Electrokinetic motion of an electrically induced Janus droplet in microchannels

The electrokinetic motion of an electrically induced Janus oil droplet with one side covered with an aluminum oxide nanoparticle film in a circular microchannel was numerically simulated in this paper. The Janus oil droplet is electrically anisotropic as the nanoparticle-covered area carries positive charges and the rest oil–water surface area carries negative charges. A theoretical model was constructed to calculate the electrokinetic velocity of the Janus droplet by considering the force balance on the surface of the Janus droplet at steady state. In the model, the effects of the electric double layer and surface charges on the motion at the oil–water interface are considered. The effects of five parameters on the electrokinetic motion of the Janus droplets were studied: the electric field, the zeta potential ratio of the positively charged side to the negatively charged side of the Janus droplet, the viscosity ratio of the oil phase to the water phase, the nanoparticle coverage of the Janus droplet, and the size ratio of the diameter of the Janus droplet to the diameter of the cylindrical microchannel. The simulation results indicate that the increase in the electrical field, the zeta potential ratio, the viscosity ratio or the nanoparticle coverage leads to faster electrokinetic motion of the Janus droplet. On the other hand, with the increase in size ratio, the electrokinetic velocity of Janus droplet first decreases gradually then increases sharply. The simulated results were compared with the experimental results and good agreement was found.     

Capillary and electrostatic limitations to the contact angle in electrowetting-on-dielectric

The shape of a conducting liquid droplet placed on a hydrophobic dielectric surface is simulated numerically by solving the Laplace–Young capillary equation. The electric force, acting on the conducting surface, distorts the droplet shape leading to a change in the apparent contact angle; its variation is compared with a theoretical Young–Lippman prediction. At sufficiently large values of voltage, applied to the droplet, the numerical algorithm fails to converge, which is interpreted as the break-up of the droplet surface with small droplets being ejected from the surface. These highly charged droplets, as well as any other electric charges near the triple contact line, generated for example by the electric corona discharge, cause a change of the distribution of the electric forces. This effect can be helpful in explaining saturation of the apparent contact angle: an appropriately selected surface charge near the contact line can completely stop droplet distortion, and the contact angle variation, despite the increased droplet voltage. Furthermore, the simulation results show the effect of the permittivity of the medium surrounding the droplet, on the contact angle variation.     

A front-tracking method with projected interface conditions for compressible multi-fluid flows

A front-tracking method for compressible multi-fluid flows is presented, where marker points are used both for tracking fluid interfaces and also for constructing the Riemann problem on the interfaces. The Riemann problem between the two fluid phases (defined in the interface normal direction) is solved using the exact Riemann solver on the marker points. The solutions are projected onto fixed grid points and then extrapolated into the corresponding ghost-fluid regions, to be used as boundary conditions. Each fluid phase is solved separately as in the ghost-fluid method. The proposed procedures, especially the projection of the exact Riemann solutions onto the fluid grids, are designed to be simple and consistent in any spatial dimensions. Several multi-fluid problems, including the breakup of a water cylinder induced by the passage of a shock wave were computed in order to demonstrate the capability of the proposed method.     

Electrowetting droplet microfluidics on a single planar surface

Electrowetting refers to an electrostatically induced reduction in the contact angle of an electrically conductive liquid droplet on a surface. Most designs ground the droplet by either sandwiching the droplet with a grounding plate on top or by inserting a wire into the droplet. Washizu and others have developed systems capable of generating droplet motion without a top plate while allowing the droplet potential to float. In contrast to these designs, we demonstrate an electrowetting system in which the droplet can be electrically grounded from below using thin conductive lines on top of the dielectric layer. This alternative method of electrically grounding the droplet, which we refer to as grounding-from-below, enables more robust droplet translation without requiring a top plate or wire. We present a concise electrical-energy analysis that accurately describes the distinction between grounded and non-grounded designs, the improvements in droplet motion, and the simplified control strategy associated with grounding-from-below designs. Electrowetting on a single planar surface offers flexibility for interfacing to liquid-handling instruments, utilizing droplet inertial dynamics to achieve enhanced mixing of two droplets upon coalescence, and increasing droplet translation speeds. In this paper, we present experimental results and a number of design issues associated with the grounding-from-below approach.     

Phase field computations for surface diffusion and void electromigration in {\mathbb{R}^3}

We consider a finite element approximation of a phase field model for the evolution of voids by surface diffusion in an electrically conducting solid. The phase field equations are given by a degenerate Cahn–Hilliard equation with an external forcing induced by the electric field. We describe the iterative scheme used to solve the resulting nonlinear discrete equations and present some numerical experiments in three space dimensions. The first author was supported by the EPSRC grant EP/C548973/1.     

应用预处理AWE技术快速计算导体目标宽带RCS

应用渐近波形估计技术计算目标宽带雷达散射截面（RCS）,可有效提高计算效率。然而当目标为电大尺寸时,阻抗矩阵求逆运算将十分耗时,甚至无法计算。提出使用Krylov子空间迭代法取代矩阵逆来求解大型矩阵方程,应用双门槛不完全LU分解预处理技术降低迭代求解所需的迭代次数。数值计算表明,该方法结果与矩量法逐点求解结果吻合良好,并且计算效率大大提高。     

Deformation and migration of a leaky-dielectric droplet in a steady non-uniform electric field

This work numerically investigates the dynamics of an initially uncharged droplet freely suspended in another immiscible fluid and influenced by a steady non-uniform electric field. Both the droplet and the suspending fluid are assumed leaky dielectric. A three-dimensional spectral boundary element method is employed. It is validated by comparing with other numerical results and experimental findings for droplet deformation in a uniform electric field. This work reveals the dominant influence of the relative conductivity of fluids on the droplet migration direction in a non-uniform electric field. We have also explored the complicated behavior of the droplet deformation and speed affected by the relative permittivity and conductivity. In addition, the impact of the electric capillary number and viscosity ratio on the droplet dynamics has also been investigated. Results found and numerical algorithms developed in this study pave ways for investigations on droplet motion in an electric field created by co-planar electrodes, which has direct applications in digital microfluidics.     

Pull-in and freestanding instability of actuated functionally graded nanobeams including surface and stiffening effects

Because of fasttechnological development, electrostatic nanoactuator devices like nanosensors, nanoswitches, and nanoresonators are highly considered by scientific community. Thus, this article presents a new solution technique in solving highly nonlinear integro-differential equation governing electrically actuated nanobeams made of functionally graded material. The modified couple stress theory and Gurtin–Murdoch surface elasticity theory are coupled together to capture the size effects of the nanoscale thin beam in the context of Euler–Bernoulli beam theory. For accurate modelling, all the material properties of the bulk and surface continuums of the FG nanoactuator are varied continuously in thickness direction according to power law. The nonlinearity arising from the electrostatic actuation, fringing field, mid-plane stretching effect, axial residual stress, Casimir dispersion, and van der Waals forces are considered in mathematical formulation. The nonlinear nonclassical equilibrium equation of FG nanobeam-based actuators and associated boundary conditions are exactly derived using Hamilton principle. The new solution methodology is combined from three phases. The first phase applies Galerkin method to get an integro-algebraic equation. The second one employs particle swarm optimization method to approximate the integral terms (i.e. electrostatic force, fringing field, and intermolecular forces) to non-integral cubic algebraic equation. Then, solved the system easily in last phase. The resulting algebraic model provides means for obtaining critical deflection, pull-in voltage, detachment length, minimum gap, and freestanding effects. A reasonable agreement is found between the results obtained from the present method and those in the available literature. A parametric study is performed to investigate the effects of the gradient index, material length scale parameter, surface energy, intermolecular forces, initial gap, and beam length on the pull-in response and freestanding phenomena of fully clamped and cantilever FG nanoactuators.

     

Modelling a droplet moving in an electric field

Droplets on insulators in outdoor high-voltage equipment move and leave water films on the insulating material. These films further the development of undesirable electric currents or even flash-overs. The paper deals with the behaviour of a single droplet laying on a solid support in a strong electric field. Inside the solid support two electrodes generate the electric field. Although the experiment is designed so that the electric field is nearly homogeneous in the absence of a droplet, the remaining inhomogeneity motivates the discussion of its influence on the droplet. Therefore, water droplets at general positions on the experimental set-up are considered. The deformation of the droplet is calculated together with the total force acting on whole the droplet. The total horizontal force initiates the droplet to move. An analytical proof of the existence of a non-vanishing total force acting on an extended uncharged body in a general electric field is given.     

Maxwell stress generated long wave instabilities in a thin aqueous film under time-dependent electro-osmotic flow

In this study the dynamics and stability of thin and electrically conductive aqueous films under the influence of a time-periodic electric field are explored. With the help of analytical linear stability analysis for long wavelength disturbances, the stability threshold of the system as a function of various electrochemical parameters and transport coefficients is presented. The contributions of parameters like surface tension, disjoining pressure, electric double layer (Debye length and interfacial zeta potential), and unsteady Maxwell and viscous stresses are highlighted with the help of appropriate dimensionless groups. The physical mechanisms affecting the stability of thin films are detailed with the above-mentioned forces and parametric dependence of stability trends is discussed.     

Vortices around Janus droplets under externally applied electrical field

In this study, the Janus droplet is an oil droplet covered with aluminum oxide nanoparticles on one side of the droplet surface under applied DC electrical field. The vortices around Janus droplets fixed on a horizontal surface were studied in this paper. A numerical model was set up to simulate the vortices around the Janus droplet in electric field. The simulation results illustrate that the electric field determines the strength of the vortices around a fixed Janus droplet, and the surface coverage of the positively charged nanoparticles on a Janus droplet affects the size and location of the vortices. The numerically predicted results were further validated experimentally by visualizing the vortices around Janus droplets in an externally applied DC electric field. Furthermore, as the Janus droplets are generated in electric field, the surface coverage by the nanoparticles depends on the strength of the electric field; therefore, the effect of the electric field on the nanoparticle covered surface area of a Janus droplet and the vortices was analyzed.     

Numerical investigation of AC electrokinetic virus trapping inside high ionic strength media

A numerical investigation of the mechanism by which viral particles suspended in physiologically relevant (i.e., high ionic strength) media can be electrokinetically sampled on a surface is presented. Specifically, sampling of virus from a droplet is taking place by means of a high frequency non-uniform electric field, generated by energized planar quadrupolar microelectrodes deposited on an oxidized silicon chip. The numerical simulations are based on experimental conditions applied in our previous work with vesicular stomatitis virus. A 3D computer model is used to yield the spatial profiles of electric field intensity, temperature, and fluid velocity inside the droplet, as well as the force balance on the virus. The results suggest that rapid virus sampling can be achieved by the synergistic action of dielectrophoresis and electrothermal fluid flow. Specifically, electrothermal fluid flow can be used to transport the virus from the bulk of a sample to the surface, where dielectrophoretic forces, which become significant only at very small length scales away from the surface, can cause its stable capture.     

Contact dynamics of nanodroplets in carbon nanotubes: effects of electric field,tube radius,and salt ions

We report contact dynamics of nanodroplets in carbon nanotubes using molecular dynamics simulations. The effects of electric field, nanotube radius, and salt ions included in the nanodroplets are explored in more detail. For the cases without applied electric field, the droplet fills the cross section of carbon nanotubes with small radius completely. When the tube radius becomes larger, the droplet retracts towards the surface of the nanotube to minimize the surface tension of the droplet and shows wider extension along the axial direction. When an electric field perpendicular to the axial direction of the carbon nanotubes is applied, the position and shape of the droplets are changed which is also related to the tube radius and whether the droplet contains salt ions. Unlike a planar surface, the nanotube limits spreading of the droplets along the radial direction. The variation of the center of mass of the droplets indicates a significant confinement to the position of the droplets in the electric field. For the salty water droplets, a strong electric field induces ejection of small water clusters from the droplet in a nanotube with large radius. As a consequence, the droplet and water clusters are separated and moved to two opposite sides of the nanotube by the electric field.     

Dynamic aspects of electroosmotic flow

This article presents an analysis of the frequency and time dependent electroosmotic flow in open-end and closed-end microchannels of arbitrary cross-section shape. In the numerical model, the modified Navier–Stokes equation governing the AC electroosmotic flow is solved using the control volume method. The iterative approach is used to determine the induced backpressure gradient. The potential distribution of the EDL in the channel is obtained by solving the non-linear 2D Poisson–Blotzmann equation. The comparison between the control volume formulation and the Green’s function method for the case of a rectangular microchannel shows a good agreement. The time evolution of the electroosmotic flow and the effect of a frequency-dependent AC electric field on the oscillating electroosmotic flow are also examined. The effect of the induced backpressure gradient with the frequency of the applied electric field is also shown.     

Modelling and simulation of electric and magnetic fields in homogeneous non-dispersive anisotropic materials

The paper describes a new efficient method for finding and simulation of electric and magnetic fields in homogeneous non-dispersive electrically anisotropic materials. Electromagnetic wave propagation in these materials is descried by the time-dependent Maxwell’s system which implies initial value problems (IVPs) for electric and magnetic fields. Our method essentially uses matrix symbolic calculations in MATLAB and allows us to compute explicit formulae of electric and magnetic fields. These formulae are used for generating images of electric and magnetic fields inside different materials. A collection of electric and magnetic field images is presented in the paper.     

Electric field driven addressing of ATPS droplets in microfluidic chips

The possibility of controlled droplet motion (droplet addressing) mediated by DC electric field in aqueous two-phase systems (ATPS) is here reported for the first time. Three ATPS of polyethylene glycol (PEG)/salt type, namely PEG/phosphate, PEG/sulphate, and PEG/carbonate, were selected for this study. We observed fast motion of salty droplets dispersed in PEG continuous phase induced by electric field of relative low strength. Hence, three fluidic systems with separated electrode chambers for the evaluation of electrophoretic mobilities and for addressing experiments were fabricated. Electrophoretic mobilities of salty droplets always exceeded the value of \(1\times 10^{-7}\, \hbox {m}^2\hbox {V}^{-1}\hbox {s}^{-1}\), which is about by one magnitude higher value than those typically measured in water–oil droplet systems. The electrophoretic mobilities in systems with free surface are the same or even smaller than in closed microfluidic structures, which is accounted mainly to the fact that a significant part of salty droplets is exposed to air and does not contribute to droplet forcing. Series of addressing and merging experiments in a microfluidic chip shows that DC electric field can be used as a powerful tool for smart manipulation of droplets in microfluidic systems with PEG/salt ATPS.     

Droplet mixing using electrically tunable superhydrophobic nanostructured surfaces

We demonstrate effective mixing of microliter droplets using electrically tunable superhydrophobic nanostructured surfaces. By applying electrical voltage and current, droplets can be reversibly switched from a wetting to a non-wetting state, which induces fluid motion within the droplet. This mixing concept was verified using a DNA hybridization assay, in which a single droplet reversibility accelerated the hybridization reaction by an order of magnitude as compared to mixing by passive diffusion. This work offers a new method to effectively mix droplets for a variety of microfluidics applications.     

Droplet creation using liquid dielectrophoresis

Dielectrophoresis (DEP) is defined as polarizable particles moving into regions of higher electric field intensity. In liquid DEP (LDEP), a dielectric liquid tends to flow toward regions of high electric field intensity under a non-uniform electric field. This work presents a theoretical model of LDEP based on parallel electrodes. The LDEP force is derived using the lump parameter electromechanical method. The relationship between the minimum actuation voltage and the electrode width is investigated experimentally and theoretically. We also propose a method for creating a 20 nl droplet of deionized water using LDEP. The creation of a water droplet containing 15 μm polystyrene beads is placed at the desired location from a continuous flow driven by LDEP using the developed method.     

Simulation of runaway electrons during tokamak disruptions

When modeling the generation of runaway electrons in tokamak disruptions, it is essential to account for the evolution of the electric field in a self-consistent way. This is achieved by the ARENA code, which is described in the present paper. In this code, the relativistic electron kinetic equation is solved by the Monte Carlo method, supplemented with a weighting scheme to enhance the accuracy of the simulated fast-electron dynamics. Finite elements are employed to solve Maxwell's equations governing the electric field, and this solution is coupled to the Monte Carlo solution of the kinetic equation in a semi-implicit way in order to maintain numerical stability. This numerical scheme thus makes it possible, for the first time, to simulate runaway avalanche kinetics in a disruption self-consistently, accounting both for the acceleration of runaway electrons by the electric field and for the change in the electric field induced by the runaway current. The first results of such a simulation of a JET-like disruption are presented.     

Design optimization and sensitivity analysis on buckling stability of piezoelectric truss structures

The design optimization of buckling behavior is studied for piezoelectric intelligent truss structures. First, on the basis of mechanical–electric coupling equation and considering electric load and mechanical loads together, the finite element model of piezoelectric trusses has been built up. Then, the computational formula has been derived for the design sensitivities of critical buckling load factor of the structure with respect to size and shape design variables. The electric voltage is taken as a new kind of design variable and the calculation method of critical load buckling factor with respect to the electric voltage variables is proposed. Particularly, the variations of the loads and pre-buckling inner forces with design variables have been accounted for. Finally, the sequential linear programming algorithm is employed to solve the optimization problem, and a new method of controlling structural buckling stability by optimizing the voltages of piezoelectric active bars is proposed. Numerical examples given in the paper have demonstrated the effectiveness of the methods presented.