Numerical simulation of deformation behavior of droplet in gas under the electric field and flow field coupling

The water droplets in the process of electrostatic coalescence are important when studying electrohydrodynamics. In the present study, the electric field and flow field are coupled through the phase field method based on the Cahn–Hilliard formulation. A numerical simulation model of single droplet deformation under the coupling field was established. It simulated the deformation behavior of the movement of a droplet in the continuous phase and took the impact of droplet deformation into consideration which is affected by two-phase flow velocity, electric field strength, the droplet diameter, and the interfacial tension. The results indicated that under the single action of the flow field, when the flow velocity was lower, the droplet diameter was greater as was the droplet deformation degree. When the flow velocity was increased, the droplet deformation degree of a small-diameter droplet was at its maximum size, the large-diameter droplet had a smaller deformation degree, and the middle-diameter droplet was at a minimum deformation degree. When the flow velocity was further increased, the droplet diameter was smaller, and the droplet deformation degree was greater. Under the coupled effect of the electric field and flow field, the two-phase flow velocity and the electric field strength were greater, and the degree of droplet deformation was greater. While the droplet diameter and interfacial tension were smaller, the degree of droplet deformation was greater. Droplet deformation degree increased along with the two-phase flow velocity. The research results provided a theoretical basis for gas–liquid separation with electrostatic coalescence technology.     

Controlled generation of droplets using an electric field in a flow-focusing paper-based device

Droplet-based microfluidics is a modular platform in high-throughput single-cell and small sample analyses. However, this droplet microfluidic system was widely fabricated using soft lithography or glass capillaries, which is expensive and technically demanding for various applications, limiting use in resource-poor settings. Besides, the variation in droplet size is also restricted due to the limitations on the operating forces that the paper-based platform is able to withstand. Herein, we develop a fully integrated paper-based droplet microfluidic platform for conducting droplet generation and cell encapsulation in independent aqueous droplets dispersed in a carrier oil by incorporating electric fields. Through imposing an electric field, the droplet size would decrease with increasing the electric field and smaller droplets can be produced at high applied voltage. The droplet diameter can be adjusted by the ratio of inner and outer flow velocities as well as the applied electric field. We also demonstrated the proof of concept encapsulation application of our paper device by encapsulating yeast cells under an electric field. Using a simple wax printing method, carbon electrodes can be integrated on the paper. The integrated paper-based microfluidic platform can be fabricated easily and conducted outside of centralized laboratories. This microfluidic system shows great potential in drug and cell investigations by encapsulating cells in resource-limited environments.     

Investigation of Micro-Perspective Coalescence Behavior of Dispersed Phase Droplets in Uniform Electric Field

COMSOL simulation based on the Cahn–Hilliard formulation and the experimental method have been adopted to predict the coalescence behavior of water droplets in uniform electric field. The results reveal that coalescence of droplets consists of the drainage process and the contact process. The coalescence mechanism of micro-droplets has been established. COMSOL simulation together with the experiment concludes that the viscosity and coalescence time are roughly in line with the trend, and an optimal electric field strength can obtain the most efficient coalescence time     

The effect of interfacial viscosity on the droplet dynamics under flow field

The effects of interfacial viscosity on the droplet dynamics in simple shear flow and planar hyperbolic flow are investigated by numerical simulation with diffuse interface model. The change of interfacial viscosity results in an apparent slip of interfacial velocity. Interfacial viscosity has been found to have different influence on droplet deformation and coalescence. Smaller interfacial viscosity can stabilize droplet shape in flow field, while larger interfacial viscosity will increase droplet deformation, or even make droplet breakup faster. Different behavior is found in droplet coalescence, where smaller interfacial viscosity speeds up film drainage and droplet coalescence, but larger interfacial viscosity postpones the film drainage process. This is due to the change of film shape from flat‐like for smaller interfacial viscosity to dimple‐like for larger interfacial viscosity. The film drainage time still scales as Ca⁰ at smaller capillary number (Ca), and Ca^1.5 at higher capillary number when the interfacial viscosity changes. The interfacial viscosity only affects the transition between these limiting scaling relationships. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1505–1514, 2008     

Numerical characterization of inter-core coalescence by AC dielectrophoresis in double-emulsion droplets

The utilization of an alternating current electric field provides a good means to achieve controlled coalescence between paired inner cores encapsulated in water-in-oil-in-water double-emulsion (DE) droplets. Although previous studies have experimentally determined the conditions under which inter-core electrokinetic fusion occurs, the transient interfacial dielectrophoretic (DEP) dynamics key to understand the underlying fluid mechanics is still unclear from a physical point of view. By coupling DEP motion of two-phase flow to phase-field formulation, bulk-coupled numerical simulations are conducted to characterize the spatial–temporal evolution of the surface charge wave and the resulting nonlinear electrical force induced at both the core/shell and medium/shell oil/water interfaces. The effect of interfacial charge relaxation and droplet geometry on inter-core attractive dipolar interaction is investigated within a wide parametric space, and four distinct device operation modes, including normal inter-core fusion, shell elongation, partial core leakage, and complete core release, are well distinguished from one another by flow regime argumentation. Our results herein reveal for the first time the hitherto unknown transient electrohydrodynamic fluid motion of DE droplet driven by Maxwell–Wagner structural polarization. The dynamic simulation method proposed in present study points out an effective outlet to predict the nonlinear electrokinetic behavior of multicore DE droplets for realizing a more controlled triggering of microscale reactions for a wide range of applications in drug discovery, skin care, and food industry.     

An Electrorheological Study on the Behavior of Water‐in‐Crude Oil Emulsions Under Influence of a DC Electric Field and Different Flow Conditions

The influence of an applied DC electric field on viscosity and droplet size distribution of different water‐in‐crude oil emulsions was monitored in order to investigate the induction of coalescence of the water droplets. The effects caused by the voltage imposition were studied by rheological analysis and the validity of the obtained results was discussed, comparing with the features of real electrocoalcscer systems. A low field NMR technique (CPMG NMR) and digital video microscopy (DVM) were used to elucidate the behavior of the emulsions. Experiments performed at low shear rate with increasing electric field magnitude showed an increase in viscosity until a critical value. E_CRIT was reached. Thereafter coalescence occurred and viscosity decreased irreversibly below its initial value. The electrorheological behavior of the emulsions can be attributed to the organization (flocculation) of water droplets induced by the electric field, accompanied by an increase in viscosity. The structure breaks down as the shear rate is increased, leading to a decrease in viscosity. Experiments performed at high shear showed only a small decline in the viscosity. Although it was evident that coalescence took place, it did not involve the whole sample, because the electrodes were uncoated. As a direct consequence, the mean value of the droplet size within the emulsion did not change noticeably. Nonetheless this mean value was less recurrent and the formation of droplets of very large diameter occurred.     

Localized electric field induced transition and miniaturization of two‐phase flow patterns inside microchannels

Strategic application of external electrostatic field on a pressure‐driven two‐phase flow inside a microchannel can transform the stratified or slug flow patterns into droplets. The localized electrohydrodynamic stress at the interface of the immiscible liquids can engender a liquid‐dielectrophoretic deformation, which disrupts the balance of the viscous, capillary, and inertial forces of a pressure‐driven flow to engender such flow morphologies. Interestingly, the size, shape, and frequency of the droplets can be tuned by varying the field intensity, location of the electric field, surface properties of the channel or fluids, viscosity ratio of the fluids, and the flow ratio of the phases. Higher field intensity with lower interfacial tension is found to facilitate the oil droplet formation with a higher throughput inside the hydrophilic microchannels. The method is successful in breaking down the regular pressure‐driven flow patterns even when the fluid inlets are exchanged in the microchannel. The simulations identify the conditions to develop interesting flow morphologies, such as (i) an array of miniaturized spherical or hemispherical or elongated oil drops in continuous water phase, (ii) “oil‐in‐water” microemulsion with varying size and shape of oil droplets. The results reported can be of significance in improving the efficiency of multiphase microreactors where the flow patterns composed of droplets are preferred because of the availability of higher interfacial area for reactions or heat and mass exchange.     

Molecular dynamics simulation on influence of temperature effect on electro-coalescence behavior of nano-droplets

In electric dehydration of crude oil, the dewatering efficiency can be improved by raising emulsion temperature properly which reduces the viscosity of crude oil. However, it should be noticed that the emulsion temperature does not only affect the emulsion viscosity but also nano-droplets dynamics behavior which impacts the coalescence efficiency either. Therefore the influence of temperature effect on the electro-coalescence of nano-droplets is studied by a molecular dynamics method. The results show that the temperature presents an active or negative effect, depending on the competitive relation between electrostatic interaction and thermal motion. Two stages are distinguished according to the dominant mechanism. During stage I, governed by the electrostatic interaction, lower temperature promotes the polarization and leads to an acceleration of the droplets coalescence, but higher temperature restrains the coalescence process due to molecules thermal motion breaking the polarization process. During stage II, governed by the thermal motion, lower temperature improves the coalescence because of a diffusion effect, but higher temperature deteriorates electro-coalescence because of a violent molecular thermal motion. Additionally, hydrogen bond and radial distribution functions are obtained by statistics to describe droplets micromorphology, which explains the reason why the droplet forms longer chain structure at the critical electric field.     

Influence of dynamic interfacial tension on droplet formation during membrane emulsification

Membrane emulsification is a promising and relatively new technique for producing emulsions. The purpose of this study was to better understand the influence of interfacial tension on droplet formation during membrane emulsification. Droplet formation experiments were carried out with a microengineered membrane; the droplet diameter and droplet formation time were studied as a function of the surfactant concentration in the continuous phase. These experiments confirm that the interfacial tension influences the process of droplet formation; higher surfactant concentrations lead to smaller droplets and shorter droplet formation times (until 10 ms). From drop volume tensiometer experiments we can predict the interfacial tension during droplet formation. However, the strong influence of the rate of flow of the to-be-dispersed phase on the droplet size cannot be explained by the predicted values. This large influence of the oil rate of flow is clarified by the hypothesis that snap-off is rather slow in the studied regime of very fast droplet formation.     

Effect of interfacial tension on the dynamic behavior of droplet formation during microchannel emulsification

Microchannel (MC) emulsification is a novel technique for producing monodisperse emulsions. In this study, we investigated the effect of interfacial tension on the dynamic behavior of droplet formation with various surfactant concentrations. Interfacial tension did not affect the resultant droplet diameter in lower flow velocity ranges, but it did affect the time-scale parameters. These results were interpreted using the droplet formation mechanism reported in our previous study. At surfactant concentrations below 0.3%, the emulsification behavior was differed from that at higher surfactant concentrations. An analysis of diffusional transfer indicated that dynamic interfacial tension affects the emulsification behavior at lower surfactant concentrations. Dynamic interfacial tension that exceeded the equilibrium value led to a shorter detachment time. This resulted in stable droplet formation of monodispersed emulsions by spontaneous transformation, even at flow velocities above the predicted critical flow velocity. A previous study predicted that the droplet formation would become unstable and polydispersed larger droplets would form over critical flow velocity. Wetting of the MC with the dispersed phase at lower surfactant concentrations induced formation of larger polydispersed droplets at high flow velocities.     

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.     

On the mechanism of extractive electrospray ionization (EESI) in the dual-spray configuration

Dual-spray extractive electrospray ionization (EESI) mass spectrometry as a versatile analytical technique has attracted much interest due to its advantages over conventional electrospray ionization (ESI). The crucial difference between EESI and ESI is that in the EESI process, the analytes are introduced in nebulized form via a neutral spray and ionized by collisions with the charged droplets from an ESI source formed by spraying pure solvent. However, the mechanism of the droplet–droplet interactions in the EESI process is still not well understood. For example, it is unclear which type of droplet–droplet interaction is dominant: bounce, coalescence, disruption, or fragmentation? In this work, droplet–droplet interaction was investigated in detail based on a theoretical model. Phase Doppler anemometry (PDA) was employed to investigate the droplet behavior in the EESI plume and provide the experimental data (droplet size and velocity) necessary for theoretical analysis. Furthermore, numerical simulations were performed to clarify the influence of the sheath gas flow on the EESI process. No coalescence between the droplets in the ESI spray and the droplets in the sample spray was observed using various geometries and sample flow rates. Theoretical analysis, together with the PDA results, suggests that droplet fragmentation may be the dominant type of droplet–droplet interaction in the EESI. The interaction time between the ESI droplet and the sample droplet was estimated to be <5 μs. This work gives a clear picture of droplet–droplet interactions in the dual-spray EESI process and detailed information for the optimization of this method for future applications that require higher sensitivity.     

Simulation of droplet heating and desolvation in inductively coupled plasma—part II: coalescence in the plasma

A numerical model is developed to consider for the first time droplet coalescence along with transport, heating and desolvation in an argon inductively coupled plasma (Ar ICP). The direct simulation Monte Carlo (DSMC) method and the Ashgriz–Poo model are used, respectively, to compute droplet–droplet interactions and to determine the outcome of droplet collisions. Molecular dynamics (MD) simulations support the use of the Ashgriz–Poo coalescence model for small droplet coalescence. Simulations predict spatial maps of droplet number and mass densities within an Ar ICP for a conventional nebulizer-spray chamber arrangement, a direct injection high efficiency nebulizer (DIHEN), and a large bore DIHEN (LB-DIHEN). The primary findings are: (1) even at 1500 W, the collisions of the droplets in the plasma lead primarily to coalescence, particularly for direct aerosol injection; (2) the importance of coalescence in a spray simulation exhibits a complex relationship with the gas temperature and droplet size; (3) DIHEN droplets penetrate further into the Ar ICP when coalescence is considered; and (4) droplets from a spray chamber or the LB-DIHEN coalesce less frequently than those from a DIHEN. The implications of these predictions in spectrochemical analysis in ICP spectrometry are discussed.     

A visible coalescence of droplets on hydrophobic and hydrophilic fibers in water-in-oil emulsion

The droplets’ coalescence is instantaneous and rather complex in emulsion. The theoretical analysis of this process was presented by a former research, while visible experiments to verify these are still scarce. This work aims to show and analyze the visible water droplets’ coalescence on hydrophobic bamboo charcoal fibers and hydrophilic glass fibers in water-in-oil emulsion. An experimental setup with microscope and high-speed camera was designed and established to record the water droplets’ coalescence. The water droplets’ collision coalescence on bamboo charcoal fibers was observed, and the diameters of water droplets detaching from the fibers with different angles were measured. The angle between the fiber and the flow velocity can affect the diameters of water droplets detaching from the bamboo charcoal fibers, and cross-fibers can the enormously increase water diameters compared with single fiber. Meanwhile, the water droplets’ collision coalescence on glass fibers was observed and the result shows that the collision coalescence also occurred on the hydrophilic glass fibers when the droplet diameter was small. In addition, other factors, including flow velocity and droplets’ diameter for the coalescence on the hydrophilic glass fibers were investigated.     

Analysis of droplet behavior in a de-oiling hydrocyclone

A mechanical separation process in a de-oiling hydrocyclone is described in which disperse oil droplets are separated from a continuous water phase. This separation process is influenced by droplet breakage and coalescence. Based on experimental data and simulation results in a stirred tank, a modified breakage model, which can be applied to droplet breakage in the de-oiling hydrocyclone, is developed. Then, a simulation model is developed coupling the numerical solution of the flow field in the hydrocyclone based on computational fluid dynamics (CFD) with population balances. The homogenous discrete method and the inhomogeneous discrete method are applied for solving the population balance model (PBM). The investigations show that the numerical results obtained by the simulation model coupled with the modified PBM using the inhomogeneous discrete method are in good accordance with experimental data under a high flow rate. According to this simulation model, the effect of three different inlet designs on the separation efficiency of the de-oiling hydrocyclone has been discussed. The results indicate that the separation efficiency of the de-oiling hydrocyclone can be improved with an appropriate inlet design.     

The influence of electric field-induced orientation on the retraction of a liquid crystal droplet immersed in a flexible polymer matrix

We measured the apparent interfacial tension between a liquid crystal and a flexible polymer by deformed droplet retraction method. An external electric field is applied to change the director orientation in liquid crystal droplet. The deformation and recovery of a single liquid crystal droplet dispersed in a polydimethylsiloxane (PDMS) matrix were realized by a transient shear flow and observed by polarized optical microscope. In order to control the director orientation in LC droplet, the electric field is applied perpendicular and parallel to the flow field, respectively. The different orientation induced by electric field in liquid crystal droplet has different behavior during droplet retraction and affect the apparent interfacial tension between liquid crystal and flexible polymer.     

Highly productive droplet formation by anisotropic elongation of a thread flow in a microchannel

We developed a microfluidic device to form monodisperse droplets with high productivity by anisotropic elongation of a thread flow, defined as a threadlike flow of a dispersed liquid phase in a flow of an immiscible, continuous liquid phase. The thread flow was anisotropically elongated in the depth direction in a straight microchannel with a step, where the microchannel depth changed. Consequently, the elongated thread flow was given capillary instability (Rayleigh-Plateau instability) and was continuously transformed into monodisperse droplets at the downstream area of the step in the microchannel. We examined the effects of the flow rates of the dispersed phase and the continuous phase on the droplet formation behavior, including the droplet diameter and droplet formation frequency. The droplet diameter increased as the fraction of the dispersed-phase flow rate relative to the total flow rate increased and was independent of the total flow rate. The droplet formation frequency proportionally increased with the total flow rate at a constant dispersed-phase flow rate fraction. These results are explained in terms of a mechanism similar to that of droplet formation from a cylindrical liquid thread flow by Rayleigh-Plateau instability. The microfluidic device described was capable of forming monodisperse droplets with a 160-microm average diameter and 3-microm standard deviation at a droplet formation frequency of 350 droplets per second from a single thread flow. The highest total flow rate achieved was 6 mL/h using the present device composed of a straight microchannel with a step. We also demonstrated parallel droplet formation by anisotropic elongation of multiple thread flows; the process was applied to form W/O and O/W droplets. The highly productive droplet formation process presented in this study is expected to be useful for future industrial applications.     

Charge carrier field emission determines the number of charges on native state proteins in electrospray ionization

Although multiple charging in electrospray ionization (ESI) is essential to protein mass spectrometry, the underlying mechanism of multiple charging has not been explicated. Here, we present a new theory to describe ESI of native-state proteins and predict the number of excess charges on proteins in ESI. The theory proposes that proteins are ionized as charged residues in ESI, as they retain residual excess charges after solvent evaporation and do not desorb from charged ESI droplets. However, their charge state is not determined by the Rayleigh limit of a droplet of similar size to the protein; rather, their final charge state is determined by the electric field-induced emission of small charged solute ions and clusters from protein-containing ESI droplets. This theory predicts that the number of charges on a protein in ESI should be directly proportional to the square of the gas-phase protein diameter and to E*, the critical electric field strength at which ion emission from droplets occurs. This critical field strength is determined by the properties of the excess charge carriers (i.e., the solute) in droplets. Charge-state measurements of native-state proteins with molecular masses in the 5-76 kDa range in ammonium acetate and triethylammonium bicarbonate are in excellent agreement with theoretical predictions and strongly support the mechanism of protein ESI proposed here.     

Selective membrane test for crude oil based model emulsions by use of video-enhanced microscopy

 A method for testing water/oil emulsion droplet membranes selectively has been demonstrated. The method uses electric fields to induce attraction, membrane thinning and coalescence between aqueous droplets deposited in an oil continuum. The coalescence process is monitored visually by the use of videomicroscopy. A set of model oils containing indigenous surfactants (asphaltenes) from a crude oil has been studied, and the effects of asphaltene concentration, oil phase aromaticity, aging of oils and interfacial exposure time have been investigated. The strength of the field at the point of coalescence is defined as the critical parameter describing membrane strength. In the current experiments a.c. fields were used and droplet sizes were of the order of 500–600 μm. Received: 8 October 1998 Accepted in revised form: 11 January 1999     

Numerical simulation of bubble dynamics in a micro-channel under a nonuniform electric field

A numerical method is used to simulate the motion and coalescence of air bubbles in a micro-channel under a nonuniform electric field. The channel is equipped with arrays of electrodes embedded in its wall and voltages are applied on the electrodes to generate a specified electric field gradient in the longitudinal direction. In the study, the Navier-Stokes equations are solved by using the level set method handling the deformable/moving interfaces between the bubbles and the ambient liquid. Both the polarization Coulomb force and the dielectrophoresis force are considered as the force source of the Navier-Stokes equations by solving the Maxwell's equations. The flow field equations and the electric field equations are coupled and solved by using the finite element method. The electric field characteristics and the dynamic behavior of a bubble are analyzed by studying the distributions of the electric field and the force, the deformation and the moving velocity of the air bubble. The result suggests that the model of dispersed drops suspended in the immiscible dielectric liquid and driven by a nonuniform electric field is an effective method for the transportation and coalescence of micro-drops.