Deformation and motion of a charged conducting drop in a dielectric liquid under a nonuniform electric field

As a tool for transporting a drop inside another fluid, a charged conducting drop driven by Coulombic force is considered. Specifically, deformation and motion of a charged conducting drop under nonuniform electric fields are studied using the perturbation method. For simplicity in analysis, the applied electric field is assumed to be expressed as the sum of a uniform field and a linear field and the flow is assumed to be in the Stokes flow range. The deformed drop shape due to electrical stress is computed to the first order of the electrical Weber number (W). Then the electric force and the hydrodynamic drag are computed to derive the formula of the translation velocity, which is valid up to O(W). Several important results have also been obtained for the effect of drop deformation on the electric and hydrodynamic forces exerted on the drop.     

Influence of particle-particle interactions and particles rotational motion in traveling wave dielectrophoresis

Traveling wave dielectrophoresis provides an interesting method for the controlled movement of microsized particles in suspended mixtures, and as such is a promising tool in microfluidic technology. In this case, the electrostatic force acting on the particles has two components: one due to the spatially varying magnitude of the electric field and the other due to the spatially varying phase. The actual movement of the particle is determined by the combined effect of these two forces and corresponding torques, the viscous drag exerted by the fluid on the particle, and the electrostatic and hydrodynamic particle-particle interactions. This paper presents the first numerical simulations of the motion of particles subjected to all previous forces and torques. Our technique is based on a finite-element scheme in which the particles are moved using a direct simulation scheme respecting the fundamental equations of motion for both the fluid and the solid particles. The fluid-particle motion is resolved by the method of distributed Lagrange multipliers and the electrostatic forces are computed using the point-dipole approximation. Our simulations show that the particle behavior strongly depends on the mismatch of the dielectric properties between the particles and the fluid, and that the particle-particle interaction force as well as particles rotation speeds play crucial roles in the various regimes.     

Axisymmetric motion of a pair of deformable heavy drops in an upward temperature gradient

The axisymmetric deformation and motion of interacting droplets under the combined influence of the gravitational force and a vertical temperature gradient is considered using boundary-integral techniques for creeping flow. The focus is on the case when the net thermocapillary and buoyancy forces acting on the drops are directed oppositely. When these forces are almost balanced our analysis shows that, though the deformations of the drops are apparently small, their influence on the motion is considerable. For highly deformable drops moving in a gravity field, even a small temperature gradient that almost does not effect the drops velocity may drastically change the deformation pattern and prevent the drops from breakup.     

脉冲电场O/W乳状液破乳的分子动力学模拟

采用分子动力学方法研究了水包油(O/W)型乳状液体系中重油油滴在脉冲电场中的聚集行为. 通过改变电场占空比的模拟参数, 探讨了一定电场强度下的油滴聚集行为, 以及电场破乳时电场强度参数与占空比参数之间的联系. 同时利用静电势分布、 相互作用势能以及结合构象统计等分析方法, 从微观角度说明在电场作用下油滴的电荷分布与聚集机制. 模拟结果表明, 在近0.40~0.75 V/nm范围内电场强度下, 距离一定的重油滴聚集, 低电场强度可通过增加占空比促使油滴聚集, 且占空比随电场强度的增大而减小; 油滴在电场中发生形变, 油滴电荷出现两极化分布, 带负电沥青质分子引导油滴朝电场反方向移动; 无电场下聚集过程中沥青质处于两油滴界面, 范德华作用力为油滴聚集的主要作用力, 同时油滴界面沥青质分子与周围分子形成π-π结合构象, 增强了油滴间的相互作用力.     

Stability of the jet flow of charged particles in a gaseous medium

The dynamics of the unidimensional straight-line motion of charged liquid droplets has been considered. Stability criterion has been derived for the jet motion of liquid droplets in a space bounded by two electrodes. The motion of an ensemble of charged droplets in a constant electric field and in a nonuniform field between a needle-like electrode and a plane has been calculated by the molecular dynamics method. Experimental data have been presented on the motion of micron and submicron charged particles formed by the electrostatic spraying of different liquids. The experimental data have been compared with the theoretical calculations and numerical simulation results.     

Key thermodynamic characteristics of nucleation on charged and neutral cores of molecular sizes in terms of the gradient density functional theory

The gradient density functional theory and the Carnahan–Starling model formulated for describing the contribution of hard spheres have been used to calculate the profiles of condensate density in small critical droplets formed via homogeneous nucleation, as well as in stable and critical droplets formed via heterogeneous nucleation on solid charged and neutral condensation cores of molecular sizes. The calculations performed for water and argon at different values of condensate chemical potential have yielded the heights of the activation barriers for homoand heterogeneous nucleation as functions of vapor supersaturation at preset system temperatures. The interaction of condensate molecules with a solid core has been described by the resultant potential of molecular attractive forces. In the case of a charged core, the long-range Coulomb potential of electric forces has additionally been taken into account. Dielectric permittivities have been calculated as known functions of the local density of the fluid and temperature. The radius of the equimolecular droplet surface has been chosen as a variable describing the droplet size. Dependences of the chemical potential of condensate molecules in a droplet on its size have been plotted for water and argon with allowance for the action of capillary, electrostatic, and molecular forces. It has been shown that the role of the molecular force potential in heterogeneous nucleation increases with the size of condensation cores.     

A numerical study on the coalescence of emulsion droplets in a constricted capillary tube

Using a new computational model, we have studied the dynamics and coalescence of a pair of two-dimensional droplets in pressure-driven flow through a constricted capillary tube, which is a prototype problem for the analysis of the interaction of emulsion droplets in porous media. We present simulations that quantify the effects of various system parameters on the droplet stability. These include the capillary number, the interfacial tension, the suspended-to-suspending-phase viscosity ratio, the valence and concentration of added electrolytes, the droplet-to-pore-size ratio, the pore-body-to-throat-size ratio, and the type of pore geometry. Our simulations show that the capillary number Ca plays an important role in determining whether the drops coalesce. At low Ca, drops deform only slightly and coalescence occurs at the entrance of the pore throat, whereas significant deformation enables the drops move through the pore without coalescence at high Ca. Coalescence is favored at intermediate values of the viscosity ratio. The destabilizing effect of added electrolytes is found to be insignificant for 10-mum drops, but significant for micron-size drops. Among the geometric-related parameters, the drop-to-pore-size ratio is the most significant.     

Dynamic and static interactions between bitumen droplets in water

In the commercial bitumen extraction operation, dynamic and static interaction forces between bitumen drops in water determine the likelihood of desirable bitumen coalescence at different process stages. These dynamic and static forces were measured using colloidal particle scattering and hydrodynamic force balance techniques, respectively. In the former technique, dynamic interactions are studied through droplet-droplet collision trajectory measurement. In the latter technique, the static attractive forces between droplets are determined when a doublet is separated with a known and adjustable hydrodynamic force. The dynamic force measurement implies the presence of rigid chains on bitumen surfaces. The mean chain lengths for deasphalted bitumen at pH 7, whole bitumen at pH 7, and whole bitumen at pH 8.5 are 50, 78, and 41 nm, respectively. However, the static force measurement indicates much shorter mean chain lengths (<9 nm) in these three bitumen systems. Shorter chain length indicates weaker repulsive force. This finding of a much weaker repulsion between bitumen droplets under static conditions has important implications on the commercial bitumen extraction operation.     

Electric field-induced self-assembly of micro- and nanoparticles of various shapes at two-fluid interfaces

Particle lithography which explores the capability of particles to self-assemble offers an attractive means to manufacture nanostructured materials. Although traditional techniques typically lead to the formation of dense crystals, adjustable non-close-packed crystals are crucial in a number of applications. We have recently proposed a novel method to assemble spherical micro- and nanoparticles into monolayers. The technique consists of trapping particles at a liquid-fluid interface and applying an electric field normal to the interface. Particles rearrange themselves under the influence of interfacial and electrostatic forces to form 2-D hexagonal arrays of long-range order and whose lattice constant depends on the electric field strength and frequency. Furthermore, the existence of an electric field-induced capillary force makes the technique applicable to submicron and nanosized particles. Although spherical particles are often used, non-spherical particles can be beneficial in practice. Here, we review the method, discuss its applicability to particles of various shapes, and present results for particles self-assembly on air-liquid and liquid-liquid interfaces. In the case of non-spherical particles, the self-assembly process, while still taking place, is more complex as particles experience a torque which causes them to rotate relative to one another. This leads to a final arrangement displaying either a dominant orientation or no well-defined orientation. We also discuss the possibility of dislodging the particles from the interface by applying a strong electric field such that the Weber number is of order 1 or larger, a phenomenon which can be utilized to clean particles from liquid-fluid surfaces.     

Pumpless dispensing of a droplet by breaking up a liquid bridge formed by electric induction

Dispensing uniform pico‐to‐nanoliter droplets has become one of essential components in various application fields from high‐throughput bio‐analysis to printing. In this study, a new method is suggested and demonstrated for dispensing a droplet on the top plate with an inverted geometry by using electric field. The process of dispensing droplets consists of two stages: (i) formation of liquid bridge by moving up the charged fluid mass using the electrostatic force between the charges on the fluid mass and the induced charges on the substrate and (ii) its break‐up by the motion of the top plate. Different from conventional electrohydrodynamic methods, electric induction enables the droplets to be dispensed on various surfaces including non‐conducting substrate. The use of capillarity with an inverted geometry removes the need of external pumps or elaborates control for constant flow feed. The droplet diameter has been characterized as a function of the nozzle‐to‐plate distance and the plate moving velocity. The robustness of the present method is shown in terms of nozzle length and applied voltage. Finally, its practical applicability is confirmed by rendering a 19 by 24 array of highly uniform droplets with only 1.8% size variation without use of any active feedback control.     

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.     

Particle interactions in electrophoresis due to inertia

The inertial forces acting on two cylinders and two spheres have been calculated. The cylinders or spheres are of the same radius and zeta potential, and arbitrarily oriented in an electric field. It is found that when two particles are aligned perpendicular to the direction of the electric field, the force between them along the line of the centers is attractive. When they are along the direction of the electric field, the force between them along the line of the centers is repulsive. On a pair of arbitrarily oriented particles, the force perpendicular to the line of the centers tends to rotate the particles around the midpoint between the particle centers such that the pair is aligned normal to the applied electric field. The stable equilibrium orientation of a pair of particles and the attractive interaction forces between the particles when they are stably orientated may give rise to aggregation of particles during electrophoretic motion of a suspension.     

Simulation and experimental demonstration of the electric field assisted electroporation microchip for in vitro gene delivery enhancement

Simulation and experimental demonstration of the in vitro gene delivery enhancement using electrostatic forces and electroporation (EP) microchips were conducted. Electroporation is a technique with which DNA molecules can be delivered into cells using electric field pulses. This study demonstrates that plasmid DNA can be attracted to the cell surfaces at the specific regions using an electrostatic force. Therefore, the DNA concentration on the cell surface is dramatically increased, which highly enhances the gene transfection efficiency compared to that without an attracting-electric field. The electrostatic force can be designed into specific regions, where the DNA plasmids are attracted to, to provide the region-targeting function. In this micro-device, the top electrode and the interdigitated electrodes provided the DNA attracting-electric field, and the interdigitated electrodes provided adequate electric fields for the electroporation process on the chip surface. Using the EP microchip, cells could be manipulated in situ without detachment if adherent cells were used for electroporation. Five different cells of two different types, primary cell and cell line, were successfully transfected under multi-pulse or single pulse electric field stimulation without applying an attracting-electric field. This study simulated and analyzed the electric field distributions at the DNA attracting and electroporation processes, and successfully demonstrated that the electrostatic force attracted DNA plasmids to specific regions and highly enhanced the gene delivery. In summary, this EP microchip should provide many potential applications for gene therapy.     

Effects of Applied Electric Fields on Drop—Interface and Drop—Drop Coalescence*

In this work, coalescence of a single organic or aqueous drop with its homophase at a horizontal liquid interface was investigated under applied electric fields. The coalescence time was found to decrease for aqueous drops as the applied voltage was increased, regardless of the polarity of the voltage. For organic drops, the coalescence time increased with increasing applied voltage of positive polarity and decreased with increasing applied voltage of negative polarity. Under an electric field, the coalescence time of aqueous drops decreases due to polarization of both the drop and the flat interface. The dependency of organic drop-interface coalescence on the polarity of the electric field may be a result of the negatively charged organic surface in the aqueous phase. Due to the formation of a double layer, organic drops are subjected to an electrostatic force under an electric field, which, depending on the field polarity, can be attractive or repulsive. Pair-drop coalescence of aqueous drops in the organic phase was also studied. Aqueous drop-drop coalescence is facilitated by polarization and drop deformation under applied electric fields. Without applied electric fields, drop deformation increases the drainage time of the liquid film between two approaching drops. Therefore, a decrease in the interfacial tension, which causes drop deformation, accelerates drop-drop coalescence under an electric field and inhibits drop coalescence in the absence of an electric field.     

Influence of attractive force on imaging micro‐droplets of water by atomic force microscope

The shape of micro‐droplets of water on a pure copper surface was investigated using the a.c. non‐contact mode of an atomic force microscope (AFM) by applying different attractive forces between the cantilever tip and the liquid surface. The forces largely influenced the observed radii of micro‐droplets; the influence can be reduced significantly by reducing the force. The same attractive force between the cantilever tip and the micro‐droplets is necessary when comparing the contact angles of micro‐droplets on different surfaces. Furthermore, the values of the contact angles of the micro‐droplets should be the average of those on at least four sides of the droplets. Copyright © 2005 John Wiley & Sons, Ltd.     

Magnetic Hetero-flocculation of Paramagnetic Colloidal Particles

The feasibility of a high-gradient magnetic separation process, utilizing magnetite as the energizable element in lieu of stainless steel wool, is evaluated by means of an equilibrium, two-particle, magnetic hetero-flocculation model. The model calculates the net force, defined as the sum of the magnetic, electrostatic, and van der Waals forces, exerted on a paramagnetic nanoparticle that is in the proximity of a fixed magnetite particle. Since the nanoparticle-magnetite system is assumed to be in direct contact with the moving fluid, the influence of the hydrodynamic force on the magnetic attractive force between the two particles is also explored. This model clearly reveals the ranges and conditions over which each of these various forces contributes to the net force relative to Brownian (thermal) motion. The model also reveals the feasibility of using magnetite particles instead of stainless steel as the energizable element for high-gradient magnetic separation. Important variables investigated include the size and surface charge of the particles, the magnetic field, the flow velocity, the electrolyte concentration, and the magnetic susceptibility of the nanoparticle. Copyright 2000 Academic Press.     

Electrophoretic motion of a spherical particle with a symmetric nonuniform surface charge distribution in a nanotube

The electrophoretic motion of a spherical nanoparticle, subject to an axial electric field in a nanotube filled with an electrolyte solution, has been investigated using a continuum theory, which consists of the Nernst-Planck equations for the ionic concentrations, the Poisson equation for the electric potential in the solution, and the Stokes equation for the hydrodynamic field. In particular, the effects of nonuniform surface charge distributions around the nanoparticle on its axial electrophoretic motion are examined with changes in the bulk electrolyte concentration and the surface charge of the tube's wall. A particle with a nonuniform charge distribution is shown to induce a corresponding complex ionic concentration field, which in turn influences the electric field and the fluid motion surrounding the particle and thus its electrophoretic velocity. As a result, contrary to the relatively simple dynamics of a particle with a uniform surface charge, dominated by the irradiating electrostatic force, that with a nonuniform surface charge distribution shows various intriguing behaviors due to the additional interplay of the nonuniform electro-osmotic effects.     

Velocity Difference of Aqueous Drop Bouncing Between Parallel Electrodes

The bouncing motion of aqueous drops between two oppositely charged electrodes has been observed. However, the forward and backward velocities of the drops are nonuniform in some cases because of unknown reasons. In this study, the velocity difference was mainly caused by the distribution of ions that altered the electric field strength between the electrodes. This result yielded accurate control of the drops in the electric field and opened opportunities for industrial applications.     

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.