
describing the low voltage behavior of the contact angle. Since Eq. (3) can be derived by combining Lippmann's equation with a voltage-
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dependent effective interfacial tension and Young's equation, it is frequently referred to as the Young–Lippmann equation or simply as Lippmann equation (despite the fact that Lippmann never studied contact angle variations). In Eq. (3) we introduced the dimensionless EW number η = cU2/ 2σlv, which measures the relative strength of electrostatic and surface tension forces in the system. By increasing the voltage it is possible to achieve arbitrarily large values of η, which should lead to complete wetting of the liquid on the substrate in contrast to the typical contact angle saturation behavior shown in Fig. 2. Contact angle saturation has been a major challenge in EW, both from a practical perspective and from a fundamental one. Early experiments and qualitative considerations by Vallet et al. [13] suggested that the non-linear materials response due to diverging electric fields in the vicinity of the three-phase contact line plays an important role. Later, Ralston et al. [14] argued that the effective solid–liquid interfacial tension should never become negative. This argument — which has not been generally accepted — leads to a very simple criterion for the minimum contact angle that agrees reasonably well with many experimental data. In recent years, detailed descriptions of the equilibrium surface shape and of the field distribution in the vicinity of the contact line were developed [15,16]. These calculations demonstrated amongst other aspects that the local contact angle at the contact line remains equal to Young's angle independent of the applied voltage. Only the apparent contact angle measured at a distance of order d away from the contact line follows Eq. (3). Moreover, the electric field displays a weak algebraic divergence upon approaching the contact line with an exponent between 0 and − 0.5, depending on θY. These results provided the basis for a more refined picture of the contact angle saturation phenomenon based on the true field distribution and a non-linear dielectric function allowing to incorporate local dielectric breakdown of the insulating layers [17,18]. A more detailed discussion of contact angle saturation can be found in Refs. [4] and [19]. In the remainder of this article, we will focus on the low voltage regime, which follows the regular EW equation. 3. Electrowetting-based microdrop tensiometry The EW equation (Eq. (3)) explicitly states that the response of a drop is inversely proportional to σlv. Several studies report that the presence of surfactants indeed substantially reduces the voltage required to achieve a certain reduction of the contact angle [20], which is obviously beneficial for applications, in particular for batterypowered portable devices. One may however also reverse the perspective and extract σlv from the observed EW response [21]. Fig. 3 illustrates this idea for a series of drops of variable composition in ambient silicone oil. For all drops the contact angle reduction follows the EW equation over a rather wide range of voltages and contact angles. This is largely due to the presence of the ambient silicone oil, which leads to both a particularly high value of Young's angle and a smooth and basically hysteresis-free motion of the (apparent) three-phase contact line. For any given voltage, the response is the weakest for pure water and becomes stronger upon adding solutes (inset of Fig. 3). If we scale the abscissa with the inverse of the interfacial tension (based on macroscopic measurements) all EW response curves collapse onto a single line as shown in the main panel of Fig. 3. The slope α of this line depends only on the device characteristic c, the capacitance per unit area as defined above. If these characteristics are determined independently, the slopes of the EW curves can be used to measure interfacial tensions of drops of unknown composition with sizes down to a few hundred micrometers (as demonstrated in Ref. [21] using interdigitated electrodes rather than a wire to apply the voltage). In practice, calibrating the device with a system of known interfacial tension (e.g. pure H2O–silicone oil) turned out to be the easiest and most reliable method (compared to measuring the
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Fig. 3. Electrowetting curves for a series of different drop fluids in ambient silicone oil with variable surface tension increasing from 5 to 38 mJ/m2 (from top (Triton X) to bottom (water) in the inset). The main panel demonstrates the collapse upon scaling the abscissa with the interfacial tension. (Adapted from Ref. [21]).
insulator thickness by some other means). Using this method, it was possible to determine interfacial tensions of a variety of simple and complex fluids with and without a surfactant for various ambient oils. Typically, the EW-based measurement yielded results that deviated less than 5% from conventional macroscopic Du Noüy measurements. EW thus provides a rather simple-to-use and robust method for measuring interfacial tensions, which is particularly attractive when the macroscopic quantities of liquid required for conventional tensiometry methods are not available. One might worry that specific attraction or repulsion of charged surfactant from the three-phase contact line might lead to deviations from the simple picture based on the EW equation, in particular for DC voltage. Yet no such effects were found up to this point. Presumably, this is due to the fact that possible surfactant concentration gradients are limited to a small region around the contact line and therefore lead to a line tension-like correction, which is overruled by the much stronger energetic contribution to the interfacial energies for the drops with dimensions of tens or hundreds of micrometers. 4. Beyond Newtonian fluids: electrowetting response of complex fluids Microfluidic devices are increasingly used to analyze and to synthesize complex fluids [8]. Compared to Newtonian fluids, complex fluids display a richer spectrum of mechanical properties, which is not only determined by interfacial tensions and viscosity but also by elastic and viscoelastic properties of both bulk materials and interfacial layers. Frequently, only small amounts of the material of interest are available — in the extreme case only a single drop. It is therefore of interest to develop tools that allow for characterizing these materials properties in situ for a single drop in a microfluidic environment. A common approach is to force drops through microfluidic channels of variable geometry and to analyze the deformation of their shape under the influence of hydrodynamic shear and elongational flows [9,22]. In principle, it should be possible to extract the same materials properties also by analyzing the response of the drop shape to electrical forces in electrowetting experiments. As a first attempt in this direction, Banpurkar et al. [23] recently measured the EW response of aqueous gelatin solutions at variable temperature under quasi-static conditions. Gelatin solutions are known to be liquid at temperatures above approximately 35 °C, whereas they display increasingly solid-like behavior at lower temperatures. The snapshots in Fig. 4 indeed show a dramatically different response to the applied voltage between the liquid-like state
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Fig. 4. Snapshots of gelatin drops at variable voltage for temperatures above (top row) and below (bottom row) the gel temperature. (Reproduced with permission from Ref. [23]).
and the solid-like gel state at low temperature. In the latter case, the resulting drop deformation is much weaker owing to the additional elastic restoring forces. Interestingly, the global shape of the drops remained approximately spherical. This observation allows for characterizing the drop shape in terms of the contact angle, as in the liquid state. A quantitative analysis yields that the overall behavior of the EW response curves remained unaffected: Δcosθ increased linearly with the EW number η. The increasing elasticity at lower temperature is reflected in a decreasing slope (see Fig. 5a). To model the behavior, one has to extend the free energy in Eq. (1) by an additional term describing the elastic energy of the system. The deformed drops at low temperature can be described to a good approximation as slightly deformed elastic spheres using Hertz's model of continuum elasticity [24]. Subtracting a correction term that accounts for the finite contact angle at zero voltage, one obtains the relation Welast = β(0.4δ5/2 − δδ3/2 0 ) [23]. Here, β is a constant proportional to the elastic modulus G′ of the material. δ and δ0 describe the indentation of the sphere at finite voltage and at zero voltage, respectively, and can be expressed as functions of the contact angle θ. Minimizing the total free energy w.r.t. θ yields a modified EW equation cos θ = cos θY + η−K Hðcos θ; cos θY Þ:
5. Electrowetting with AC voltage The energy minimization argument leading to the EW equation (Eq. (3)) is equally applicable for both DC and AC voltages. For typical drop sizes in EW experiments, the (hydrodynamic) eigenfrequency of
ð4Þ
In this equation, K ≈ GR0/σ is a constant measuring the relative importance of elasticity and surface tension forces. H(cosθ, cosθY) is a geometric function that increases approximately quadratically from 0 to 3 for −1 b cosθ b 0 for typical values of θY. Eq. (4) is an implicit equation relating cosθ and cosθY with the free parameter K. For purely liquid drops (K = 0), Eq. (4) reduces to the conventional EW equation (Eq. (1)), as expected. The dashed lines in Fig. 5a represent fits of Eq. (4) to the experimental data. Notwithstanding some systematic deviations (in particular for strongly deformed drops at η N 1), the model reproduces both the almost linear EW response and the decreasing slope with increasing voltage. The elastic moduli G′ extracted by fitting the experimental data compare favorably to the low frequency elastic modulus measured on a macroscopic sample in a cone-plate shear rheometer, as shown in Fig. 5b. The method thus produces reliable values for the bulk elastic modulus of the drops in a range from a few Pa to several hundred Pa. Thus similar to interfacial tensions in the case of Newtonian drops, the elasticity of gelled drops can also be determined from the equilibrium shape of sessile drops in EW experiments. An extension of the method to viscous and viscoelastic properties of both bulk and interfacial layers should be possible by monitoring the drop response as a function of time either in an oscillatory fashion or following a step change in the applied voltage.
Fig. 5. EW response of a gelatin drop. a) Variation of cosθ vs. EW number for temperatures decreasing from top to bottom from 25 °C to 18 °C. Colored solid lines: experimental data. Dashed black lines: model results according to Eq. (4). b) Comparison of the elastic modulus G′ determined from the EW response and from macroscopic rheological measurements. (Reproduced with permission from Ref. [23]). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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the drops is in the range of a few tens of Hertz. If AC frequencies are chosen in the kHz range, drops cannot follow the time-dependent electric forces and therefore “see” only the root-mean-square voltage URMS. For even higher AC frequencies, however, the drop phase may no longer behave as a perfect conductor. Jones et al. [25] was the first to demonstrate this effect experimentally by measuring the EWinduced height of rise as a function of frequency for a variety of liquids. For sessile drops, the contact angle of a millimeter-sized drop of water with a low salt concentration (conductivity ≈200 µS/cm) was found to increase by approximately 20° upon increasing the applied frequency from DC to 20 kHz [26]. Moreover, the contact angle was found to depend on the position of the electrode inside the drop for high frequencies and low conductivities. To minimize this geometry-dependence, Kumar et al. [27] performed experiments with drops in a sandwich geometry with a plate separation h. This geometry guarantees that the distance between the electrode in direct contact with the drop and the contact line is essentially independent of the applied voltage (see Fig. 6a). For a conductivity of 300 µS/cm, the contact angle reduction is found to be independent of the AC frequency up to 100 kHz, as shown in Fig. 7c. For lower
Fig. 6. Parallel plate geometry (a) and electric equivalent circuit model for AC measurements of contact angle response. For typical geometries Rd and Cl are frequently negligible. (Adapted from Ref. [27]).
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conductivities, however, the contact angle response is substantially weaker at high frequencies (Fig. 7a and b). The data can be analyzed in terms of a simple effective circuit model as shown in Fig. 6b. Upon inserting typical material parameters, it becomes clear that the system can be reduced to a simple equivalent RC circuit, in which Rl, is the Ohmic resistance of the drop and Cd is the capacitance of the dielectric layer. The degree of contact angle reduction is determined by the voltage at the contact line, which is equal to the voltage drop across Cd in Fig. 6b. The circuit model results in a cut-off frequency ωc = ωbulk· d/h, where ωbulk = ρl/ε0ε is the bulk charge relaxation frequency and ρl is the resistivity of the liquid. A simple analysis leads to a frequencydependent EW equation for the present situation cos θ = cos θY + f ðωÞ η
ð5Þ
where η is the EW number based on the root-mean-square (RMS) voltage URMS. f(ω) = 1 / (1 + (ωRlCd)2) is the frequency response of the RC circuit. This result is found to agree well with the experimental data (see Fig. 8). From a practical perspective, one can extract from the present experiments that the drops can be considered as perfectly conductive within the typical range of AC frequencies in EW experiments up to a few tens of kHz as soon as the conductivity exceeds a few hundred µS/cm, corresponding to salt concentrations of order mM. Recently, Hong et al. [28] presented a numerical study of the same situation for three-dimensional sessile drops at variable frequencies. As in the case of the sandwich drops (and as shown experimentally before in Ref. [26]), they observed that the electric field penetrates into the drop above some critical frequencies. The field penetration is found to relieve the singularity of the electric field, which otherwise occurs upon approaching the contact line [13,15,29]. The authors point out that this effect should postpone the contact angle saturation due to local dielectric breakdown, as studied in recent models by Papathanasiou et al. [17]. Finite conductivity effects in electrowetting also play a crucial role in at least two other situations: (i) EW of complex topographic structures and (ii) pinch-off and drop generation in AC-EW. In a series of publications Seemann et al. [30,31] investigated the wetting of topographically structured hydrophobized Si surfaces with one dimensional rectangular and triangular grooves. For grooves with chemically defined surface energies, a variety of possible liquid morphologies has been observed [32]. The important parameters controlling the stability of these morphologies are the pressure inside the drop, the geometry of the groove (i.e. aspect ratio and opening angle for rectangular and triangular grooves, respectively), and the contact angle on the side walls. According to these experiments, EW should allow for voltage-controlled reversible filling of grooves that
Fig. 7. Electrowetting response for various AC frequencies (DC, 0.5, 1, 5, 10, 20, 40, and 100 kHz) increasing along the arrow for liquid conductivities of ρl = 5 (a), 17 (b), and 300 μS/cm (c). (Adapted from Ref. [27]).
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Fig. 8. EW response f(ω) = (cosθ − cosθY) / ηRMS versus normalized AC frequency shown in Fig. 7. The dotted line represents the RC-cut-off behavior expected from the equivalent circuit model shown in Fig. 6. (Adapted from Ref. [27]).
are empty in equilibrium at zero voltage. Indeed, the experiments showed that liquid fingers extended from drops placed on such surfaces beyond a certain critical voltage (see Fig. 9). In contrast to the expectations, however, these fingers displayed a voltage-dependent finite length rather than extending indefinitely. For fixed voltage, this length was found to decrease with decreasing salt concentration and with increasing AC frequency. These observations could be explained quantitatively by considering the voltage drop along the groove using a transmission line model [30]: the longer the liquid finger, the lower the voltage at the contact line and hence the higher the local contact angle. Beyond a certain critical length, the local angle was thus larger than the critical angle required for filling and hence the liquid fingers stopped growing. Baret et al. [33,34] studied in detail the break-up of capillary bridges in AC electric fields under electrowetting following up on earlier experiments by Klingner et al. [35]. Whenever drops are generated in EW, e.g. upon detaching smaller drops from larger reservoirs, this process involves the generation and break-up of a capillary bridge. For situations in which the drops are not connected to an electrode at all times (such as the increasingly popular “open” configurations with a single substrate [7,36]) the isolated drops carry a finite fixed charge that is determined during the break-up of the capillary bridge. For satellite drops generated at high voltage along the contact line, there is substantial evidence that the conductivity of the liquid plays a crucial
Fig. 9. Drop spreading on a surface with rectangular grooves (width 10 µm; depth 15 µm). a) Top view of drops at various voltages. Note the onset of liquid fingers filling the grooves at 36 V. b) Length of liquid fingers vs. applied voltage for frequencies increasing from 1 kHz (top curve) to 30 kHz (bottom). Inset: Data collapse upon plotting (length · √frequency) vs. applied voltage. (Reprinted with permission from Ref. [30]).
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role [13,37]. In the standard configuration of EW, this phenomenon can lead to self-excited drop oscillations if one immerses the contacting wire only slightly into the drop at zero voltage (see Fig. 10). The phenomenon can be understood by comparing the AC frequency ν and the RC-time constant related to the capacitance between the drop and the substrate electrode and the finite resistance of the capillary bridge. Upon breaking up, the latter increases beyond ν− 1 such that the charge on the drop cannot follow the applied AC voltage anymore. Two situations can be distinguished: (i) provided that the hydrodynamic time scale of the pinch-off is sufficiently long, this process allows for discharging the drop during pinch-off. If so, the drop charge after pinch-off is zero and hence the contact angle is equal to Young's angle (see Fig. 10) [34]. As a consequence, the contact line recedes and the drop grows in height until it touches the wire again. At that moment, the contact angle decreases again, the drop begins to spread and the cycle repeats itself indefinitely. Moreover, self-excited oscillations were also found to induce internal flow patterns inside the drops that promote mixing of the liquid within the drop [38]. The latter is crucial for (bio)chemical applications. (ii) If the AC frequency is low compared to the inverse of the hydrodynamic time scale, the opposite behavior is observed: rather than discharging, the generated isolated drop carries a finite charge. Assuming that the hydrodynamics of the break-up and the applied voltage are independent of each other, one would expect that the charge would be randomly distributed between zero and the maximum value ±cU (see equivalent circuit in Fig. 10). Experimentally, however, it is found that the drops preferentially assume an (absolute) value of the charge close to the maximum value [39]. The origin of this phenomenon is again related to finite conductivity: upon approaching break-up the capacitive current through the capillary bridge gives rise to a voltage drop and to tangential electric fields along the bridge. These fields produce a Maxwell stress that stabilizes the capillary bridge [40]. As a consequence, break-up will be suppressed at moments where the electric field during the AC cycle becomes maximum leading to a synchronization between the hydrodynamics of the break-up and the applied AC voltage.
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materials inside microfluidic chips as well as logic operations in advanced fluidic devices. The stability of the flow is known to depend strongly on the wettability of the two phases. Generally, stable flow conditions and drop generation are only achieved in situations where the continuous phase wets the walls of the microchannel. The primary process in any two-phase flow microfluidic device is the generation of drops by injecting the dispersed phase into a flow of the continuous phase, typically at T-junctions or in a flow focusing geometry. Viscous shear forces in conjunction with interfacial tension control the generation of drops. Compared to conventional digital microfluidic systems based on EW, this approach offers a much higher throughput, however, there is little control over the individual drops. Both the size of the drops and the moment of drop generation are fixed by the imposed average flow rates of the two phases. To achieve more control over these processes it is attractive to combine the advantages of both worlds, the high throughput of continuous flow microfluidic systems and the exquisite control of individual drops of EW systems. The EW-enhanced two-phase microfluidics resulting from this approach consists of microfluidic channels with electrodes embedded into the walls that allow for controlling the wettability of the channel walls locally at the location of the electrodes and temporally whenever a voltage (e.g. a pulse) is applied. A first application of this concept was given by Huh et al. [42], who switched the location of a water jet bounded by two gas jets inside a microfluidic channel. To demonstrate the principle in the context of drop generation, different types of flow focusing devices were fabricated [43–45] including a 90° junction area, where two oil inlets and one water inlet channel merge and subsequently jointly flow towards the outlet of the device on the right-hand side, as shown in Fig. 11. The vertical crosssection of the device (Fig. 11b) also displays the shape of the liquid– liquid interface and its variation upon increasing the applied voltage.
6. Controlling drop generation in two-phase flow in microchannels The generation of micrometer-sized drops in two-phase flows has become a very active field in microfluidic research in recent years [8,41]. Microdrops are used for both analysis and synthesis of novel
Fig. 10. Snapshots from a movie of EW-driven self-excited drop oscillations. (Water in silicone oil; drop size: approx. 1 mm; time between frames: 2 ms) Inset: equivalent circuit model with time-dependent resistance Rn due to breaking capillary bridge and drop-substrate capacitance C. (Reproduced with permission from Ref. [33]).
Fig. 11. Schematic of a flow focusing device with electrowetting functionality. a) Top view of microfluidic channel network including inlets for water and oil held at controlled pressures Pw and Po. The dotted square indicates the location of the electrode in the junction area. b) Vertical cross-section through the junction area showing the EW functionality on the bottom surface, which gives rise to a tunable water–oil interface, as indicated. (Adapted from Ref. [44]).
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Fig. 12. Operating diagram of the device shown in Fig. 11 indicating the regions of stable interfaces at low Pw, drop generation at intermediate Pw, and jetting at high Pw. The hatched area indicates the drop-on-demand region where drops are only generated upon activating the electrode. (See Ref. [44]).
The generation of drops in this configuration is controlled by three parameters, the inlet pressures of the oil (Po) and the water (Pw) phases and the applied voltage U. Three basic operation modes can be distinguished (see Fig. 12): at low water pressures, the oil–water interface is pinned statically in the junction region. No drops are generated. Within the triangular region at intermediate Pw in Fig. 12, drops are periodically generated at a (rather low) rate of a few drops per second that increases upon increasing Pw. For very high values of Pw, a continuous water jet is ejected into the outlet channel. Upon applying a voltage, the onset of both drop generation and jet generation is shifted towards lower water pressures. Physically, the onset of drop generation is determined by a pressure balance: in order to generate drops, Pw has to exceed the sum of the local hydrostatic oil
pressure in the junction and the maximum Laplace pressure ΔPL,max that the oil–water interface can sustain. The former is proportional to Po with a slope that is determined by the hydraulic resistance of the various segments of the channels in analogy with Ohm's law. The latter is determined by the mean curvature κ of the interface, which can be approximated by κ = (2 / w + 1 / R(U)), where w is the width of the water inlet channel and R(U) is the voltage-dependent curvature in the plane depicted in Fig. 11b. Increasing U reduces this maximum curvature and thereby shifts the lower boundary of the drop generation region towards lower water pressures, as seen in Fig. 12. The maximum range of pressure actuation is given by ΔPL,max = ση/h (h: channel height). Two aspects are worth noting: first, if the device is operated in the parameter region just below the onset of drop generation at zero voltage, the generation of drops can be triggered by applying voltage (hatched area in Fig. 12). When the voltage is turned off, the generation of drops ceases. This drop-on-demand capability offers the possibility of timing and synchronizing the generation of drops, which is of interest in more complex microfluidic devices, e.g. for liquid logics applications [46]. Second, the 1/h scaling of ΔPL,max, which is in quantitative agreement with experiments, indicates that the pressure actuation range that can be addressed by EW increases with decreasing channel dimensions. For channel dimensions of 1 µm and below one thus expects a pressure tuning range of the order 1 bar and higher. The effect of EW on the drop generation has also been explored in the somewhat different flow focusing geometry [45] adapted from the classical experiments by Anna et al. [47]. This geometry lends itself more readily to higher drop generation rates in the range of a few kHz. Fig. 13 shows the morphology of drops generated as a function of the water inlet pressure and the applied voltage at a fixed flow rate of the continuous oil phase. Note that the drop size can be tuned much more gradually between several micrometers and a few tens of micrometers in the presence of an applied voltage. (The width of the constriction in Fig. 13 is 50 µm.) At the highest voltage and at low Pw, drops of several micrometers are generated that seem to repel each
Fig. 13. Drop generation in EW-enhanced flow focusing device at variable water inlet pressure Pw and variable voltage for a fixed flow rate of the continuous oil phase. Width of constriction: 50 µm. (Reproduced with permission from Ref. [45]).
F. Mugele et al. / Advances in Colloid and Interface Science 161 (2010) 115–123
other, presumably due to a finite electrostatic charge that they assume while being formed. This behavior is reminiscent of conical sprays in electrospraying. Compared to purely hydrodynamically driven flow focusing devices, for which the dripping mode generally displays a certain minimum drop size, the EW-enhanced device allows for a more continuous coverage of a larger range of drop sizes. These experiments demonstrate the principle of EW-enhanced two-phase flow microfluidic devices. It is expected that the flexibility of this approach can be further improved by using specifically patterned electrodes, which affect the wall wettability only locally, and by applying specific waveforms such as voltage pulses. 7. Conclusion Electrowetting has a wide variety of applications in generating and manipulating drops on (sub)millimeter length scales that are dominated by capillary forces. For perfectly conductive Newtonian liquids, the equilibrium morphology of drops is determined by the minimum of surface energies and electrostatic energy. Any deviation from the ideal situation such as elastic contributions to the drop energy and the penetration of electric fields into the drops as discussed here, gives rise to deviations from the ideal electrowetting behavior. Under favorable conditions (simple geometries, small deformations, and static behavior) analytical models can be developed to quantify these deviations, implying that the corresponding materials properties can be determined from EW experiments. This approach has been demonstrated for various quasi-static situations. Future extensions to dynamic situations would be highly desirable since they would give access to various additional physico-chemical quantities such as dynamic surface tension, viscoelastic properties, and contact line motion. In many cases, we anticipate that such experiments will have to be accompanied by numerical studies to extract quantitative materials properties. Yet, the large number of biophysical and biomedical problems, in which only very little sample is available, makes the development of such EW-based tools a worthwhile goal. Acknowledgements We thank J.-C. Baret, A. Banpurkar, B. Cross, H. Gu, F. Malloggi, and S. Vanapalli for their contributions over the years to the work reviewed here. This work has partially been supported by the research institutes MESA+ and Impact at Twente University as well as MicroNed, and the Microtechnology Research Programme of the Netherlands. References [1] Quere D. Rep Prog Phys 2005;68(11):2495. [2] Darhuber AA, Troian SM. Ann Rev Fluid Mech 2005;37:425. [3] Quilliet C, Berge B. Curr Opinion Coll Interf Sci 2001;6(34):1. [4] Mugele F, Baret J-C. J Phys Cond Matt 2005;17:R705. [5] Fair RB. Microfluidics Nanofluidics 2007;3(3):245. Miller EM, Wheeler AR. Anal Bioanal Chem 2007;393(2):419. [6] Cho SK, Moon HJ, Kim CJ. J Microelectromechanical Syst 2003;12(1):70.
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Pollack MG, Fair RB, Shenderov AD. Appl Phys Lett 2003;77(11):1725. [7] Wheeler AR. Science 2008;322(5901):539. [8] Song H, Chen DL, Ismagilov RF. Angew Chem Int Ed 2006;45:7336. Teh SY, Lin R, Hung LH, Lee AP. Lab Chip 2006;8(2):198. [9] Hudson SD, Cabral JT, Goodrum WJ, Beers KL, Amis EJ. Appl Phys Lett 2005;87(8). [10] Xu JH, Li SW, Lan WJ, Luo GS. Langmuir 2008;24(19):11287. Li SW, Xu JH, Wang YJ, Luo GS. J Colloid Interface Sci 2009;331(1):127. Harvie DJE, Cooper-White JJ, Davidson MR. J Non-Newton Fluid Mech 2008;155(1–2):67. Harvie DJE, Davidson MR, Cooper-White JJ, Rudman M. Int J Multiphase Flow 2007;33 (5):545. Husny J, Cooper-White JJ. J Non-Newton Fluid Mech 2006;137(1–3):121. [11] Abkarian M, Faivre M, Stone HA. Proc Natl Acad Sci USA 2006;103(3):538. Vanapalli SA, Van den Ende HTM, Duits MHG, Mugele F. Appl Phys Lett 2007;90:114109. Abkarian M, Faivre M, Horton R, Smistrup K, Best-Popescu CA, Stone HA. Biomed Mater 2008;3(3). Vanapalli SA, Banpurkar AG, van den Ende D, Duits MHG, Mugele F. Lab Chip 2009;9 (7):982. [12] Lippmann G. Ann Chim Phys 1875;5:494. [13] Vallet M, Vallade M, Berge B. Eur Phys J, B 1999;11:583. [14] Peykov V, Quinn A, Ralston J. Coll Polym Sci 2000;278:789. Quinn A, Sedev R, Ralston J. J Phys Chem, B 2000;109(13):6268. [15] Buehrle J, Herminghaus S, Mugele F. Phys Rev Lett 2003;91:086101. [16] Buehrle J, Mugele F. J Phys Cond Matt 2007;19:375112. [17] Drygiannakis AI, Papathanasiou AG, Boudouvis AG. Langmuir 2009;25(1):147. Papathanasiou AG, Boudouvis AG. Appl Phys Lett 2009;16. [18] Papathanasiou AG, Papaioannou AT, Boudouvis AG. J Appl Phys 2008;103(3). [19] F. Mugele, Soft Matter submitted for publication. [20] Berry S, Kedzierski J, Abedian B. J Colloid Interface Sci 2006;303(2):517. [21] Banpurkar AG, Nichols KP, Mugele F. Langmuir 2008;24(19):10549. [22] Nguyen NT, Lassemono S, Chollet FA, Yang C. IEE Proc Nanobiotechnol 2006;153:102. [23] Banpurkar AG, Duits MHG, van den Ende D, Mugele F. Langmuir 2009;25(2):1245. [24] Landau LD, Lifshitz EM. Lehrbuch der Theoretischen Physik VII: Elastizitätstheorie; 1991. [25] Jones TB, Wang KL, Yao DJ. Langmuir 2004;20(7):2813. [26] Mugele F, Klingner A, Buehrle J, Steinhauser D, Herminghaus S. J Phys, Condens Matter 2005;17:S559. [27] Kumar A., Pluntke, M., Cross, B., Baret, J.-C., and Mugele, F. in Mater. Res. Soc. Symp. (Boston, 2005), Vol. Proc. 899 N06-01. [28] Hong JS, Ko SH, Kang KH, Kang IS. Microfluid Nanofluid 2008;5(2):263. [29] Kang KH. Langmuir 2002;18:10318. [30] Baret JC, Decre M, Herminghaus S, Seemann R. Langmuir 2005;21(26):12218. [31] Baret JC, Decre MMJ, Herminghaus S, Seemann R. Langmuir 2007;23(9):5200. Khare K, Herminghaus S, Baret JC, Law BM, Brinkmann M, Seemann R. Langmuir 2007;23(26):12997. [32] Seemann R, Brinkmann M, Kramer EJ, Lange FF, Lipowsky R. Proc Natl Acad Sci USA 2005;102(6):1848. [33] Baret JC, Decre MMJ, Mugele F. Langmuir 2007;23(9):5173. [34] Baret J-C, Mugele F. Phys Rev Lett 2006;96:016106. [35] Klingner A, Buehrle J, Mugele F. Langmuir 2004;20(16):6770. Klingner A, Herminghaus S, Mugele F. Appl Phys Lett 2004;82(23):4187. [36] Abdelgawad M, Freire SLS, Yang H, Wheeler AR. Lab Chip 2008;8(5):672. [37] Mugele F, Herminghaus S. Appl Phys Lett 2002;81:2303. [38] Mugele F, Baret J-C, Steinhauser D. Appl Phys Lett 2006;88:204106. [39] Malloggi F, van den Ende D, Mugele F. Langmuir 2008;24(20):11847. [40] Saville DA. Annu Rev Fluid Mech 1997;29:27. [41] Stone HA, Stroock AD, Ajdari A. Annu Rev Fluid Mech 2004;36:381. Squires TM, Quake SR. Rev Mod Phys 2004;77:977. [42] Huh D, Tkaczyk AH, Bahng JH, Chang Y, Wei HH, Grotberg JB, et al. J Am Chem Soc 2003;125(48):14678. [43] Malloggi F, Gu H, Banpurkar AG, Vanapalli SA, Mugele F. Eur Phys J, E 2008;26(1–2):91. [44] Malloggi F, Vanapalli SA, Gu H, van den Ende D, Mugele F. J Phys, Condens Matter 2007;19(46). [45] Gu H, Malloggi F, Vanapalli SA, Mugele F. Appl Phys Lett 2008;93:183507. [46] Fuerstman MJ, Garstecki P, Whitesides GM. Science 2007;315(5813):828. Garstecki P, Fuerstman MJ, Whitesides GM. Nat Phys 2007;1(3):168. Prakash M, Gershenfeld N. Science 2007;315(5813):832. [47] Anna SL, Bontoux N, Stone HA. Appl Phys Lett 2003;82(3):364.
Contents lists available at ScienceDirect
Advances in Colloid and Interface Science j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c i s
Electrowetting: A versatile tool for drop manipulation, generation, and characterization Frieder Mugele ⁎, Michel Duits, Dirk van den Ende Physics of Complex Fluids, Univ. of Twente, MESA+ Institute for Nanotechnology and Institute for Mechanics Processes and Control Twente, PO Box 217, 7500 AE Enschede, The Netherlands
a r t i c l e
i n f o
Available online 18 November 2009 Keywords: Microfluidics Electrowetting Two-phase flow Drop generation Wetting Interfacial tension
a b s t r a c t Electrowetting is arguably the most flexible tool to control and vary the wettability of solid surfaces by an external control parameter. In this article we briefly discuss the physical origin of the electrowetting effect and subsequently present a number of approaches for selected novel applications. Specifically, we will discuss the use of EW as a tool to extract materials properties such as interfacial tensions and elastic properties of drops. We will describe some modifications of the EW equation that apply at finite AC voltage for low conductivity fluids when the electric field can partially penetrate into the drops. We will discuss two examples where finite conductivity effects have important consequences, namely electrowetting of topographically structured surfaces as well as the generation of drops in AC electric fields. Finally, we review recent attempts to incorporate electrowetting into conventional channel-based microfluidic devices in order to enhance the flexibility of controlling the generation of drops. © 2009 Elsevier B.V. All rights reserved.
Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Electrowetting basics . . . . . . . . . . . . . . . . . . . . . . . 3. Electrowetting-based microdrop tensiometry . . . . . . . . . . . 4. Beyond Newtonian fluids: electrowetting response of complex fluids 5. Electrowetting with AC voltage . . . . . . . . . . . . . . . . . . 6. Controlling drop generation in two-phase flow in microchannels . . 7. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction On small scales the behavior of liquid drops is dominated by surface tension and wetting forces. By controlling the interaction between liquid and solid we can qualitatively alter the behavior of drops on surfaces. Chemically patterned surfaces give rise to complex drop morphologies, topographically structured hydrophobic surfaces display superhydrophobicity, and surfaces with a gradient in wettability give rise to drop motion [1,2]. From a practical perspective, active means of controlling the wettability of surfaces are very attractive. Many approaches such as thermocapillarity [2] and chemically switchable molecular layers are very attractive. Yet ⁎ Corresponding author. E-mail address: [email protected] (F. Mugele). 0001-8686/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cis.2009.11.002
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limitations regarding the range, speed, flexibility, and long term reliability of the actuation have so far prevented the broad application of these effects. In contrast, electrowetting (EW) [3,4] allows for contact angle variations in excess of 90° at speeds that are only limited by the intrinsic hydrodynamic response time of the fluid for any kind of conductive fluid (and even some strongly polarizable nonconductive ones) for hundreds of thousands of actuation cycles without any sign of degradation. As a consequence, EW has become the most popular platform for ‘digital’ microfluidic systems that are based on the manipulation of discrete drops in a microfluidic chip [4–6]. Using a large number of individually addressable electrodes, EW allows for generating, moving, merging, splitting, and mixing of individual drops. While these basic drop manipulation operations were initially demonstrated with simple liquids (aqueous salt solutions), recent biotechnological applications make use of a large
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variety of fluids with an increasingly complex ‘cocktail’ of solutes as required for instance for immunoassays and DNA replication using polymerase chain reaction (PCR) [5,7]. In these applications, EW makes use of discrete drops as individual (bio)chemical microreactors with well-defined and/or well-controlled chemical composition — an approach that is shared with microchannel-based two-phase flow systems [8]. Compared to EW devices, the latter offer the advantage of high throughput capability, which makes them suitable for combinatorial screening applications and for the synthesis of novel materials, such as micrometer-sized colloidal particles, functional microparticles, capsules, emulsions, etc. with a high degree of monodispersity. Both in EW and in channel-based microfluidic systems, the generation and manipulation of drops depend crucially on the materials properties of the liquid, including in particular interfacial tensions and rheological properties. The desire to generate and manipulate drops of liquids with increasingly complex composition therefore asks for tools to characterize these properties on chip. For continuous flow systems a variety of approaches have been proposed based either on the hydrodynamically induced deformation of flowing drops in channels of variable geometry [9,10] or on the comparator principle, which makes use of the excess hydraulic resistance generated by a ‘drop’ (which can be as complex as living cells) inside a microfluidic channel with respect to a droplet-free reference channel [11]. In this article, we review briefly the basic principle of the electrowetting effect and its derivation from the minimization of interfacial and electrostatic energies. A more detailed review can be found in [4]. Subsequently, we present a number of applications of EW focusing on recent work in our laboratory. First, we demonstrate that materials properties such as the interfacial tension and elasticity can be extracted with remarkable accuracy from the EW response of submillimeter sessile drops. Second, we discuss modifications of the EW due to effects of finite conductivity in the case of electrowetting with AC voltage. Finally, we present several proof-of-principle experiments demonstrating the capability of EW to manipulate two-phase flows inside microchannels. 2. Electrowetting basics Fig. 1 shows the generic configuration of an electrowetting setup. It consists of a sessile drop of a partially wetting conductive liquid on an electrically insulating dielectric layer covering a flat electrode. Typically the drop size is of order 0.1 to 1 mm and is much larger than the thickness d of the dielectric layer, which mostly lies between 0.1 µm and a few micrometers. Since electrowetting can only reduce the contact angle of conductive liquids, which are typically used as the droplet phase, one usually chooses dielectric layers (e.g. fluoropolymers) that display a high contact angle at zero voltage. Upon applying a voltage U between the electrode on the substrate and the drop — in the generic configuration via the immersed wire — the contact angle is reduced as shown in Fig. 2. The contact angle reduction displays two regimes. At low
Fig. 2. Typical electrowetting response of an aqueous drop in ambient silicone oil displaying a parabolic increase of cosθ up to a voltage of approximately 250 V and contact angle saturation at higher voltages.
voltage, the contact angle reduction is characterized by a quadratic increase of cosθ with increasing U. At higher voltage, this dependence becomes weaker and eventually the contact angle saturates at some finite value, which depends on the specific system. The low voltage regime can be understood by minimizing at fixed volume the interfacial energies and electrostatic energies assuming that the drop phase is perfectly conductive and that the ambient phase and the dielectric layer behave as perfect dielectrics. Since one fixes the electrical potentials of the drop and of the electrode on the substrate, the electrostatic contribution enters with a negative sign in the Gibbs free energy G 1 → → ! G = ∑ σi Ai − ∫ D E dV = min : 2 i
ð1Þ
Here σi and Ai are the interfacial tensions and the interfacial areas of the interfaces i between the substrate and the drop, the substrate and the ambient phase, and the drop and the ambient phase. For convenience, we denote these as solid–liquid (sl), solid–vapor (sv), and liquid–vapor (lv) interfaces, respectively, noting that the ambient → phase may consist of a second immiscible liquid rather than vapor. E → and D are the electric field and the electric displacement, respectively, and the volume integral extends over the entire system. For perfectly conductive drops the electric field assumes non-zero values only within the dielectric layer below the drop and in a small region of order d around the three-phase contact line. If the drop size is large compared to d, the latter line contribution can be neglected and the electrostatic volume integral reduces to the energy of a parallel plate capacitor cU2 Asl/2, where c = ε0ε/d is the capacitance per unit area (ε0ε: dielectric permittivity of the insulating layer). Hence, the Gibbs free energy reduces to 2
G≈σlv Alv + ðσsl −cU = 2ÞAsl + σsv Asv ;
ð2Þ
which shows that σsl and the electric contribution can be combined to 2 an effective solid–liquid interfacial tension σeff sl = σsl − cU /2. The electrocapillarity relation has first been derived by Gabriel Lippmann, who investigated the capillary depression of mercury in electrolytefilled glass capillaries at variable applied voltage [12]. Upon minimizing Eq. (2) at constant volume or upon simply inserting Lippmann's effective interfacial tension into Young's equation cosθy = (σsv − σsl) / σlv, one obtains the electrowetting equation 2
Fig. 1. Schematic setup of a generic electrowetting experiment involving a sessile drop with a high Young angle at zero volt (dashed drop) on an insulating substrate of thickness d and dielectric constant ε covering a metal electrode (thick black line). Upon applying a voltage U via the immersed wire to the drop, the contact angle decreases.
cos θ = cos θY + cU =2σlv = cos θY + η
ð3Þ
describing the low voltage behavior of the contact angle. Since Eq. (3) can be derived by combining Lippmann's equation with a voltage-
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dependent effective interfacial tension and Young's equation, it is frequently referred to as the Young–Lippmann equation or simply as Lippmann equation (despite the fact that Lippmann never studied contact angle variations). In Eq. (3) we introduced the dimensionless EW number η = cU2/ 2σlv, which measures the relative strength of electrostatic and surface tension forces in the system. By increasing the voltage it is possible to achieve arbitrarily large values of η, which should lead to complete wetting of the liquid on the substrate in contrast to the typical contact angle saturation behavior shown in Fig. 2. Contact angle saturation has been a major challenge in EW, both from a practical perspective and from a fundamental one. Early experiments and qualitative considerations by Vallet et al. [13] suggested that the non-linear materials response due to diverging electric fields in the vicinity of the three-phase contact line plays an important role. Later, Ralston et al. [14] argued that the effective solid–liquid interfacial tension should never become negative. This argument — which has not been generally accepted — leads to a very simple criterion for the minimum contact angle that agrees reasonably well with many experimental data. In recent years, detailed descriptions of the equilibrium surface shape and of the field distribution in the vicinity of the contact line were developed [15,16]. These calculations demonstrated amongst other aspects that the local contact angle at the contact line remains equal to Young's angle independent of the applied voltage. Only the apparent contact angle measured at a distance of order d away from the contact line follows Eq. (3). Moreover, the electric field displays a weak algebraic divergence upon approaching the contact line with an exponent between 0 and − 0.5, depending on θY. These results provided the basis for a more refined picture of the contact angle saturation phenomenon based on the true field distribution and a non-linear dielectric function allowing to incorporate local dielectric breakdown of the insulating layers [17,18]. A more detailed discussion of contact angle saturation can be found in Refs. [4] and [19]. In the remainder of this article, we will focus on the low voltage regime, which follows the regular EW equation. 3. Electrowetting-based microdrop tensiometry The EW equation (Eq. (3)) explicitly states that the response of a drop is inversely proportional to σlv. Several studies report that the presence of surfactants indeed substantially reduces the voltage required to achieve a certain reduction of the contact angle [20], which is obviously beneficial for applications, in particular for batterypowered portable devices. One may however also reverse the perspective and extract σlv from the observed EW response [21]. Fig. 3 illustrates this idea for a series of drops of variable composition in ambient silicone oil. For all drops the contact angle reduction follows the EW equation over a rather wide range of voltages and contact angles. This is largely due to the presence of the ambient silicone oil, which leads to both a particularly high value of Young's angle and a smooth and basically hysteresis-free motion of the (apparent) three-phase contact line. For any given voltage, the response is the weakest for pure water and becomes stronger upon adding solutes (inset of Fig. 3). If we scale the abscissa with the inverse of the interfacial tension (based on macroscopic measurements) all EW response curves collapse onto a single line as shown in the main panel of Fig. 3. The slope α of this line depends only on the device characteristic c, the capacitance per unit area as defined above. If these characteristics are determined independently, the slopes of the EW curves can be used to measure interfacial tensions of drops of unknown composition with sizes down to a few hundred micrometers (as demonstrated in Ref. [21] using interdigitated electrodes rather than a wire to apply the voltage). In practice, calibrating the device with a system of known interfacial tension (e.g. pure H2O–silicone oil) turned out to be the easiest and most reliable method (compared to measuring the
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Fig. 3. Electrowetting curves for a series of different drop fluids in ambient silicone oil with variable surface tension increasing from 5 to 38 mJ/m2 (from top (Triton X) to bottom (water) in the inset). The main panel demonstrates the collapse upon scaling the abscissa with the interfacial tension. (Adapted from Ref. [21]).
insulator thickness by some other means). Using this method, it was possible to determine interfacial tensions of a variety of simple and complex fluids with and without a surfactant for various ambient oils. Typically, the EW-based measurement yielded results that deviated less than 5% from conventional macroscopic Du Noüy measurements. EW thus provides a rather simple-to-use and robust method for measuring interfacial tensions, which is particularly attractive when the macroscopic quantities of liquid required for conventional tensiometry methods are not available. One might worry that specific attraction or repulsion of charged surfactant from the three-phase contact line might lead to deviations from the simple picture based on the EW equation, in particular for DC voltage. Yet no such effects were found up to this point. Presumably, this is due to the fact that possible surfactant concentration gradients are limited to a small region around the contact line and therefore lead to a line tension-like correction, which is overruled by the much stronger energetic contribution to the interfacial energies for the drops with dimensions of tens or hundreds of micrometers. 4. Beyond Newtonian fluids: electrowetting response of complex fluids Microfluidic devices are increasingly used to analyze and to synthesize complex fluids [8]. Compared to Newtonian fluids, complex fluids display a richer spectrum of mechanical properties, which is not only determined by interfacial tensions and viscosity but also by elastic and viscoelastic properties of both bulk materials and interfacial layers. Frequently, only small amounts of the material of interest are available — in the extreme case only a single drop. It is therefore of interest to develop tools that allow for characterizing these materials properties in situ for a single drop in a microfluidic environment. A common approach is to force drops through microfluidic channels of variable geometry and to analyze the deformation of their shape under the influence of hydrodynamic shear and elongational flows [9,22]. In principle, it should be possible to extract the same materials properties also by analyzing the response of the drop shape to electrical forces in electrowetting experiments. As a first attempt in this direction, Banpurkar et al. [23] recently measured the EW response of aqueous gelatin solutions at variable temperature under quasi-static conditions. Gelatin solutions are known to be liquid at temperatures above approximately 35 °C, whereas they display increasingly solid-like behavior at lower temperatures. The snapshots in Fig. 4 indeed show a dramatically different response to the applied voltage between the liquid-like state
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Fig. 4. Snapshots of gelatin drops at variable voltage for temperatures above (top row) and below (bottom row) the gel temperature. (Reproduced with permission from Ref. [23]).
and the solid-like gel state at low temperature. In the latter case, the resulting drop deformation is much weaker owing to the additional elastic restoring forces. Interestingly, the global shape of the drops remained approximately spherical. This observation allows for characterizing the drop shape in terms of the contact angle, as in the liquid state. A quantitative analysis yields that the overall behavior of the EW response curves remained unaffected: Δcosθ increased linearly with the EW number η. The increasing elasticity at lower temperature is reflected in a decreasing slope (see Fig. 5a). To model the behavior, one has to extend the free energy in Eq. (1) by an additional term describing the elastic energy of the system. The deformed drops at low temperature can be described to a good approximation as slightly deformed elastic spheres using Hertz's model of continuum elasticity [24]. Subtracting a correction term that accounts for the finite contact angle at zero voltage, one obtains the relation Welast = β(0.4δ5/2 − δδ3/2 0 ) [23]. Here, β is a constant proportional to the elastic modulus G′ of the material. δ and δ0 describe the indentation of the sphere at finite voltage and at zero voltage, respectively, and can be expressed as functions of the contact angle θ. Minimizing the total free energy w.r.t. θ yields a modified EW equation cos θ = cos θY + η−K Hðcos θ; cos θY Þ:
5. Electrowetting with AC voltage The energy minimization argument leading to the EW equation (Eq. (3)) is equally applicable for both DC and AC voltages. For typical drop sizes in EW experiments, the (hydrodynamic) eigenfrequency of
ð4Þ
In this equation, K ≈ GR0/σ is a constant measuring the relative importance of elasticity and surface tension forces. H(cosθ, cosθY) is a geometric function that increases approximately quadratically from 0 to 3 for −1 b cosθ b 0 for typical values of θY. Eq. (4) is an implicit equation relating cosθ and cosθY with the free parameter K. For purely liquid drops (K = 0), Eq. (4) reduces to the conventional EW equation (Eq. (1)), as expected. The dashed lines in Fig. 5a represent fits of Eq. (4) to the experimental data. Notwithstanding some systematic deviations (in particular for strongly deformed drops at η N 1), the model reproduces both the almost linear EW response and the decreasing slope with increasing voltage. The elastic moduli G′ extracted by fitting the experimental data compare favorably to the low frequency elastic modulus measured on a macroscopic sample in a cone-plate shear rheometer, as shown in Fig. 5b. The method thus produces reliable values for the bulk elastic modulus of the drops in a range from a few Pa to several hundred Pa. Thus similar to interfacial tensions in the case of Newtonian drops, the elasticity of gelled drops can also be determined from the equilibrium shape of sessile drops in EW experiments. An extension of the method to viscous and viscoelastic properties of both bulk and interfacial layers should be possible by monitoring the drop response as a function of time either in an oscillatory fashion or following a step change in the applied voltage.
Fig. 5. EW response of a gelatin drop. a) Variation of cosθ vs. EW number for temperatures decreasing from top to bottom from 25 °C to 18 °C. Colored solid lines: experimental data. Dashed black lines: model results according to Eq. (4). b) Comparison of the elastic modulus G′ determined from the EW response and from macroscopic rheological measurements. (Reproduced with permission from Ref. [23]). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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the drops is in the range of a few tens of Hertz. If AC frequencies are chosen in the kHz range, drops cannot follow the time-dependent electric forces and therefore “see” only the root-mean-square voltage URMS. For even higher AC frequencies, however, the drop phase may no longer behave as a perfect conductor. Jones et al. [25] was the first to demonstrate this effect experimentally by measuring the EWinduced height of rise as a function of frequency for a variety of liquids. For sessile drops, the contact angle of a millimeter-sized drop of water with a low salt concentration (conductivity ≈200 µS/cm) was found to increase by approximately 20° upon increasing the applied frequency from DC to 20 kHz [26]. Moreover, the contact angle was found to depend on the position of the electrode inside the drop for high frequencies and low conductivities. To minimize this geometry-dependence, Kumar et al. [27] performed experiments with drops in a sandwich geometry with a plate separation h. This geometry guarantees that the distance between the electrode in direct contact with the drop and the contact line is essentially independent of the applied voltage (see Fig. 6a). For a conductivity of 300 µS/cm, the contact angle reduction is found to be independent of the AC frequency up to 100 kHz, as shown in Fig. 7c. For lower
Fig. 6. Parallel plate geometry (a) and electric equivalent circuit model for AC measurements of contact angle response. For typical geometries Rd and Cl are frequently negligible. (Adapted from Ref. [27]).
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conductivities, however, the contact angle response is substantially weaker at high frequencies (Fig. 7a and b). The data can be analyzed in terms of a simple effective circuit model as shown in Fig. 6b. Upon inserting typical material parameters, it becomes clear that the system can be reduced to a simple equivalent RC circuit, in which Rl, is the Ohmic resistance of the drop and Cd is the capacitance of the dielectric layer. The degree of contact angle reduction is determined by the voltage at the contact line, which is equal to the voltage drop across Cd in Fig. 6b. The circuit model results in a cut-off frequency ωc = ωbulk· d/h, where ωbulk = ρl/ε0ε is the bulk charge relaxation frequency and ρl is the resistivity of the liquid. A simple analysis leads to a frequencydependent EW equation for the present situation cos θ = cos θY + f ðωÞ η
ð5Þ
where η is the EW number based on the root-mean-square (RMS) voltage URMS. f(ω) = 1 / (1 + (ωRlCd)2) is the frequency response of the RC circuit. This result is found to agree well with the experimental data (see Fig. 8). From a practical perspective, one can extract from the present experiments that the drops can be considered as perfectly conductive within the typical range of AC frequencies in EW experiments up to a few tens of kHz as soon as the conductivity exceeds a few hundred µS/cm, corresponding to salt concentrations of order mM. Recently, Hong et al. [28] presented a numerical study of the same situation for three-dimensional sessile drops at variable frequencies. As in the case of the sandwich drops (and as shown experimentally before in Ref. [26]), they observed that the electric field penetrates into the drop above some critical frequencies. The field penetration is found to relieve the singularity of the electric field, which otherwise occurs upon approaching the contact line [13,15,29]. The authors point out that this effect should postpone the contact angle saturation due to local dielectric breakdown, as studied in recent models by Papathanasiou et al. [17]. Finite conductivity effects in electrowetting also play a crucial role in at least two other situations: (i) EW of complex topographic structures and (ii) pinch-off and drop generation in AC-EW. In a series of publications Seemann et al. [30,31] investigated the wetting of topographically structured hydrophobized Si surfaces with one dimensional rectangular and triangular grooves. For grooves with chemically defined surface energies, a variety of possible liquid morphologies has been observed [32]. The important parameters controlling the stability of these morphologies are the pressure inside the drop, the geometry of the groove (i.e. aspect ratio and opening angle for rectangular and triangular grooves, respectively), and the contact angle on the side walls. According to these experiments, EW should allow for voltage-controlled reversible filling of grooves that
Fig. 7. Electrowetting response for various AC frequencies (DC, 0.5, 1, 5, 10, 20, 40, and 100 kHz) increasing along the arrow for liquid conductivities of ρl = 5 (a), 17 (b), and 300 μS/cm (c). (Adapted from Ref. [27]).
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Fig. 8. EW response f(ω) = (cosθ − cosθY) / ηRMS versus normalized AC frequency shown in Fig. 7. The dotted line represents the RC-cut-off behavior expected from the equivalent circuit model shown in Fig. 6. (Adapted from Ref. [27]).
are empty in equilibrium at zero voltage. Indeed, the experiments showed that liquid fingers extended from drops placed on such surfaces beyond a certain critical voltage (see Fig. 9). In contrast to the expectations, however, these fingers displayed a voltage-dependent finite length rather than extending indefinitely. For fixed voltage, this length was found to decrease with decreasing salt concentration and with increasing AC frequency. These observations could be explained quantitatively by considering the voltage drop along the groove using a transmission line model [30]: the longer the liquid finger, the lower the voltage at the contact line and hence the higher the local contact angle. Beyond a certain critical length, the local angle was thus larger than the critical angle required for filling and hence the liquid fingers stopped growing. Baret et al. [33,34] studied in detail the break-up of capillary bridges in AC electric fields under electrowetting following up on earlier experiments by Klingner et al. [35]. Whenever drops are generated in EW, e.g. upon detaching smaller drops from larger reservoirs, this process involves the generation and break-up of a capillary bridge. For situations in which the drops are not connected to an electrode at all times (such as the increasingly popular “open” configurations with a single substrate [7,36]) the isolated drops carry a finite fixed charge that is determined during the break-up of the capillary bridge. For satellite drops generated at high voltage along the contact line, there is substantial evidence that the conductivity of the liquid plays a crucial
Fig. 9. Drop spreading on a surface with rectangular grooves (width 10 µm; depth 15 µm). a) Top view of drops at various voltages. Note the onset of liquid fingers filling the grooves at 36 V. b) Length of liquid fingers vs. applied voltage for frequencies increasing from 1 kHz (top curve) to 30 kHz (bottom). Inset: Data collapse upon plotting (length · √frequency) vs. applied voltage. (Reprinted with permission from Ref. [30]).
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role [13,37]. In the standard configuration of EW, this phenomenon can lead to self-excited drop oscillations if one immerses the contacting wire only slightly into the drop at zero voltage (see Fig. 10). The phenomenon can be understood by comparing the AC frequency ν and the RC-time constant related to the capacitance between the drop and the substrate electrode and the finite resistance of the capillary bridge. Upon breaking up, the latter increases beyond ν− 1 such that the charge on the drop cannot follow the applied AC voltage anymore. Two situations can be distinguished: (i) provided that the hydrodynamic time scale of the pinch-off is sufficiently long, this process allows for discharging the drop during pinch-off. If so, the drop charge after pinch-off is zero and hence the contact angle is equal to Young's angle (see Fig. 10) [34]. As a consequence, the contact line recedes and the drop grows in height until it touches the wire again. At that moment, the contact angle decreases again, the drop begins to spread and the cycle repeats itself indefinitely. Moreover, self-excited oscillations were also found to induce internal flow patterns inside the drops that promote mixing of the liquid within the drop [38]. The latter is crucial for (bio)chemical applications. (ii) If the AC frequency is low compared to the inverse of the hydrodynamic time scale, the opposite behavior is observed: rather than discharging, the generated isolated drop carries a finite charge. Assuming that the hydrodynamics of the break-up and the applied voltage are independent of each other, one would expect that the charge would be randomly distributed between zero and the maximum value ±cU (see equivalent circuit in Fig. 10). Experimentally, however, it is found that the drops preferentially assume an (absolute) value of the charge close to the maximum value [39]. The origin of this phenomenon is again related to finite conductivity: upon approaching break-up the capacitive current through the capillary bridge gives rise to a voltage drop and to tangential electric fields along the bridge. These fields produce a Maxwell stress that stabilizes the capillary bridge [40]. As a consequence, break-up will be suppressed at moments where the electric field during the AC cycle becomes maximum leading to a synchronization between the hydrodynamics of the break-up and the applied AC voltage.
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materials inside microfluidic chips as well as logic operations in advanced fluidic devices. The stability of the flow is known to depend strongly on the wettability of the two phases. Generally, stable flow conditions and drop generation are only achieved in situations where the continuous phase wets the walls of the microchannel. The primary process in any two-phase flow microfluidic device is the generation of drops by injecting the dispersed phase into a flow of the continuous phase, typically at T-junctions or in a flow focusing geometry. Viscous shear forces in conjunction with interfacial tension control the generation of drops. Compared to conventional digital microfluidic systems based on EW, this approach offers a much higher throughput, however, there is little control over the individual drops. Both the size of the drops and the moment of drop generation are fixed by the imposed average flow rates of the two phases. To achieve more control over these processes it is attractive to combine the advantages of both worlds, the high throughput of continuous flow microfluidic systems and the exquisite control of individual drops of EW systems. The EW-enhanced two-phase microfluidics resulting from this approach consists of microfluidic channels with electrodes embedded into the walls that allow for controlling the wettability of the channel walls locally at the location of the electrodes and temporally whenever a voltage (e.g. a pulse) is applied. A first application of this concept was given by Huh et al. [42], who switched the location of a water jet bounded by two gas jets inside a microfluidic channel. To demonstrate the principle in the context of drop generation, different types of flow focusing devices were fabricated [43–45] including a 90° junction area, where two oil inlets and one water inlet channel merge and subsequently jointly flow towards the outlet of the device on the right-hand side, as shown in Fig. 11. The vertical crosssection of the device (Fig. 11b) also displays the shape of the liquid– liquid interface and its variation upon increasing the applied voltage.
6. Controlling drop generation in two-phase flow in microchannels The generation of micrometer-sized drops in two-phase flows has become a very active field in microfluidic research in recent years [8,41]. Microdrops are used for both analysis and synthesis of novel
Fig. 10. Snapshots from a movie of EW-driven self-excited drop oscillations. (Water in silicone oil; drop size: approx. 1 mm; time between frames: 2 ms) Inset: equivalent circuit model with time-dependent resistance Rn due to breaking capillary bridge and drop-substrate capacitance C. (Reproduced with permission from Ref. [33]).
Fig. 11. Schematic of a flow focusing device with electrowetting functionality. a) Top view of microfluidic channel network including inlets for water and oil held at controlled pressures Pw and Po. The dotted square indicates the location of the electrode in the junction area. b) Vertical cross-section through the junction area showing the EW functionality on the bottom surface, which gives rise to a tunable water–oil interface, as indicated. (Adapted from Ref. [44]).
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Fig. 12. Operating diagram of the device shown in Fig. 11 indicating the regions of stable interfaces at low Pw, drop generation at intermediate Pw, and jetting at high Pw. The hatched area indicates the drop-on-demand region where drops are only generated upon activating the electrode. (See Ref. [44]).
The generation of drops in this configuration is controlled by three parameters, the inlet pressures of the oil (Po) and the water (Pw) phases and the applied voltage U. Three basic operation modes can be distinguished (see Fig. 12): at low water pressures, the oil–water interface is pinned statically in the junction region. No drops are generated. Within the triangular region at intermediate Pw in Fig. 12, drops are periodically generated at a (rather low) rate of a few drops per second that increases upon increasing Pw. For very high values of Pw, a continuous water jet is ejected into the outlet channel. Upon applying a voltage, the onset of both drop generation and jet generation is shifted towards lower water pressures. Physically, the onset of drop generation is determined by a pressure balance: in order to generate drops, Pw has to exceed the sum of the local hydrostatic oil
pressure in the junction and the maximum Laplace pressure ΔPL,max that the oil–water interface can sustain. The former is proportional to Po with a slope that is determined by the hydraulic resistance of the various segments of the channels in analogy with Ohm's law. The latter is determined by the mean curvature κ of the interface, which can be approximated by κ = (2 / w + 1 / R(U)), where w is the width of the water inlet channel and R(U) is the voltage-dependent curvature in the plane depicted in Fig. 11b. Increasing U reduces this maximum curvature and thereby shifts the lower boundary of the drop generation region towards lower water pressures, as seen in Fig. 12. The maximum range of pressure actuation is given by ΔPL,max = ση/h (h: channel height). Two aspects are worth noting: first, if the device is operated in the parameter region just below the onset of drop generation at zero voltage, the generation of drops can be triggered by applying voltage (hatched area in Fig. 12). When the voltage is turned off, the generation of drops ceases. This drop-on-demand capability offers the possibility of timing and synchronizing the generation of drops, which is of interest in more complex microfluidic devices, e.g. for liquid logics applications [46]. Second, the 1/h scaling of ΔPL,max, which is in quantitative agreement with experiments, indicates that the pressure actuation range that can be addressed by EW increases with decreasing channel dimensions. For channel dimensions of 1 µm and below one thus expects a pressure tuning range of the order 1 bar and higher. The effect of EW on the drop generation has also been explored in the somewhat different flow focusing geometry [45] adapted from the classical experiments by Anna et al. [47]. This geometry lends itself more readily to higher drop generation rates in the range of a few kHz. Fig. 13 shows the morphology of drops generated as a function of the water inlet pressure and the applied voltage at a fixed flow rate of the continuous oil phase. Note that the drop size can be tuned much more gradually between several micrometers and a few tens of micrometers in the presence of an applied voltage. (The width of the constriction in Fig. 13 is 50 µm.) At the highest voltage and at low Pw, drops of several micrometers are generated that seem to repel each
Fig. 13. Drop generation in EW-enhanced flow focusing device at variable water inlet pressure Pw and variable voltage for a fixed flow rate of the continuous oil phase. Width of constriction: 50 µm. (Reproduced with permission from Ref. [45]).
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other, presumably due to a finite electrostatic charge that they assume while being formed. This behavior is reminiscent of conical sprays in electrospraying. Compared to purely hydrodynamically driven flow focusing devices, for which the dripping mode generally displays a certain minimum drop size, the EW-enhanced device allows for a more continuous coverage of a larger range of drop sizes. These experiments demonstrate the principle of EW-enhanced two-phase flow microfluidic devices. It is expected that the flexibility of this approach can be further improved by using specifically patterned electrodes, which affect the wall wettability only locally, and by applying specific waveforms such as voltage pulses. 7. Conclusion Electrowetting has a wide variety of applications in generating and manipulating drops on (sub)millimeter length scales that are dominated by capillary forces. For perfectly conductive Newtonian liquids, the equilibrium morphology of drops is determined by the minimum of surface energies and electrostatic energy. Any deviation from the ideal situation such as elastic contributions to the drop energy and the penetration of electric fields into the drops as discussed here, gives rise to deviations from the ideal electrowetting behavior. Under favorable conditions (simple geometries, small deformations, and static behavior) analytical models can be developed to quantify these deviations, implying that the corresponding materials properties can be determined from EW experiments. This approach has been demonstrated for various quasi-static situations. Future extensions to dynamic situations would be highly desirable since they would give access to various additional physico-chemical quantities such as dynamic surface tension, viscoelastic properties, and contact line motion. In many cases, we anticipate that such experiments will have to be accompanied by numerical studies to extract quantitative materials properties. Yet, the large number of biophysical and biomedical problems, in which only very little sample is available, makes the development of such EW-based tools a worthwhile goal. Acknowledgements We thank J.-C. Baret, A. Banpurkar, B. Cross, H. Gu, F. Malloggi, and S. Vanapalli for their contributions over the years to the work reviewed here. This work has partially been supported by the research institutes MESA+ and Impact at Twente University as well as MicroNed, and the Microtechnology Research Programme of the Netherlands. References [1] Quere D. Rep Prog Phys 2005;68(11):2495. [2] Darhuber AA, Troian SM. Ann Rev Fluid Mech 2005;37:425. [3] Quilliet C, Berge B. Curr Opinion Coll Interf Sci 2001;6(34):1. [4] Mugele F, Baret J-C. J Phys Cond Matt 2005;17:R705. [5] Fair RB. Microfluidics Nanofluidics 2007;3(3):245. Miller EM, Wheeler AR. Anal Bioanal Chem 2007;393(2):419. [6] Cho SK, Moon HJ, Kim CJ. J Microelectromechanical Syst 2003;12(1):70.
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