Forming concentric double-emulsion droplets using electric fields

Double-emulsion droplets may be assembled into highly concentric shells using a uniform AC electric field to induce dipole/dipole interactions. The resulting force centers the inner droplet with respect to the outer shell if the outer droplet has a higher dielectric constant than the ambient, suspending liquid. The dielectric constant of the inner droplet does not influence this condition. Applying an electric field >10⁴ V_rms/m achieves centering of approximately 3–6 mm diameter droplets suspended in ～10 centipoise liquids within ～60 s. If the outer shell is electrically conductive, the effect depends strongly on frequency. In the case of the monomer-containing liquids requisite to forming foam shells for laser target fabrication, the electrical field frequency must be ～10 MHz or higher. Because of very stringent requirements imposed on the concentricity and sphericity of laser targets, electric field induced droplet distortion must be minimized. Consequently, the liquid constituents must be matched in density to ～0.1%.     

电场对协流式微流控装置中乳液液滴生成行为的调控机理

建立了直流电场作用下协流式微流控装置中单乳液液滴乳化生成过程的非稳态理论模型,并开展了数值模拟研究,揭示了电场对液滴乳化生成动力学行为的调控机理,阐明了流场/电场参数对液滴乳化生成特性的影响规律.研究结果表明:沿流体流动方向施加静电场可在电物性参数不同的两相流体界面法线方向上产生指向内相流体的电场力,进而强化了内相流体界面的颈缩和断裂,提升了液滴生成速率和形变程度,减小了液滴生成尺寸;在同一毛细数下,随着电毛细数的增大,乳液乳化流型由每周期仅有单一液滴生成的滴式流型转变为每周期有一个主液滴并伴随有卫星液滴生成的滴式流型;随着毛细数和电毛细数的增大,黏性拖曳力以及电场力作用增强,使内相流体颈缩过程后期更容易形成细长型液线,从而有助于诱发液线上产生Rayleigh-Plateau不稳定现象,继而促进卫星液滴的形成.     

Dynamics of a dielectric droplet suspended in a magnetic fluid in electric and magnetic fields

The behavior of a microdrop of dielectric liquid suspended in a magnetic fluid and exposed to the action of electric and magnetic fields is studied experimentally. With increasing electric field, the deformation of droplets into oblate ellipsoid, toroid and curved toroid was observed. At the further increase in the electric field, the bursting of droplets was also revealed. The electrorotation of deformed droplets was observed and investigated. The influence of an additional magnetic field on the droplet dynamics was studied. The main features of the droplet dynamics were interpreted and theoretically examined.     

Branching of colloidal chains in capillary-confined nematics

We report on the observation of colloidal chain assembly and branching inside capillaries filled with a nematic liquid crystal. Because of the homeotropic anchoring of liquid crystalline molecules on the capillary and colloidal droplet surfaces, the assembly of droplets along the capillary axis is expected, producing a transformation of the nematic director field from an escape-radial to quasiradial configuration. However, the subsequent over time branching of the straight colloidal chains is counterintuitive. By numerical simulations, we demonstrate that chain branching can occur by overcoming an energy barrier and can at least dwell as a metastable configuration. Moreover, manipulation of colloidal chains by electric fields and their gradients demonstrates various regimes of chain behavior in electric fields.     

Electro-hydrodynamic behavior and interface instability of double emulsion droplets under high electric field

Dynamics of multiphase flow under high voltage has attracted extensive research interests due to its wide industrial applications. In this paper, numerical solution of electro-hydrodynamic behavior and interface instability of double emulsion droplet is presented. Level set method and leaky dielectric model coupled with Navier-Stokes equation are used to solve the electro-hydrodynamic problem. The method is validated against the theoretical analysis and the simulation results of the other researchers. Double emulsion droplet with inner droplet (core) and outer droplet (shell) phases immersed in continuous phase is subjected to high electric field. Shell/continuous and core/shell interfaces of the droplet undergo prolate-oblate or oblate-prolate deformation depending on the extent of the penetration of electric potential and sense of charge distribution at the interfaces. The deformation of the shell deviates from theory at larger volume fraction of core for oblate-prolate case whereas it follows theory for prolate-oblate case. The interfaces showing oblate-prolate deformation split at the poles whereas, for prolate-oblate, they split away along the equator. The re-union of the interfaces under high electric field results with production of daughter droplet at the core. The large decrease in critical electric field for oblate-prolate case shows their less interface stability at larger volume fraction of core. When the core is eccentric, the electric field drives it towards the shell center or to the shell/continuous interface depending on electrical parameters. The study is beneficial in understanding the electro-hydrodynamic behavior of emulsion droplets and efficient design of related industrial processes.     

Modeling simple-jet mode electrohydrodynamic-atomization droplets' trajectories and spray pattern for a single nozzle system

Electrohydrodynamic atomization (EHDA), or simply Electrospraying is the process of influencing the breakup of a liquid into droplets by using a strong electric field. There can be different modes of Electrospraying depending, basically, on the created electric field strength and the liquid flowrate, for a specified liquid. Among these modes, the so-called cone-jet mode is the most explored one. This is due to its ability to produce highly charged monodisperse droplets in the nano- to micro-meter size range. Another mode of interest, which can also produce monodisperse droplets is the simple-jet mode. This mode is less explored when compared to the former. Within the papers that were explored by the authors, Agostinho et al. (2012) were the first authors to carefully investigate and characterize this mode. In their work, the authors reported about the influence of the electric field and the liquid flowrate on the droplets' size and spray dispersion. They also pointed out that the charge on these droplets can be expressed as a certain percentage of their Rayleigh limit.So far, there has been no model proposed to describe the droplets' trajectories in the simple-jet mode. This paper describes the design and the implementation of a physical model for determining the droplet trajectories in this mode. The model is done, specifically, for a single nozzle/ring-up configuration. It is a two-dimensional model, which solves the force balance equation for each droplet breaking up from the jet. It takes into consideration; the initial droplet velocity, the force of gravity, the electric field force, the inter-droplet coulombic force and the drag force. The droplets' deformation and reorientation were hypothesized, from observations, to play a major role in initiating the droplets' dispersion. They were simulated by implementing periodic displacements on the droplets' center of charge from its center of mass. The calculated droplets' trajectories' envelope angle was fitted to the experimental envelope angle by adjusting the droplet charge around the values that were reported by Agostinho et al. (2012). The model was validated by comparing the shapes of the theoretical and experimental sprays.The model offers new possibilities of modeling the droplets' trajectories in complex geometries, and of introducing additional forces to manipulate their trajectories in the simple-jet mode.     

A discrete droplet transport model for predicting spray coating patterns of an electrostatic rotary atomizer

Electrostatic spray (E-spray) coating is widely used for coating conductive substrates. The combination of a high-velocity shaping air, an imposed electric field and charged droplets, leads to higher transfer efficiency than conventional spray coating. In this paper, a mathematical model of droplet transport in E-spray is presented which enables simulating the coating deposition rate profile. A dilute spray assumption (no particle–particle interactions) allows modeling single-droplet trajectories resulting from a balance of electrostatic force, drag and inertia. Atomization of liquid droplets is not modeled explicitly—rather an empirical correlation is used for the mean droplet size while individual droplet sizes and starting locations are determined using random distributions. Strong coupling requires the electrostatic field and droplet trajectories be determined iteratively by successive substitution with relaxation. The influences of bell-cup voltage and atomization constant on the coating deposition rate profile, mass transfer efficiency and droplet trajectories are also shown. Using individually predicted droplet trajectories and impact locations, a static coating deposition rate profiles is determined. For the parametric values considered in this paper, the predicted spray is a cone hollow with no deposition in the center, a heavy ring near the center, and a tapering of thickness toward the outer edge.     

Fabrication of PDLC films based on acrylic monomers and study of the electric field effect on the alignment structure of liquid crystal droplets in PDLC films

Polymer Dispersed Liquid Crystal (PDLC) films are prepared by the polymerization induced method of phase separation. Initial configurations of the director of liquid crystal droplets inside the films are found using a polarized microscope. The effect of an electric field on the alignment structure of droplets is studied. Two mechanisms of droplet orientation by the electric field are determined as smooth and spontaneous. The processes observed are compared with the results of electro-optical studies.     

Rotation of a droplet in a viscous fluid

Unique capabilities for modeling the bulk motion of one liquid in another arise from the use of droplets made of a magnetic liquid. In this paper the low-frequency rotational motion of a magnetic droplet suspended in a viscous liquid is investigated. In this frequency range, the shape of the droplet does not depend on the field frequency and is determined only by its amplitude. An analytic solution has been found in the Stokes approximation to the problem, which generalizes the classic problem of Jeffrey to the case of a liquid ellipsoidal particle. This solution makes it possible to determine the velocity field inside and outside the liquid particle, the moments of the viscous forces acting on the droplet, its coefficient of rotational mobility. Zh. éksp. Teor. Fiz. 112, 1340–1350 (October 1997)     

Water vapor condensation and the collapse of superheated water drops as possible causes of ball lightning

Ball lightning is modeled by the bulk of humid air heated to temperatures of 600–650 K and containing a multitude of charged drops and microbubbles of size 10⁻⁵ cm or less, as well as water vapor heated to a near-critical temperature. The condensation of the vapor in the microbubbles, followed by the cooling of resulting droplets, generates energy spent on the thermal radiation of ball lightning. The radiation of light and radio waves is explained by the motion of ions and electrons in the electric field of charged bubbles and droplets and by the thermal rotational motion of charged droplets. As a result of coagulation, the droplets overheat and tend to collapse. An external electric field, supersaturated water vapor condensation, and a number of other factors may contribute to the ball lightning explosion energy.     

Electromagnetic emission of a strongly charged oscillating droplet

Analytical expressions for electric field in the vicinity of an oscillating strongly charged droplet of nonviscous conducting liquid and intensity of electromagnetic radiation are derived in the linear approximation with respect to perturbation amplitude of the droplet surface. Order-of-magnitude estimations of the radiation intensity are presented. The intensity of electromagnetic radiation of a ball lightning that can be simulated using a charged droplet is not related to the surface oscillations.     

Polydisperse spray diffusion flames in oscillating flow

The phenomenon of droplet clustering or grouping found when a spray of droplets is moving in an oscillating host flow field is investigated for the case of a polydisperse spray that fuels a laminar co-flow diffusion flame. A mathematical solution is developed for the liquid phase based on use of small Stokes numbers for size sections into which the polydisperse spray size distribution is divided. Droplet clustering in the oscillatory flow field is accounted for by constructing a special model for the sectional vaporization Damkohler numbers in accordance with droplet size. Combining this with a formal solution for a gas phase Schvab-Zel'dovich variable yields the means whereby flame dynamics can be described. Results calculated from this solution demonstrate that preferential droplet size behaviour (with smaller droplets tending to cluster to a greater extent and reduce the vaporization Damkohler number more than larger ones) can have a major impact on the flame dynamics through local droplet enrichment with attendant consequences on the production of fuel vapour. The dynamics of the sort of flame (over- or under-ventilated) and the occurrence of flame pinching leading to multiple flame sheets are altered under these circumstances. However, potential control of the actual initial spray polydispersity may reduce the intensity of such effects.     

Cavitation model of micropoint explosion

In a strong electric field, liquid metal of a micropoint is in the extended metastable state. At a certain degree of superheating, rapidly growing vapor bubbles arise spontaneously in it (vapor cavitation or explosive boiling), leading to the explosion of the micropoint. The resulting mixture of droplets in vapor expands with a high velocity to transform into plasma bunches. The field dependences obtained with this model for the explosion delay time and for the droplet size agree qualitatively with the experimental data for tungsten micropoints.     

Wetting of liquid droplets on two parallel filaments

Droplet wetting on two parallel filaments may assume a barrel-shaped morphology or a liquid bridge depending upon the filament diameter and spacing, droplet volume, and contact angle. This paper is aimed to examine the dependency of droplet wetting length upon the above parameters. In the process, morphology of either a barrel-shaped droplet or a liquid bridge sitting on two parallel filaments is determined numerically by using surface finite element method (SFEM). Variation of wetting length with contact angle is examined at varying droplet volume, filament spacing, and droplet morphology. It is found that the droplet wetting length increases with decreasing filament spacing ratio as well as contact angle while it also increases with the growth of droplet volume. The dependency of wetting length upon contact angle behaves sensitive to filament spacing in the case of stable liquid bridges, while it exhibits nearly constant sensitivity to the contact angle in the case of barrel-shaped droplets. The quantitative relations yielded in this study can be considered as characteristic curves applicable for a variety of droplet-on-filament systems, particularly useful to wetting property characterization of filaments, micro liquid delivery, biological cell manipulation, etc.     

微尺度下锥形微操作探针表面液滴形成的研究（英）

基于液滴的转移方法可实现微操作任务中微对象的拾取,锥形操作探针则常作为一种毛细力微操作执行工具。主要研究在空气冷凝模式下锥形探针端面的液滴形成。建立了微液滴形成的数学模型,主要包括初始液滴的形成、液滴的合并和液滴的移动,研究了影响操作液滴的关键参数,分析表明:过冷度决定最小液滴半径。对单液滴的生长机制进行理论分析,并通过数值求解的方法模拟了锥形操作探针端面的液滴形成。搭建实验测试平台,实验研究了微尺度下锥形微操作探针端面的液滴形成。实验结果表明:在空气冷凝模式下,操作探针端面能够形成微液滴。经过初始液滴的形成,液滴的合并和移动等过程最终可形成稳定的微液滴,且不同锥顶角下液滴的形成呈现多样化。     

Small-angle light scattering symmetry breaking in polymer-dispersed liquid crystal films with inhomogeneous electrically controlled interface anchoring

We have described the method of analyzing and reporting on the results of calculation of the small-angle structure of radiation scattered by a polymer-dispersed liquid crystal film with electrically controlled interfacial anchoring. The method is based on the interference approximation of the wave scattering theory and the hard disk model. Scattering from an individual liquid crystal droplet has been described using the anomalous diffraction approximation extended to the case of droplets with uniform and nonuniform interface anchoring at the droplet–polymer boundary. The director field structure in an individual droplet is determined from the solution of the problem of minimizing the volume density of the free energy. The electrooptical effect of symmetry breaking in the angular distribution of scattered radiation has been analyzed. This effect means that the intensities of radiation scattered within angles +θ _s and–θ _s relative to the direction of illumination in the scattering plane can be different. The effect is of the interference origin and is associated with asymmetry of the phase shift of the wavefront of an incident wave from individual parts of the droplet, which appears due to asymmetry of the director field structure in the droplet, caused by nonuniform anchoring of liquid crystal molecules with the polymer on its surface. This effect is analyzed in the case of normal illumination of the film depending on the interfacial anchoring at the liquid crystal–polymer interface, the orientation of the optical axes of droplets, their concentration, sizes, anisometry, and polydispersity.     

The influence of droplet grouping on a Burke-Schumann spray diffusion flame in an oscillating flow field

A new mathematical analysis of a laminar Burke-Schumann type of spray diffusion flame in an oscillating flow field is presented within a framework in which mild slip is permitted between the droplets and their host surroundings. A perturbation analysis using a small Stokes number is used for solving the liquid phase governing equations. The effect of droplet grouping in the oscillatory flow field is accounted for by constructing an appropriate model for the vaporization Damkohler number. A formal analytical solution is developed for the Schwab-Zeldovitch parameter through which instantaneous flame front shapes are found. Computed results based on the solution expose the strong impact that the phenomenon of droplet grouping can have on flame characteristics such as flame height, shape and type (over- or under-ventilated). Despite the models simplicity its predictions offer an opening insight into the mechanisms prevalent in more complex spray-combustion situations in which droplet grouping may occur.     

Frequency-dependent deformation of liquid crystal droplets in an external electric field

Nematic droplets suspended in the isotropic phase of the same substance were subjected to alternating electrical fields of varying frequency. To keep the system at a constant nematic/isotropic volume ratio with constant droplet size, we carefully kept the temperature in the isotropic/nematic coexistence region, which was broadened by adding small amounts of a non-mesogenic liquid. Whereas the nematic droplets remained spherical at low (in the order of 10 Hz) and high frequencies (in the order of 1 kHz), at intermediate frequencies we observed a marked flattening of the droplets in the plane perpendicular to the applied field. Droplet deformation occurred both in liquid crystals (LCs) with positive and negative dielectric anisotropy. The experimental data can be quantitatively modelled with a combination of the leaky dielectric model and screening of the applied electric field due to finite conductivity.     

Phase transition in ellipsoidal droplets of nematic liquid crystals

We developed a simple method for the calculation of the director field distribution in the droplets of nematic liquid crystals (LCs) of any shape, allowing for the interaction of LCs with the droplet surface, as well as the influence of constant electric field. In contrast to different approaches, the approach that is developed in the present paper does not require any simplifying suppositions about the structure of the LC director field. The elastic-continuum theory is used, complemented with the possibility of consideration of point and linear defects. Calculations are performed using the Monte Carlo method on a simple grid. The triangulation technique is used to take the boundary conditions of droplets of a complex shape into account. The developed approach can be used for investigation of the properties of polymer-dispersed liquid crystals (PDLCs). The topological phase transitions in the nematic LC 4-cyano-4′-pentyl-biphenyl (5CB) in spherical and ellipsoidal droplets are investigated in this paper.     

Wettability control of droplet deposition and detachment

The conditions for droplet deposition on plane substrates are studied using electrowetting to continuously modulate the surface wettability. Droplets of controlled volume attached to the tip of a pipette are brought into contact with the surface. During retraction of the pipette the droplets are deposited or detach completely depending on volume and contact angle. The experimental limit of deposition in the contact angle or volume plane is in good agreement with analytical and numerical predictions obtained within the capillary model.