Deformation of water droplets on solid surface in electric field

The purpose of this paper is to analyze the deformation of water droplets on a solid surface under electric stress. A mathematical model making it possible to simulate the axisymmetric as well as non-axisymmetric deformations of droplets is developed. According to this model, the droplet deformation depends on several parameters such as the volume and the number of droplets, the conductivity and the permittivity of droplets, their proximity to one another, the surface of the solid material, and the location of each droplet on the dielectric surface. The results of the simulation show the disturbance of the background field through the presence of a single or multiple droplets. An experimental study is also achieved by considering one to three droplets aligned simultaneously on a dielectric smooth surface between two electrodes subjected to AC voltages. The influence of the background field and the droplet location regarding the electrodes on the deformation of water droplets are evidenced.     

Functional bionetworks from nanoliter water droplets

We form networks from aqueous droplets by submerging them in an oil/lipid mixture. When the droplets are joined together, the lipid monolayers surrounding them combine at the interface to form a robust lipid bilayer. Various protein channels and pores can incorporate into the droplet-interface bilayer (DIB), and the application of a potential with electrodes embedded within the droplets allows ionic currents to be driven across the interface and measured. By joining droplets in linear or branched geometries, functional bionetworks can be created. Although the interfaces between neighboring droplets comprise only single lipid bilayers, the structures of the networks are long-lived and robust. Indeed, a single droplet can be "surgically" excised from a network and replaced with a new droplet without rupturing adjacent DIBs. Networks of droplets can be powered with internal "biobatteries" that use ion gradients or the light-driven proton pump bacteriorhodopsin. Besides their interest as coupled protocells, the droplets can be used as devices for ultrastable bilayer recording with greatly reduced electrolyte volume, which will permit their use in rapid screening applications.     

Transport and deformation of droplets in a microdevice using dielectrophoresis

In microfluidic devices the fluid can be manipulated either as continuous streams or droplets. The latter is particularly attractive as individual droplets can not only move but also split and fuse, thus offering great flexibility for applications such as laboratory-on-a-chip. We consider the transport of liquid drops immersed in a surrounding liquid by means of the dielectrophoretic force generated by electrodes mounted at the bottom of a microdevice. The direct numerical simulation (DNS) approach is used to study the motion of droplets subjected to both hydrodynamic and electrostatic forces. Our technique is based on a finite element scheme using the fundamental equations of motion for both the droplets and surrounding fluid. The interface is tracked by the level set method and the electrostatic forces are computed using the Maxwell stress tensor. The DNS results show that the droplets move, and deform, under the action of nonuniform electric stresses on their surfaces. The deformation increases as the drop moves closer to the electrodes. The extent to which the isolated drops deform depends on the electric Weber number. When the electric Weber number is small, the drops remain spherical; otherwise, the drops stretch. Two droplets, however, that are sufficiently close to each other, can deform and coalesce, even if the electric Weber number is small. This phenomenon does not rely on the magnitude of the electric stresses generated by the bulk electric field, but instead is due to the attractive electrostatic drop-drop interaction overcoming the surface tension force. Experimental results are also presented and found to be in agreement with the DNS results.     

Mechanisms of equilibrium shape transitions of liquid droplets in electrowetting

Liquid droplets bridging the gap between two dielectric-coated horizontal electrode plates suffer breakup instabilities when a voltage applied between the electrodes exceeds a threshold. Interestingly enough, broken liquid bridges (i.e. a pair of a sessile and a pendant drop) can spontaneously rejoin if the voltage is still applied to the electrodes. Here we study the electro-hydrostatics of the liquid bridges in the joined or broken state and we illuminate the mechanisms of the shape transitions that lead to bridge rupture or droplet joining. The governing equations of the capillary electro-hydrostatics form nonlinear and free boundary problems which are solved numerically by the Galerkin/finite element method. On one hand, we found that capillary bridges become unstable at a turning point bifurcation in their solution space. The solutions past the turning point are unstable and the instability signals the bridge rupture. On the other hand, the separate droplets approach each other as the applied voltage increases. However, solutions become unstable past a critical voltage at a turning point bifurcation and the droplets join. By studying the relative position of the turning points corresponding to bridge rupture and droplet joining, respectively, we define parameter regions where stable bridges or separate droplets or oscillations between them can be realized.     

High-throughput sorting of nanoliter droplets enabled by a sequentially addressable dielectrophoretic array

Droplet microfluidics has emerged as a powerful tool for a diverse range of biomedical and industrial applications such as single-cell analysis, directed evolution, and metabolic engineering. In these applications, droplet sorting has been effective for isolating small droplets encapsulating molecules, cells, or crystals of interest. Recently, there is an increased interest in extending the applicability of droplet sorting to larger droplets to utilize their size advantage. However, sorting throughputs of large droplets have been limited, hampering their wide adoption. Here, we report our demonstration of high-throughput fluorescence-activated droplet sorting of 1 nL droplets using an upgraded version of the sequentially addressable dielectrophoretic array (SADA), which we reported previously. The SADA is an array of electrodes that are individually and sequentially activated/deactivated according to the speed and position of a droplet passing nearby the array. We upgraded the SADA by increasing the number of driving electrodes constituting the SADA and incorporating a slanted microchannel. By using a ten-electrode SADA with the slanted microchannel, we achieved fluorescence-activated droplet sorting of 1 nL droplets at a record high throughput of 1752 droplets/s, twice as high as the previously reported maximum sorting throughput of 1 nL droplets.     

Voltage-expandable liquid crystal surface

Based on dielectrophoretic effect, we report a novel approach which can extensively spread a liquid crystal (LC) interface. With interdigitated striped electrodes, the droplets can be stretched along the striped electrode direction; while with zigzag interdigitated electrodes, the droplets can be further stretched sidewise. In our demonstration, the occupied area of a 1.9-mm-aperture LC droplet doped with 1.2 wt% black dye could be expanded over ～3.5× at 78 V(rms). The spreading and recovering times were measured to be ～0.39 s and ～0.75 s, respectively. The slower response time confirms the extreme expanding of the LC surface. The contrast ratio is over ～120?:?1 in transmissive mode. Color light switch was also demonstrated by spreading colored-dye doped LC droplets. The mechanical stability of the device was also evaluated. Liquid devices based on this cell structure have the advantages of good stability, simple operation and low power consumption. This work opens a new gateway for voltage controllable, polarization-insensitive, and broadband liquid photonic devices which may find numerous applications in switchable windows, variable optical attenuators, and displays.     

Droplet fusion by alternating current (AC) field electrocoalescence in microchannels

We present a system for the electrocoalescence of microfluidic droplets immersed in an immiscible solvent, where the undeformed droplet diameters are comparable to the channel diameter. The electrodes are not in direct contact with the carrier liquid or the droplets, thereby minimizing the risk of cross-contamination between different coalescence events. Results are presented for the coalescence of buffered aqueous droplets in both quiescent and flowing fluorocarbon streams, and on-flight coalescence is demonstrated. The capillary-based system presented here is readily amenable to further miniaturization to any lab-on-a-chip application where the conductivity of the droplets is much greater than the conductivity of the stream containing them, and should aid in the further application of droplet microreactors to biological analyses.     

Electrochemical detection on electrowetting-on-dielectric digital microfluidic chip

In this work, the use of three-electrode electrochemical sensing system with an electrowetting-on-dielectric (EWOD) digital microfluidic device is reported for quantitative analysis of iodide. T-junction EWOD mixer device was designed using arrays of 50-μm spaced square electrodes for mixing buffer reagent and analyte droplets. For fabrication of EWOD chips, 5-μm thick silver EWOD electrodes were formed on a glass substrate by means of sputtering and lift-off process. PDMS and Teflon thin films were then coated on the electrodes by spin coating to yield hydrophobic surface. An external three-electrode system consisting of Au working, Ag reference and Pt auxiliary wires were installed over EWOD electrodes at the end of T-junction mixer. In experiment, a few-microliter droplets of Tris buffer and iodide solutions were moved toward the mixing junction and transported toward electrochemical electrodes by EWOD process. A short processing time within seconds was achieved at EWOD applied voltage of 300 V. The analyte droplets mixed with different concentrations were successfully analyzed by cyclic voltametry. Therefore, the combination of EWOD digital microfluidic and electrochemical sensing system has successfully been demonstrated for rapid chemical analysis with minimal reagent consumption.     

A microfluidic device for self-synchronised production of droplets

The primary requirement for a mixing operation in droplet-based microfluidic devices is an accurate pairing of droplets of reaction fluids over an extended period of time. In this paper, a novel device for self-synchronous production of droplets has been demonstrated. The device uses a change in impedance across a pair of electrodes introduced due to the passage of a pre-formed droplet to generate a second droplet at a second pair of electrodes. The device was characterised using image analysis. Droplets with a volume of ~23.5 ± 3.1 nl (i.e.~93% of the volume of pre-formed droplets) were produced on applying a voltage of 500 V. The synchronisation efficiency of the device was 83%. As the device enables self-synchronised production of droplets, it has a potential to increase the reliability and robustness of mixing operations in droplet-based microfluidic devices.     

A feedback control system for high-fidelity digital microfluidics

Digital microfluidics (DMF) is a technique in which discrete droplets are manipulated by applying electrical fields to an array of electrodes. In an ideal DMF system, each application of driving potential would cause a targeted droplet to move onto an energized electrode (i.e., perfect fidelity between driving voltage and actuation); however, in real systems, droplets are sometimes observed to resist movement onto particular electrodes. Here, we implement a sensing and feedback control system in which all droplet movements are monitored, such that when a movement failure is observed, additional driving voltages can be applied until the droplet completes the desired operation. The new system was evaluated for a series of liquids including water, methanol, and cell culture medium containing fetal bovine serum, and feedback control was observed to result in dramatic improvements in droplet actuation fidelity and velocity. The utility of the new system was validated by implementing an enzyme kinetics assay with continuous mixing. The new platform for digital microfluidics is simple and inexpensive and thus should be useful for scientists and engineers who are developing automated analysis platforms.     

Capacitance-based droplet position estimator for digital microfluidic devices

Digital microfluidic (DMF) devices manipulate minuscule droplets through basic fluidic operations including droplet transport, mixing and splitting commonly known as the building blocks for complete laboratory analyses on a single device. A DMF device can house various chemical species and confine chemical reactions within the volume of a droplet much like a micro-reactor. The automation of fluidic protocols requires a feedback controller whose sensor is capable of locating droplets independent of liquid composition (or previous knowledge of liquid composition). In this research, we present an estimator that tracks the continuous displacement of a droplet between electrodes of a DMF device. The estimator uses a dimensionless ratio of two electrode capacitances to approximate the position of a droplet, even, in the domain between two adjacent electrodes. This droplet position estimator significantly enhances the control precision of liquid handling in DMF devices compared to that of the techniques reported in the literature. It captures the continuous displacement of a droplet; valuable information for a feedback controller to execute intricate fluidic protocols including droplet positioning between electrodes, droplet velocity and acceleration control. We propose a state estimator for tracking the continuous droplet displacement between two adjacent electrodes. The dimensionless nature of this estimator means that any droplet composition can be sensed. Thus, no calibration for each chemical species within a single DMF device is required. We present theoretical and experimental results that demonstrate the efficacy of the position estimator in approximating the position of the droplet in the interval between two electrodes.     

Evaporation-induced particle microseparations inside droplets floating on a chip

We describe phenomena of colloidal particle transport and separation inside single microdroplets of water floating on the surface of dense fluorinated oil. The experiments were performed on microfluidic chips, where single droplets were manipulated with alternating electric fields applied to arrays of electrodes below the oil. The particles suspended in the droplets were collected in their top region during the evaporation process. Experimental results and numerical simulations show that this microsepration occurs as a result of a series of processes driven by mass and heat transfer. An interfacial tension gradient develops on the surface of the droplet as a result of the nonuniform temperature distribution during the evaporation. This gradient generates an internal convective Marangoni flow. The colloidal particles transported by the flow are collected in the top of the droplets by the hydrodynamic flux, compensating for evaporation through the exposed top surface. The internal flow pattern and temperature distribution within evaporating droplets were simulated using finite element calculations. The results of the simulation were consistent with experiments using tracer particles. Such microseparation processes can be used for on-chip synthesis of advanced particles and innovative microbioassays.     

Enzymatic Reaction in Droplets Manipulated with Liquid Dielectrophoresis

Droplet generation and transportation for biological reactions are conducted with liquid dielectrophoresis (LDEP), forming two hundred picoliter droplets and aligning them in an open environment above the micro‐machined electrodes. The generation of the dielectrophoresis signals was critically examined to actuate droplets in biological solutions without excessive Joule heating. Enzymatic reactions between β‐galactosidase and fluorescein di‐β‐D ‐galactopyranoside were succeeded in manipulated droplets, which was confirmed by fluorescence imaging. These results allow us to propose the integration of LDEP actuation in high throughput biomolecular assays.     

Droplet-based chemistry on a programmable micro-chip

We describe the manipulation of aqueous droplets in an immiscible, low-permittivity suspending medium. Such droplets may serve as carriers for not only air- and water-borne samples, contaminants, chemical reagents, viral and gene products, and cells, but also the reagents to process and characterise these samples. We present proofs-of-concept for droplet manipulation through dielectrophoresis by: (1). moving droplets on a two-dimensional array of electrodes, (2). achieving dielectrically-activated droplet injection, (3). fusing and reacting droplets, and (4). conducting a basic biological assay through a combination of these steps. A long-term goal of this research is to provide a platform fluidic processor technology that can form the core of versatile, automated, micro-scale devices to perform chemical and biological assays at or near the point of care, which will increase the availability of modern medicine to people who do not have ready access to modern medical institutions, and decrease the cost and delays associated with that lack of access.     

Electronic drop sensing in microfluidic devices: automated operation of a nanoliter viscometer

We describe three droplet sensing techniques: a digital electrode, an analog electrode, and a thermal method. All three techniques use a single layer of metal lines that is easy to microfabricate and an electronic signal can be produced using low DC voltages. While the electrode methods utilize changes in electrical conductivity when the air/liquid interface of the droplet passes over a pair of electrodes, the thermal method is based on convective heat loss from a locally heated region. For the electrode method, the analog technique is able to detect 25 nL droplets while the digital technique is capable of detecting droplets as small as 100 pL. For thermal sensing, temperature profiles in the range of 36 degrees C and higher were used. Finally, we have used the digital electrode method and an array of electrodes located at preset distances to automate the operation of a previously described microfluidic viscometer. The viscometer is completely controlled by a laptop computer, and the total time for operation including setup, calibration, sample addition and viscosity calculation is approximately 4 minutes.     

Pluronic additives: a solution to sticky problems in digital microfluidics

Digital microfluidics (DMF) is a promising technique for carrying out miniaturized, automated biochemical assays in which discrete droplets of reagents are actuated on the surface of an array of electrodes. A limitation for DMF is nonspecific protein adsorption to device surfaces, which interferes with assay fidelity and can cause droplets to become unmovable. Here, we report the results of a quantitative analysis of protein adsorption on DMF devices by means of confocal microscopy and secondary ion mass spectrometry. This study led us to a simple and effective method for limiting the extent of protein adsorption: the use of low concentrations of Pluronic F127 as a solution additive. This strategy has a transformative effect on digital microfluidics, facilitating the actuation of droplets containing greater than 1000-fold higher protein concentrations than is possible without the additive. To illustrate the benefits of this new method, we implemented a DMF-driven protein digest assay using large concentrations (1 mg/mL) of protein-substrate. The use of Pluronic additives solves a sticky problem in DMF, which greatly expands the range of applications that are compatible with this promising technology.     

Capacitive sensing of droplets for microfluidic devices based on thermocapillary actuation

The design and performance of a miniaturized coplanar capacitive sensor is presented whose electrode arrays can also function as resistive microheaters for thermocapillary actuation of liquid films and droplets. Optimal compromise between large capacitive signal and high spatial resolution is obtained for electrode widths comparable to the liquid film thickness measured, in agreement with supporting numerical simulations which include mutual capacitance effects. An interdigitated, variable width design, allowing for wider central electrodes, increases the capacitive signal for liquid structures with non-uniform height profiles. The capacitive resolution and time response of the current design is approximately 0.03 pF and 10 ms, respectively, which makes possible a number of sensing functions for nanoliter droplets. These include detection of droplet position, size, composition or percentage water uptake for hygroscopic liquids. Its rapid response time allows measurements of the rate of mass loss in evaporating droplets.     

Capillary bridges in electric fields

We analyzed the morphology of droplets of conductive liquids placed between two parallel plate electrodes as a function of the two control parameters electrode separation and applied voltage. Both electrodes were covered by thin insulating layers, as in conventional electrowetting experiments. Depending on the values of the control parameters, three different states of the system were found: stationary capillary bridges, stationary separated droplets, and periodic self-excited oscillations between both morphologies, which appear only above a certain threshold voltage. In the two stationary states, the morphology of the liquid is modified by the electric fields due to electrowetting and due to mutual electrostatic attraction, respectively. We determined a complete phase diagram within the two-dimensional phase space given by the control parameters. We discuss a model based on the interfacial and electrostatic contributions to the free energy. Numerical solutions of the model are in quantitative agreement with the phase boundaries found in the experiments. The dynamics in the oscillatory state are governed by electric charge relaxation and by contact angle hysteresis.     

Simulations of a dielectrophoretic membrane filtration process for removal of water droplets from water-in-oil emulsions

A novel separation technique based on simultaneous application of AC dielectrophoresis and preferential transport through a semipermeable hydrophilic membrane is proposed for separation of small amounts of emulsified water droplets from a water-in-oil emulsion. Embedding an array of parallel microelectrodes on a membrane matrix, followed by application of an AC potential to these electrodes, can result in capturing the water droplets onto the membranes from the emulsion during a crossflow filtration process. The present paper describes the theoretical principles underlying such a process, and describes a simple mathematical framework based on trajectory analysis for assessing the separation efficiency of such a technique. The results indicate that superimposition of an AC dielectrophoretic field can significantly enhance the preferential transport of the emulsified water through the membrane in a crossflow filtration device. This can lead to a highly efficient continuous separation process for dilute emulsions.     

Droplet-based microfluidics with nonaqueous solvents and solutions

In droplet-based ("digital") microfluidics, liquid droplets in contact with dielectric surfaces are created, moved, merged and mixed by applying AC or DC potentials across electrodes patterned beneath the dielectric. We show for the first time that it is possible to manipulate droplets of organic solvents, ionic liquids, and aqueous surfactant solutions in air by these mechanisms using only modest voltages (<100 V) and frequencies (<10 kHz). The feasibility of moving any liquid can be predicted empirically from its frequency-dependent complex permittivity, epsilon*. The threshold for droplet actuation in air with our two-plate device configuration is /epsilon*/>8x10(-11). The mechanistic implications of these results are discussed, along with the greatly expanded range of applications for digital microfluidics that these results suggest are now feasible.