Interface profiles near three-phase contact lines in electric fields

Chip-integrated non-mechanical microfluidic pump driven by electrowetting on dielectrics

A microfluidic pump is presented that generates its pumping action via the EWOD (electrowetting-on-dielectric) effect. The flow is generated by the periodic movement of liquid-vapor interfaces in a large number (≈106) of microcavities resulting in a volume change of approx. 0.5 pl per cavity per pump stroke. The total flow resulting from all microcavities adds up to a few hundred nanolitres per cycle. Passive, topologically optimized, non-mechanical Tesla valves are used to rectify the flow. As a result, the micropump operates without any moving components. The dimensioning, fabrication, and characterization process of the micropump are described. Device fabrication is done using conventional manufacturing processes from microsystems technology, enabling cost-effective mass production on wafer-level without additional assembly steps like piezo chip-level bonding, etc. This allows for direct integration into wafer-based microfluidic or lab-on-a-chip applications. Furthermore, first measurement results obtained with prototypes of the micropump are presented. The voltage- and frequency-dependent pump performance is determined. The measurements show that a continuous flow rate larger than 0.2 ml min-1 can be achieved at a maximum pump pressure larger than 12 mbar.

Statistical Mechanics of Electrowetting

We derive the ab initio equilibrium statistical mechanics of the gas-liquid-solid contact angle on planar periodic, monodisperse, textured surfaces subject to electrowetting. To that end, we extend an earlier theory that predicts the advance or recession of the contact line amount to distinct first-order phase transitions of the filling state in the ensemble of nearby surface cavities. Upon calculating the individual capacitance of a cavity subject to the influence of its near neighbors, we show how hysteresis, which is manifested by different advancing and receding contact angles, is affected by electrowetting. The analysis reveals nine distinct regimes characterizing contact angle behavior, three of which arise only when a voltage is applied to the conductive liquid drop. As the square voltage is progressively increased, the theory elucidates how the drop occasionally undergoes regime transitions triggering jumps in the contact angle, possibly changing its hysteresis, or saturating it at a value weakly dependent on further voltage growth. To illustrate these phenomena and validate the theory, we confront its predictions with four data sets. A benefit of the theory is that it forsakes trial and error when designing textured surfaces with specific contact angle behavior.

Surface Charge Deposition by Moving Drops Reduces Contact Angles

Slide electrification-the spontaneous charge separation by sliding aqueous drops-can lead to an electrostatic potential in the order of 1 kV and change drop motion substantially. To find out how slide electrification influences the contact angles of moving drops, we analyzed the dynamic contact angles of aqueous drops sliding down tilted plates with insulated surfaces, grounded surfaces, and while grounding the drop. The observed decrease in dynamic contact angles at different salt concentrations is attributed to two effects: An electrocapillary reduction of contact angles caused by drop charging and a change in the free surface energy of the solid due to surface charging.

Thermodynamic Study of the Electric Field Effect on Liquid-Vapor Mixture at Equilibrium: An Analysis on a Water-Ethanol Mixture

In this paper, the effect of electric fields on phase equilibria through polarization is investigated. A relation is derived for the chemical potential of a system, where the electric field is localized over a liquid phase mixture in equilibrium with a vapor phase mixture. This relation is then applied to a water-ethanol mixture to explore the effect of polarization-based electric fields on the liquid phase composition. It is observed that the quadratic dependence on electric field strength produces little effect below field strengths of approx. 10 MV/m. However, above this field strength, the mole fraction of water in the liquid phase grows rapidly, increasing by a factor of 8 for a water vapor phase fraction of 0.2 and a field strength of 500 MV/m, which approaches the dielectric breakdown strength of water. Nonetheless, this field strength could be achievable with microfluidic experimental setups.

Electrowetting lattice Boltzmann method for micro- and nano-droplet manipulations

Electrowetting has become a widely used tool for manipulating tiny amounts of liquids on surfaces. This paper proposes an electrowetting lattice Boltzmann method for manipulating micro-nano droplets. The hydrodynamics with the nonideal effect is modeled by the chemical-potential multiphase model, in which the phase transition and equilibrium are directly driven by chemical potential. For electrostatics, droplets in the micro-nano scale cannot be considered as equipotential as macroscopic droplets due to the Debye screening effect. Therefore, we linearly discretize the continuous Poisson-Boltzmann equation in a Cartesian coordinate system, and the electric potential distribution is stabilized by iterative computations. The electric potential distribution of droplets at different scales suggests that the electric field can still penetrate micro-nano droplets even with the screening effect. The accuracy of the numerical method is verified by simulating the static equilibrium of the droplet under the applied voltage, and the results show the apparent contact angles agree very well with the Lippmann-Young equation. The microscopic contact angles present some obvious deviations due to the sharp decrease of electric field strength near the three-phase contact point. These are consistent with previously reported experimental and theoretical analyses. Then, the droplet migrations on different electrode structures are simulated, and the results show that droplet speed can be stabilized more quickly due to the more uniform force on the droplet in the closed symmetric electrode structure. Finally, the electrowetting multiphase model is applied to study the lateral rebound of droplets impacting on the electrically heterogeneous surface. The electrostatic force prevents the droplets from contracting on the side which is applied voltage, resulting in the lateral rebound and transport toward the side.

Microdroplet Actuation via Light Line Optoelectrowetting (LL-OEW)

Meanwhile, electrowetting-on-dielectric (EWOD) is a well-known phenomenon, even often exploited in active micro-optics to change the curvature of microdroplet lenses or in analytical chemistry with digital microfluidics (DMF, lab on a chip 2.0) to move/actuate microdroplets. Optoelectrowetting (OEW) can bring more flexibility to DMF because in OEW, the operating point of the lab chip is locally controlled by a beam of light, usually impinging onto the chip perpendicularly. As opposed to pure EWOD, for OEW, none of the electrodes has to be structured, which makes the chip design and production technology simpler; the path of any actuated droplet is determined by the movement of the light spot. However, for applications in analytical chemistry, it would be helpful if the space both below as well as that above the lab chip were not obstructed by any optical components and light sources. Here, we report on the possibility to actuate droplets by laser light beams, which traverse the setup parallel to the chip surface and inside the OEW layer sequence. Since microdroplets are grabbed by this surface-parallel, nondiverging, and nonexpanded light beam, we call this principle "light line OEW" (LL-OEW).

Charge Trapping-Based Electricity Generator (CTEG): An Ultrarobust and High Efficiency Nanogenerator for Energy Harvesting from Water Droplets

Strategies toward harvesting energy from water movements are proposed in recent years. Reverse electrowetting allows high efficiency energy generation, but requires external electric field. Triboelectric nanogenerators, as passive energy harvesting devices, are limited by the unstable and low density of tribo-charges. Here, a charge trapping-based electricity generator (CTEG) is proposed for passive energy harvesting from water droplets with high efficiency. The hydrophobic fluoropolymer films utilized in CTEG are pre-charged by a homogeneous electrowetting-assisted charge injection (h-EWCI) method, allowing an ultrahigh negative charge density of 1.8 mC m^-2 . By utilizing a dedicated designed circuit to connect the bottom electrode and top electrode of a Pt wire, instantaneous currents beyond 2 mA, power density above 160 W m^-2 , and energy harvesting efficiency over 11% are achieved from continuously falling water droplets. CTEG devices show excellent robustness for energy harvesting from water drops, without appreciable degradation for intermittent testing during 100 days. These results exceed previously reported values by far. The approach is not only applicable for energy harvesting from water droplets or wave-like oscillatory fluid motion, but also opens up avenues toward other applications requiring passive electric responses, such as diverse sensors and wearable devices.

Electrically Controlled Localized Charge Trapping at Amorphous Fluoropolymer-Electrolyte Interfaces

Charge trapping is a long-standing problem in electrowetting on dielectric, causing reliability reduction and restricting its practical applications. Although this phenomenon is investigated macroscopically, the microscopic investigations are still lacking. In this work, the trapped charges are proven to be localized at the three-phase contact line (TPCL) region by using three detecting methods-local contact angle measurements, electrowetting (EW) probe, and Kelvin probe force microscopy. Moreover, it is demonstrated that this EW-assisted charge injection (EWCI) process can be utilized as a simple and low-cost method to deposit charges on fluoropolymer surfaces. Charge densities near the TPCL up to 0.46 mC m^-2 and line widths of the deposited charge ranging from 20 to 300 µm are achieved by the proposed EWCI method. Particularly, negative charge densities do not degrade even after a "harsh" testing with a water droplet on top of the sample surfaces for 12 h, as well as after being treated by water vapor for 3 h. These findings provide an approach for applications which desire stable and controllable surface charges.

Electric field effect on the contact angle for non-wetting drops

A microscopic model is formulated concerning the electrowetting of an electrically conducting drop on a dielectric substrate. The interaction energy between the drop and substrate includes both van der Waals attractive forces and Born repulsive forces resulting in an equilibrium gap. An augmented Young-Laplace equation is derived and used as the basis for calculations of wetting phenomena both with and without an applied voltage. In the absence of an electric field, a well-defined Young's angle is established at a distance from the meniscus incipience that is less than 100 times the equilibrium gap. An expression for Young's angle is determined showing its dependence on material properties of the system. With an electric field applied, the meniscus angle changes continuously from the three-phase line (TPL), where it is near zero, until after a distance of at least ten times the thickness of the dielectric where the Lippmann angle is established. Therefore, the initial angle is not the Lippmann angle and care must be taken in the interpretation of measurements of an apparent contact angle.

Soft electrowetting

Electrowetting is a commonly used tool to manipulate sessile drops on hydrophobic surfaces. By applying an external voltage over a liquid and a dielectric-coated surface, one achieves a reduction of the macroscopic contact angles for increasing voltage. The electrostatic forces all play out near the contact line, on a scale of the order of the thickness of the solid dielectric layer. Here we explore the case where the dielectric is a soft elastic layer, which deforms elastically under the effect of electrostatic and capillary forces. The wetting behaviour is quantified by measurements of the static and dynamic contact angles, complemented by confocal microscopy to reveal the elastic deformations. Even though the mechanics near the contact line is highly intricate, the macroscopic contact angles can be understood from global conservation laws in the spirit of Young-Lippmann. The key finding is that, while elasticity has no effect on the static electrowetting angle, the substrate's viscoelasticity completely dictates the spreading dynamics of electrowetting.

Lattice-Boltzmann Simulations of Electrowetting Phenomena

When a voltage difference is applied between a conducting liquid and a conducting (solid) electrode, the liquid is observed to spread on the solid. This phenomenon, generally referred to as electrowetting, underpins a number of interfacial phenomena of interest in applications that range from droplet microfluidics to optics. Here, we present a lattice-Boltzmann method that can simulate the coupled hydrodynamics and electrostatics equations of motion of a two-phase fluid as a means to model the electrowetting phenomena. Our method has the advantage of modeling the electrostatic fields within the lattice-Boltzmann algorithm itself, eliminating the need for a hybrid method. We validate our method by reproducing the static equilibrium configuration of a droplet subject to an applied voltage and show that the apparent contact angle of the drop depends on the voltage following the Young-Lippmann equation up to contact angles of ≈50°. At higher voltages, we observe a saturation of the contact angle caused by the competition between electric and capillary stresses, similar to previous experimental observations. We also study the stability of a dielectric film trapped between a conducting fluid and a solid electrode and find a good agreement with analytical predictions based on lubrication theory. Finally, we investigate the film dynamics at long times and report observations of film breakup and entrapment similar to previously reported experimental results.

Specific ion effects on electrocapillarity in aqueous electrolytes confined within nanochannels

A nanoslit is a long, extremely narrow (nanometers apart) opening between two parallel plates. An overlapped electric double layer is formed when an electrolyte is present inside the slit and there exist distributions of the osmotic pressure and the Maxwell stress across the nanoslit, which lead to the electrocapillarity effect. This feature can be incorporated with the specific ion effects by considering the nonelectrostatic interactions between ions and confining walls, as they significantly influence the potential, electric field, and ion distributions across the nanoslit. In the present work, the electromechanical approach is integrated with the concept of specific ion effects to analyze the behavior of an electrolyte confined in a one-dimensional nanochannel. For a nanochannel, the average outward normal stress exerted on the cross section of a channel (P_{zz}[over ¯]) can be regarded as a measure of electrocapillarity and it is the driving force of the flow. This electrocapillarity measure is analyzed by using the solution of the modified Poisson-Boltzmann equation as a function of the bulk concentration of the electrolyte, the boundary potential, and most importantly, the ion-specific interfacial interactions. The significance of the present work can be manifested by the increasing usage of extremely narrow channels in nanoscaled systems, which will require proper consideration of specific ion effects in determining the behavior of the confined electrolyte.

Field-Assisted Contact Line Motion in Thin Films

The balance of intermolecular and surface forces plays a critical role in the transport phenomena near the contact line region of an extended meniscus in several technologically important processes. Externally applied fields can alter the equilibrium and stability of the meniscus with concomitant effects on its shape and spreading characteristics and may even lead to an oscillation. This feature article provides a detailed account of the present and past efforts in exploring the behavior of curved thin liquid films subjected to mild thermal perturbations, heat input, and electrical and magnetic fields for pure as well as colloidal suspensions, including the effects of particle charge and polarity. The shape-dependent intermolecular force field has been evaluated in situ by a nonobtrusive optical technique utilizing the interference phenomena and subsequent image processing. The critical role of disjoining pressure is identified along with the determination of the Hamaker constant. The spatial and temporal variations of the capillary forces are evaluated for the advancing and receding menisci. The Maxwell-stress-induced enhanced spreading during electrowetting, at relatively low voltages, and that due to the application of a magnetic field are discussed with respect to their distinctly different characteristics and application potentials. The use of the augmented Young-Laplace equation elicited additional insights into the fundamental physics for flow in ultrathin liquid films.

Contact line friction of electrowetting actuated viscous droplets

We examine the contact line friction coefficient of viscous droplets spreading and retracting on solid surfaces immersed in ambient oil. By using the electrowetting effect, we generate a surface tension imbalance to drive the spreading and the retracting motion of the three-phase contact line (TCL). We show that neither the driving force intensity nor TCL direction significantly influences the friction coefficient. Instead, the friction coefficient depends equivalently on the viscosity of liquid droplets and the surrounding oil. We derive and experimentally verify a transient timescale that can be used to characterize both the spreading and retracting dynamics.

On-chip integration of droplet microfluidics and nanostructure-initiator mass spectrometry for enzyme screening

Biological assays often require expensive reagents and tedious manipulations. These shortcomings can be overcome using digitally operated microfluidic devices that require reduced sample volumes to automate assays. One particular challenge is integrating bioassays with mass spectrometry based analysis. Towards this goal we have developed μNIMS, a highly sensitive and high throughput technique that integrates droplet microfluidics with nanostructure-initiator mass spectrometry (NIMS). Enzyme reactions are carried out in droplets that can be arrayed on discrete NIMS elements at defined time intervals for subsequent mass spectrometry analysis, enabling time resolved enzyme activity assay. We apply the μNIMS platform for kinetic characterization of a glycoside hydrolase enzyme (CelE-CMB3A), a chimeric enzyme capable of deconstructing plant hemicellulose into monosaccharides for subsequent conversion to biofuel. This study reveals NIMS nanostructures can be fabricated into arrays for microfluidic droplet deposition, NIMS is compatible with droplet and digital microfluidics, and can be used on-chip to assay glycoside hydrolase enzyme in vitro.

Three-phase contact line and line tension of electrolyte solutions in contact with charged substrates

The three-phase contact line formed by the intersection of a liquid-vapor interface of an electrolyte solution with a charged planar substrate is studied in terms of classical density functional theory applied to a lattice model. The influence of the substrate charge density and of the ionic strength of the solution on the intrinsic structure of the three-phase contact line and on the corresponding line tension is analyzed. We find a negative line tension for all values of the surface charge density and of the ionic strength considered. The strength of the line tension decreases upon decreasing the contact angle via varying either the temperature or the substrate charge density.

Ion size effects on the osmotic pressure and electrocapillarity in a nanoslit: Symmetric and asymmetric ion sizes

We analyze the effect of asymmetric finite ion size in nanoconfinement in the view of osmotic pressure and electrocapillarity. When the confinement width becomes comparable with the Debye length, the overlapped electric double layer is significantly deformed by the steric effects. We derive the osmotic pressure from the modified Poisson-Boltzmann equation in a nanoslit to examine the deviation from the ideal osmotic pressure and the repulsive force on the wall considering the asymmetry of ion sizes. Then the electrocapillarity due to the steric effect is investigated under constant potential condition with the flat interface assumption. Later, the deformation by the electrocapillarity is also considered in the first order approximation.

Harvesting vibrational energy with liquid-bridged electrodes: thermodynamics in mechanically and electrically driven RC-circuits

Young–Laplace modeling and a new operation mode are proposed for a device which harvests vibrational energy with liquid-bridged electrodes.

Pulsating electric field modulated contact line dynamics of immiscible binary systems in narrow confinements under an electrical double layer phenomenon

We investigate the interfacial electro-chemical-hydrodynamics of an incompressible immiscible binary fluid system that moves in a narrow fluidic channel under time-periodic electroosmotic effects. We apply an alternating electrical voltage that sets the binary fluids in motion along the channel, whereas the channel walls are lined with chemical patch to alter the wetting characteristics of the surface. We demonstrate that the pulsating nature of the externally applied electric field in conjunction with the wetting characteristics of the surface may lead to some fascinating behavior of the contact line motion; which, in turn, may affect the capillary filling dynamics in an intriguing manner. Our results also unveil the profound influence of two important governing factors actuating the flow, namely, the frequency and amplitude of the time periodic electric field, on the tunability of the capillary filling rate and power requirement for filling the fluids into the channel.

Optofluidic lens with tunable focal length and asphericity

Adaptive micro-lenses enable the design of very compact optical systems with tunable imaging properties. Conventional adaptive micro-lenses suffer from substantial spherical aberration that compromises the optical performance of the system. Here, we introduce a novel concept of liquid micro-lenses with superior imaging performance that allows for simultaneous and independent tuning of both focal length and asphericity. This is achieved by varying both hydrostatic pressures and electric fields to control the shape of the refracting interface between an electrically conductive lens fluid and a non-conductive ambient fluid. Continuous variation from spherical interfaces at zero electric field to hyperbolic ones with variable ellipticity for finite fields gives access to lenses with positive, zero, and negative spherical aberration (while the focal length can be tuned via the hydrostatic pressure).

Nonlinear oscillations of a sessile drop on a hydrophobic surface induced by ac electrowetting

We examine the nature of ac electrowetting (EW)-driven axisymmetric oscillations of a sessile water drop on a dielectric substrate. In ac EW, small-amplitude oscillations of a drop differ from the Rayleigh linear modes of freely oscillating drops. In this paper, we demonstrate that changes in the time-averaged contact angle of the sessile drop attributed to the presence of an electric field and a solid substrate mainly caused this discrepancy. We combine the domain perturbation method with the Lindsted-Poincaré method to derive an asymptotic formula for resonant frequency. Theoretical analysis shows that the resonant frequency is a function of the time-averaged contact angle. Each mode of the resonance frequency is a linear function of ɛ(1), which is the magnitude of the cosine of the time-averaged contact angle. The most dominant mode in this study, that is, the fundamental mode n=2, decreases linearly with ɛ(1). The results of the theoretical model are compared with those of both the experiments and numerical simulations. The average resonant frequency deviation between the perturbation solutions and numerical simulations is 4.3%, whereas that between the perturbation solutions and the experiments is 1.8%.

Electrocapillarity of an electrolyte solution in a nanoslit with overlapped electric double layer: continuum approach

A nanoslit is a long narrow opening between two parallel plates that are nanometers apart from each other. When an electrolyte solution is present inside a nanoslit, an overlapped electrical double layer (EDL) is formed and there exist distributions of the osmotic pressure and the Maxwell stress across the nanoslit. It is well known that the total normal stress (osmotic pressure contribution + Maxwell stress contribution) in the direction normal to the nanoslit surface is uniform and the value is the same as the osmotic pressure at the centerline. On the other hand, it is not well known that the total normal stress in the direction parallel to the slit surface is not uniform. When there is an electrolyte-gas interface inside a nanoslit, this total normal stress in the direction parallel to the slit surface generates the electrocapillarity effect. In the present work, the electromechanical approach is adopted to estimate the electrocapillarity effect in terms of the slit surface potential (or the surface charge density), the gap size, and the bulk ion concentrations. In order to handle the problem analyically, it is assumed that the nanoslit problem is in the continuum range and the interface is initially flat. The deformation of the interface due to the nonuniform total normal stress along the interface is also obtained by using the first order perturbation method. The significance of the present work can be manifested by the fact that external voltage is frequently used in nanoscaled systems and the electrocapillarity effect should be considered in addition to the intrinsic capillarity due to surface tension.

Electrowetting -- from statics to dynamics

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.

Spontaneous electrical charging of droplets by conventional pipetting

We report that a droplet dispensed from a micropipette almost always has a considerable electrical charge of a magnitude dependent on the constituents of the droplet, on atmospheric humidity and on the coating material of pipette tip. We show that this natural electrification of a droplet originates from the charge separation between a droplet and pipette tip surface by contact with water due to the ionization of surface chemical groups. Charge on a droplet can make it difficult to detach the droplet from the pipette tip, can decrease its surface tension, can affect the chemical characteristics of solutions due to interactions with charged molecules, and can influence the combination and localization of charged bio-molecules; in all cases, the charge may affect results of experiments in which any of these factors is important. Thus, these findings reveal experimental parameters that should be controlled in experiments that use micropipettes.

Neither Lippmann nor Young: enabling electrowetting modeling on structured dielectric surfaces

Aiming to illuminate mechanisms of wetting transitions on geometrically patterned surfaces induced by the electrowetting phenomenon, we present a novel modeling approach that goes beyond the limitations of the Lippmann equation and is even relieved from the implementation of the Young contact angle boundary condition. We employ the equations of the capillary electrohydrostatics augmented by a disjoining pressure term derived from an effective interface potential accounting for solid/liquid interactions. Proper parametrization of the liquid surface profile enables efficient simulation of multiple and reconfigurable three-phase contact lines (TPL) appearing when entire droplets undergo wetting transitions on patterned surfaces. The liquid/ambient and the liquid/solid interfaces are treated in a unified context tackling the assumption that the liquid profile is wedge-shaped at any three-phase contact line. In this way, electric field singularities are bypassed, allowing for accurate electric field and liquid surface profile computation, especially in the vicinity of TPLs. We found that the invariance of the microscopic contact angle in electrowetting systems is valid only for thick dielectrics, supporting published experiments. By applying our methodology to patterned dielectrics, we computed all admissible droplet equilibrium profiles, including Cassie-Baxter, Wenzel, and mixed wetting states. Mixed wetting states are computed for the first time in electrowetting systems, and their relative stability is presented in a clear and instructive way.

Buoyant droplets on functional fibers

In the absence of gravity, the wetting of droplets on fibers is characterized by the competition between an axisymmetric barrel morphology engulfing the fiber and a symmetry-broken clamshell morphology with the droplet sitting on the side of the fiber. In the generic case of nonzero buoyancy the cylindrical symmetry of the barrel morphology is broken, yet barrels and clamshells can still be distinguished based on their different interfacial topologies being multiply and simply connected, respectively. Next to contact angle and droplet size the capillary length appears as a third parameter controlling the droplet morphology. For droplets of variable size, contact angle and buoyancy are independently varied in experiments by use of electrowetting and density mismatch. This approach--together with the complementary numerical calculations--provides new insights into the gradual shifts of the stability limits in the presence of an external volume force. Overall, the parameter space for stable clamshells is found to expand with increasing gravitational forces, gradually shrinking the regimes of stable barrels and bistability. In addition, a new stability limit is introduced for the clamshell morphology related to a partial detachment of the wetting liquid from the fiber, appearing toward higher droplet volumes.

On-demand separation of oil-water mixtures

In this work, the first-ever membrane-based single unit operation that enables gravity driven, on-demand separation of various oil-water mixtures is developed. Using this methodology, the on-demand separation of free oil and water, oil-in-water emulsions, and water-in-oil emulsions is demonstrated, with ≥99.9% separation efficiency. A scaled-up apparatus to separate larger quantities (several liters) of oil-water emulsions is also developed.

Uncovering molecular mechanisms of electrowetting and saturation with simulations

Molecular dynamics simulations are used to explore the physical mechanisms of electrowetting and the limits of continuum theories. Nanoscale drops exhibit the same behavior seen in macroscopic experiments: The contact angle θ follows continuum theory at low voltages and then saturates. Saturation limits applications of electrowetting and its origin is of great interest. In the simulations, saturation occurs when ions are pulled from the drop by large local fields. Saturation can be controlled by changing temperature, screening, or the energy binding ions to the fluid. We show a local force balance equation for θ remains valid even after saturation and that the interface approaches the equilibrium contact angle within a few nanometers of the solid.

Impact of pinning of the triple contact line on electrowetting performance

Pinning of the triple contact line adversely affects electrowetting on dielectric. Electrowetting response of substrates with contact angle hysteresis ranging from 1° to 30° has been characterized, and the results are interpreted within the framework of electromechanics corrected for pinning. The relationship between contact angle hysteresis, threshold potential for liquid actuation, and electrowetting hysteresis is quantified. Our results demonstrate that a modified electrowetting equation, based on balance of forces (including the pinning forces) acting on the triple contact line and on the drop, describes the electrowetting response of substrates with significant contact angle hysteresis. Finally, the surface properties of PDMS Sylgard 184 were found to be influenced by the electric field.

Electric field enhanced spreading of partially wetting thin liquid films

Equilibrium and dynamic electrowetting behavior of ultrathin liquid films of surfactant (SDS) laden water over silicon substrate (with native oxide) is investigated. A nonobtrusive optical method, namely, image analyzing interferometry, is used to measure the meniscus profile, adsorbed film thickness, and the curvature of the capillary meniscus. Significant advancement of the contact line of the liquid meniscus, as a result of the application of electric field, is observed even at relatively lower values of applied voltages. The results clearly demonstrate the balance of intermolecular and surface forces with additional contribution from Maxwell stress at the interline. The singular nature of Maxwell stress is exploited in this analysis to model the equilibrium meniscus profile using the augmented Young-Laplace equation, leading to the in situ evaluation of the dispersion constant. The electrowetting dynamics has been explored by measuring the velocity of the advancing interline. The interplay of different forces at the interface is modeled using a control volume approach, leading to an expression for the interline velocity. The model-predicted interline velocities are successfully compared with the experimentally measured velocities. Beyond a critical voltage, contact line instability resulting in emission of droplets from the curved meniscus has been observed.

Effect of added salt on preformed surface nanobubbles: a scaling estimate

In this paper we propose a scaling argument to quantify the role of added electrolyte salt in affecting the stability and the morphology of preformed surface nanobubbles on hydrophobic substrates like the water-OTS-silicon or the water-HOPG interfaces. The added salt controls the electric double layer formation as well as affects the zeta (ζ) potential at the air-water and solid-water interfaces. The resulting electrostatic wetting tension acts in conjunction with the air-water surface tension (analogous to electrowetting scenarios), thereby affecting the nanobubble morphologies. Weak ζ potential of the water-HOPG interface or the water-OTS-silicon interface at acidic pH ensures that the added salt will have imperceptible effect on the corresponding preformed surface nanobubbles, validating the experimental observations. However, at alkaline buffer pH for the OTS-silicon substrate, under certain system conditions, salt-induced ζ potential can be substantially high so that the properties of preformed surface nanobubbles will be affected. This paper will thus readdress the long-held universal notion that added salt, no matter in what concentration, will not influence the properties of preformed surface nanobubbles.

Dynamics of droplet motion under electrowetting actuation

The static shape of droplets under electrowetting actuation is well understood. The steady-state shape of the droplet is obtained on the basis of the balance of surface tension and electrowetting forces, and the change in the apparent contact angle is well characterized by the Young-Lippmann equation. However, the transient droplet shape behavior when a voltage is suddenly applied across a droplet has received less attention. Additional dynamic frictional forces are at play during this transient process. We present a model to predict this transient behavior of the droplet shape under electrowetting actuation. The droplet shape is modeled using the volume of fluid method. The electrowetting and dynamic frictional forces are included as an effective dynamic contact angle through a force balance at the contact line. The model is used to predict the transient behavior of water droplets on smooth hydrophobic surfaces under electrowetting actuation. The predictions of the transient behavior of droplet shape and contact radius are in excellent agreement with our experimental measurements. The internal fluid motion is explained, and the droplet motion is shown to initiate from the contact line. An approximate mathematical model is also developed to understand the physics of the droplet motion and to describe the overall droplet motion and the contact line velocities.

Wetting morphologies and their transitions in grooved substrates

When exposed to a partially wetting liquid, many natural and artificial surfaces equipped with complex topographies display a rich variety of liquid interfacial morphologies. In the present article, we focus on a few simple paradigmatic surface topographies and elaborate on the statics and dynamics of the resulting wetting morphologies. It is demonstrated that the spectrum of wetting morphologies increases with increasing complexity of the groove structure. On elastically deformable substrates, additional structures in the liquid morphologies can be observed, which are caused by deformations of the groove geometry in the presence of capillary forces. The emergence of certain liquid morphologies in grooves can be actively controlled by changes in wettability and geometry. For electrically conducting solid substrates, the apparent contact angle can be varied by electrowetting. This allows, depending on groove geometry, a reversible or irreversible transport of liquid along surface grooves. In the case of irreversible liquid transport in triangular grooves, the dynamics of the emerging instability is sensitive to the apparent hydrodynamic slip at the substrate. On elastic substrates, the geometry can be varied in a straightforward manner by stretching or relaxing the sample. The imbibition velocity in deformable grooves is significantly reduced compared to solid grooves, which is a result of the microscopic deformation of the elastic groove material close to the three phase contact line.

Wetting of a drop on a sphere

In this work, the equilibrium morphology of a drop on a sphere is analyzed as a function of the contact angle and drop volume experimentally and with analytical effective interfacial energy calculations. Experimentally, a drop on a sphere geometry is realized in an oil bath by placing a water drop on a sphere coated with a dielectric, of which the radii of curvature are comparable with that of the drop. Electrowetting (EW) is used to change the contact angle of the water drop on the sphere. To validate the applicability of EW and the Lippman-Young equation on nonflat surfaces, we systematically investigate the response of the contact angle to the applied voltage (EW response) for various drop volumes and compared the results with the case of a planar surface. The effective interfacial energy of two competing morphologies, namely, the spherically symmetric "completely engulfing" and "partially engulfing" morphologies are calculated analytically. The analytical calculations are then compared to the experimental results to confirm which morphology is energetically more favored for a given contact angle and drop volume. Our findings indicate that the "partially engulfing" morphology is always the energetically more favorable morphology.

Electrical switching of wetting states on superhydrophobic surfaces: a route towards reversible Cassie-to-Wenzel transitions

We demonstrate that the equilibrium shape of the composite interface between superhydrophobic surfaces and drops in the superhydrophobic Cassie state under electrowetting is determined by the balance of the Maxwell stress and the Laplace pressure. Energy barriers due to pinning of contact lines at the edges of the hydrophobic pillars control the transition from the Cassie to the Wenzel state. Barriers due to the narrow gap between adjacent pillars control the lateral propagation of the Wenzel state. We demonstrate how reversible switching between the two wetting states can be achieved locally using suitable surface and electrode geometries.

Electrowetting: a versatile tool for drop manipulation, generation, and characterization

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.

Asymptotic analysis of the dewetting rim

Consider a film of viscous liquid covering a solid surface, which it does not wet. If there is an initial hole in the film, the film will retract further, forming a rim of fluid at the receding front. We calculate the shape of the rim as well as the speed of the front using lubrication theory. We employ asymptotic matching between the contact line region, the rim, and the film. Our results are consistent with simple ideas involving dynamic contact angles and permit us to calculate all free parameters of this description, previously unknown.

Invariance of the solid-liquid interfacial energy in electrowetting probed via capillary condensation

Capillary condensation is employed to probe the solid-liquid interfacial energy in electrowetting on dielectric. The height of an annular water meniscus formed via capillary condensation inside the surface force apparatus is measured as a function of the potential applied across the meniscus and the dielectric stack where the meniscus is formed. According to the Kelvin equation, a decrease in the solid-liquid interfacial energy at constant temperature and relative humidity should lead to an increase in the meniscus height. Our experimental results on nanometer-sized meniscus are in agreement with the work of Mugele [J. Phys.: Condens. Matter 2007, 19, 375112] and unequivocally demonstrate that the real contact angle (or the solid-liquid interfacial energy) remains unaltered in electrowetting on dielectric.

A hybrid microfluidic chip with electrowetting functionality using ultraviolet (UV)-curable polymer

Electrowetting (EW) is widely used in digital microfluidics for the manipulation of drops sandwiched between two parallel plates. In contrast, demonstrations of closed microfluidic channels enhanced with EW functionality are scarce. Here, we report a simple, low-cost method to construct such microchannels enclosed between two glass plates, each of which comprises electrodes and insulating layers. Our method uses soft imprint lithography with thiolene precursors to design the channel geometry. UV exposure is used to seal the chips permanently and a silanization treatment renders all inner channel surfaces hydrophobic. Compared to earlier polydimethylsiloxane-based designs, this method allows us to make microchannels with smaller dimensions (down to 10 microns), lower aspect ratios (down to height/length=1/10), and symmetric electrodes both on the top and the bottom of the channel. We demonstrate the new capabilities with two examples: (i) EW-enhanced drop generation in a flow focusing geometry allows precise and continuous control on drop diameter in the range approximately 1-15 microns while maintaining monodispersity; (ii) EW allows tuning of the excess water pressure needed to displace oil in a microchannel, leading to spontaneous imbibition at EW number eta>0.89.

Steric effects of ions in the charge-related wetting phenomena

Steric effects of ions on the charge-related wetting phenomena are studied. Along with a general treatment, three specific problems in two-dimensional system are considered: a droplet on an electrode, a droplet on a charged surface, and an electrowetting phenomenon on a dielectric. For computation of wetting tension, the electromechanical approach is adopted with the principle of mechanical force balance for each phase. The modified Poisson-Boltzmann equation, which was originally proposed by Bikerman [Philos. Mag. 33, 384 (1942)], is adopted for the analysis of the steric effects. It is found that the steric hindrance reduces significantly both the osmotic pressure and the electrical stress near the triple contact line. This reduction results in a considerable decrease in the wetting tension when the ratio of the capacitance per unit area of the electrical double layer to that of the dielectric layer is small.

Basic principles of electrolyte chemistry for microfluidic electrokinetics. Part II: Coupling between ion mobility, electrolysis, and acid-base equilibria

We present elements of electrolyte dynamics and electrochemistry relevant to microfluidic electrokinetics experiments. In Part I of this two-paper series, we presented a review and introduction to the fundamentals of acid-base chemistry. Here, we first summarize the coupling between acid-base equilibrium chemistry and electrophoretic mobilities of electrolytes, at both infinite and finite dilution. We then discuss the effects of electrode reactions on microfluidic electrokinetic experiments and derive a model for pH changes in microchip reservoirs during typical direct-current electrokinetic experiments. We present a model for the potential drop in typical microchip electrophoresis device. The latter includes finite element simulation to estimate the relative effects of channel and reservoir dimensions. Finally, we summarize effects of electrode and electrolyte characteristics on potential drop in microfluidic devices. As a whole, the discussions highlight the importance of the coupling between electromigration and electrophoresis, acid-base equilibria, and electrochemical reactions.