Instability of the interface between thin fluid films subjected to electric fields

The effect of an externally applied electric field on the stability of the interface between two thin leaky dielectric fluid films of thickness ratio and viscosity ratio ris analyzed using a linear stability analysis in the long-wave limit. A systematic asymptotic expansion is employed in this limit to derive the coupled nonlinear differential equations describing the evolution of the position of the interface between the fluids and the interfacial free charge distribution. The linearized stability of these equations is determined and the effect of the ratio of the conductivities, dielectric constants, thicknesses, and viscosities on the wavenumber of the fastest growing mode, kmax, and the growth rate of the most unstable mode, smax, is examined in detail. Specific configurations considered in previous studies, such as a perfect dielectric-air interface, leaky dielectric-air interface, etc., emerge as limiting cases from the general formulation developed in this paper. Our results show that the viscosity ratio, mur, does not have any significant effect on kmax for the interface between perfect and leaky dielectric fluids. In marked contrast, however, mur is shown to have a significant effect on the interface between two leaky dielectrics. Increasing mur from 0.1 to 10 could decrease kmax up to a factor of 5. In general, our results show that the presence of nonzero conductivity in either one or both of the fluids has a profound influence on the length-scale characteristic of the linear instability: a reduction even by a factor of 1/50 in the length scale can be effected when compared to the interface between two perfect dielectrics. These predictions could have important implications in pattern formation applications in thin fluid films that employ electric fields. The variation of kmax and smax on the thickness ratio, beta, indicates in general that kmaxalpha(beta-apha), and smaxalpha(beta-theta), where the exponents alpha and theta (both >0) are found to depend only on the ratio of conductivities, and are largely independent of other system parameters.     

A 2D electrohydrodynamic model for electrorotation of fluid drops

A theoretical analysis of spontaneous electrorotation of deformable fluid drops in a DC electric field is presented with a 2D electrohydrodynamic model. The fluids in the system are assumed to be leaky dielectric and Newtonian. If the rotating flow is dominant over the cellular convection type of electrohydrodynamic flow, closed-form solutions for drops of small deformations can be obtained. Because the governing equations are in general nonlinear even when drop deformations are ignored, the general solution for even undeformed drop takes a form of infinite series and can only be evaluated by numerical means. Both closed-form solutions for special cases and numerical solutions for more general cases are obtained here to describe steady-state field variables and first-order drop deformations. In a DC electric field of strength beyond the threshold value, spontaneous electrorotation of a drop is shown to occur when charge relaxation in the surrounding fluid is faster than the fluid inside the drop. With increasing the strength of the applied electric field from the threshold for onset of electrorotation, the axis of drop contraction deviates from from that of the applied electric field in the direction of the rotating flow with an angle increasing with the field strength.     

Dielectric permittivity profiles of confined polar fluids

The dielectric response of a simple model of a polar fluid near neutral interfaces is examined by a combination of linear response theory and extensive molecular dynamics simulations. Fluctuation expressions for a local permittivity tensor epsilon(r) are derived for planar and spherical geometries, based on the assumption of a purely local relationship between polarization and electric field. While the longitudinal component of epsilon exhibits strong oscillations on the molecular scale near interfaces, the transverse component becomes ill defined and unphysical, indicating nonlocality in the dielectric response. Both components go over to the correct bulk permittivity beyond a few molecular diameters. Upon approaching interfaces from the bulk, the permittivity tends to increase, rather than decrease as commonly assumed, and this behavior is confirmed for a simple model of water near a hydrophobic surface. An unexpected finding of the present analysis is the formation of "electrostatic double layers" signaled by a dramatic overscreening of an externally applied field inside the polar fluid close to an interface. The local electric field is of opposite sign to the external field and of significantly larger amplitude within the first layer of polar molecules.     

Electric field inside a "Rossky cavity" in uniformly polarized water

Electric field produced inside a solute by a uniformly polarized liquid is strongly affected by dipolar polarization of the liquid at the interface. We show, by numerical simulations, that the electric "cavity" field inside a hydrated non-polar solute does not follow the predictions of standard Maxwell's electrostatics of dielectrics. Instead, the field inside the solute tends, with increasing solute size, to the limit predicted by the Lorentz virtual cavity. The standard paradigm fails because of its reliance on the surface charge density at the dielectric interface determined by the boundary conditions of the Maxwell dielectric. The interface of a polar liquid instead carries a preferential in-plane orientation of the surface dipoles thus producing virtually no surface charge. The resulting boundary conditions for electrostatic problems differ from the traditional recipes, affecting the microscopic and macroscopic fields based on them. We show that relatively small differences in cavity fields propagate into significant differences in the dielectric constant of an ideal mixture. The slope of the dielectric increment of the mixture versus the solute concentration depends strongly on which polarization scenario at the interface is realized. A much steeper slope found in the case of Lorentz interfacial polarization also implies a higher free energy penalty for polarizing such mixtures.     

Stability conditions of an electrified miscible viscous fluid sheet

The Kelvin-Helmholtz problem of viscous fluids under the influence of a normal periodic electric field in the absence of surface charges is studied. The system is composed of a streaming dielectric fluid sheet of finite thickness embedded between two different streaming finite dielectric fluids. The interfaces permit mass and heat transfer. Because of the complexity of the considered system, a mathematical simplification is adopted. The weak viscous effects are taken into account so that their contributions are incorporated into the boundary conditions. Therefore, the equations of motion are solved in the absence of viscous effects. The boundary value problem leads to two simultaneous Mathieu equations of damped terms having complex coefficients. The symmetric and antisymmetric deformations reduced the coupled Mathieu equations to a single Mathieu equation. The classical stability criterion is found to be substantially modified due to the effect of mass and heat transfer. The analytical results are numerically confirmed. It is found that the sheet thickness and mass and heat transfer parameters have a dual influence on the stability criteria. It is also found that the field frequency has a stabilizing influence especially at small values of the wave number. In contrast to the case of a pure inviscid fluid, it is found that the uniform normal electric field plays a dual role in the stability criteria. This role depends on the choice of the numerical values of the physical parameters of the system under consideration.     

Investigation of the role of template features on the electrically induced structure formation (EISF) for a faithful duplication

Electrically induced structure formation, as a physical approach to fabricate micro/nanostructures, has attracted much attention because of the simple process, low‐cost, high‐efficiency, and wide applications on electronics, microfluidics, and so forth. Hitherto, the influence of some process parameters, such as voltage, air gap, film thickness, polymer properties, on the polymeric behavior, and the structure formation has been explored, neglecting the effects of the template features, which affect the polymer deformation. Especially for the conductive protrusions directly contacting the polymer, the phenomenon of electric breakdown may occur, leading to a failure of structure formation. The limitation of the research on the template features triggers the necessity to study its influence for a faithful deformation. In this paper, three types of patterned template are studied based on the electric field at the air‐polymer interface, consisting of completely conductive template, partially conductive template, and dielectric template. Comprehensive consideration of the electric intensity for a sufficient driving pressure and the leaky current for preventing damaging the polymer, some guiding opinions on the template material and geometry can be provided to design the patterned template for the electrically induced structure formation process with a purpose for a faithful structure.     

Experimental study of dielectrophoresis and liquid dielectrophoresis mechanisms for particle capture in a droplet

This work presents a microfluidic system that can transport, concentrate, and capture particles in a controllable droplet. Dielectrophoresis (DEP), a phenomenon in which a force is exerted on a dielectric particle when it is subjected to a non-uniform electric field, is used to manipulate particles. Liquid dielectrophoresis (LDEP), a phenomenon in which a liquid moves toward regions of high electric field strength under a non-uniform electric field, is used to manipulate the fluid. In this study, a mechanism of droplet creation presented in a previous work that uses DEP and LDEP is improved. A driving electrode with a DEP gap is used to prevent beads from getting stuck at the interface between air and liquid, which is actuated with an AC signal of 200 V(pp) at a frequency of 100 kHz. DEP theory is used to calculate the DEP force in the liquid, and LDEP theory is used to analyze the influence of the DEP gap. The increment of the actuation voltage due to the electrode with a DEP gap is calculated. A set of microwell electrodes is used to capture a bead using DEP force, which is actuated with an AC signal of 20 V(pp) at a frequency of 5 MHz. A simulation is carried out to investigate the dimensions of the DEP gap and microwell electrodes. Experiments are performed to demonstrate the creation of a 100-nL droplet and the capture of individual 10-μm polystyrene latex beads in the droplet.     

Nonlinear EHD Stability of the Interfacial Waves of Two Superposed Dielectric Fluids

The slow modulation of the interfacial capillary–gravity waves of two superposed dielectric fluids with uniform depths and solid horizontal boundaries, under the influence of a normal electric field and in the absence of surface charges at their interface, is investigated by using the multiple-time scales method. It is found that the complex amplitude of quasi-monochromatic traveling waves can be described by a nonlinear Schrödinger equation in a frame of reference moving with the group velocity. The stability characteristics of a uniform wave train are examined analytically and numerically on the basis of the nonlinear Schrödinger equation, and some limiting cases are recovered. Three cases appear, depending on whether the depth of the lower fluid is equal to, greater than, or less than the depth of the upper fluid. The effect of the normal electric field is determined for the three stability regions of the pure hydrodynamic case. It is found that the normal electric field has a destabilizing influence in the first stability region and a stabilizing effect in the second and third stability regions. Moreover, one new unstable region or two new stable and unstable regions appear, all of which increase when the electric field increases. On the other hand, the complex amplitude of quasi-monochromatic standing waves near the cutoff wavenumber is governed by a similar type of nonlinear Schrödinger equation in which the roles of time and space are interchanged. This equation makes it possible to estimate the nonlinear effect on the cutoff wavenumber.     

AC field induced-charge electroosmosis over leaky dielectric blocks embedded in a microchannel

An effective electrical boundary condition is formulated to describe AC field-driven induced-charge electrokinetic (ICEK) phenomena at the interface between a liquid and a leaky dielectric solid. Since most materials in reality possess finite dielectric and conductive properties, i.e. leaky dielectric, the present boundary condition can be used to describe the induced zeta potential on a leaky dielectric surface with consideration of both bond charges (due to polarization) and free charges (due to conduction). Two well-known limiting cases, i.e. the perfectly dielectric and the perfectly conducting wall boundary conditions can be recovered from the present formulation. Utilizing the derived boundary condition, we obtain analytical solutions in closed form for the AC field-driven induced-charge electroosmosis (ICEO) over two symmetric leaky dielectric blocks embedded in the walls of an infinitely long microchannel. Two important factors for the induced zeta potential are identified to respectively account for the polarization charges and the free charges, and their effects on AC field-driven ICEO oscillating flow patterns are analyzed. It is found that the flow patterns exhibit two counter-rotating vortices, which can be deformed, relocated, eliminated and even reverse their rotating directions. It is very promising that such temporary evolution of flow patterns can possibly induce chaotic advection which can enhance microfluidic mixing.     

Stability of Streaming in an Electrified Maxwell Fluid Sheet Influenced by a Vertical Periodic Field in the Absence of Surface Charges

The problem of electroviscoelastic Kelvin-Helmholtz waves of Maxwellian fluids under the influence of a vertical periodic electric field is studied in the absence of surface charges. The system is composed of a streaming dielectric fluid sheet of finite thickness embedded between two different streaming semi-infinite dielectric fluids. Due to the streaming flow and the influence of a periodic force, a mathematical simplification is considered. The weak viscoelastic effects are taken into account so that their contributions are demonstrated in the boundary conditions. The approximate equations of motion are solved in the absence of viscoelastic effects. The solutions of the linearized equations of motion and boundary conditions lead to two simultaneous Mathieu equations of damping terms having complex coefficients. Symmetric or antisymmetric deformation that relaxes the coupled Mathieu equations and yields a single Mathieu equation is considered. Stability criteria are discussed and numerical estimation shows that the increase in the sheet thickness plays a destabilizing effect in the presence or in the absence of the field frequency as well as the field intensity. In the absence of the field frequency the velocity ratio between the upper fluid velocity and the sheet velocity has a destabilizing influence, while that between the velocity of the lower fluid and the velocity of the sheet has a stabilizing influence. Moreover, the viscosity ratios have a damping influence while the elasticity ratios have a destabilizing influence. Furthermore, a range of general deformations of the surface deflections is studied. Moreover, the stability behavior for the resonance cases is studied and discussed. The coupled Mathieu equations are analyzed by the multiple scale method. The numerical examination for stability yields some changes in the stability behavior. The fluid sheet thickness plays a stabilizing role in the presence of a constant field while the damping role is observed for the resonance case. Similar results are found for both the stratified velocities and the stratified relaxation times. The dual role of the stratified viscosities is observed in the presence or the absence of the field frequency. Copyright 2000 Academic Press.     

Dielectric spectroscopy in a micromachined flow cytometer: theoretical and practical considerations

We propose a model to determine the influence of different cell properties, such as size, membrane capacitance and cytoplasm conductivity, on the impedance spectrum as measured in a microfabricated cytometer. A dielectric sphere of equivalent complex permittivity is used as a simplified model to describe a biological cell. The measurement takes place between a pair of facing microelectrodes in a microchannel filled with a saline solution. The model incorporates various cell parameters, such as dielectric properties, size and position in the channel. A 3D finite element model is used to evaluate the magnitude of the electric field in the channel and the resultant changes in charge densities at the measurement electrode boundaries as a cell flows past. The charge density is integrated on the electrode surface to determine the displacement current and the channel impedance for the computed frequency range. The complete impedance model combines the finite element model, the electrode-electrolyte interface impedance and stray impedance, which are measured from a real device. The modeled dielectric complex spectra for various cell parameters are discussed and a measurement strategy for cell discrimination with such a system is proposed. We finally discuss the amount of noise and measurement fluctuations of the sensor.     

Electrorheological fluids based on glycerol-activated titania gel particles and silicone oil with high yield strength

This article describes an electrorheological (ER) fluid based on glycerol-activated titania organic-inorganic hybrid gel particles and silicone oil with high yield strength. Based on a physical picture of a water-activated ER system, glycerol that has a high dielectric constant and boiling point is in situ prepared in the amorphous titania gel during the sol-gel processing. A small amount of ionic surfactant hexadecyltrimethylammonium bromide (CTAB) is employed to enhance charge carriers in particles. FTIR and XRD techniques are used to determine the nature and structure of the hybrid gel. Rheology test results show that a large static yield stress greater than 12.6 kPa is obtained when 3 kV/mm dc electric field is applied. This value is close to the value predicted by H. Conrad (MRS Bull. 8 (1998) 35) in theory. Furthermore, dynamic shear stress as a function of shear rate and temperature is also investigated. This ER fluid exhibits strong temperature dependence and a wide working temperature range from 0 to 120 degrees C, while its leaking current density is still low. More interesting is that the glycerol content is demonstrated to have an influence on ER effect and temperature dependence. Measurement of the dielectric properties of ER fluids shows enhancement of the dielectric constant and dielectric loss due to addition of glycerol and a regular dependence of them on temperature, which well explains the strong ER effect.     

Electroosmotic flow in a water column surrounded by an immiscible liquid

In this paper, we conducted numerical simulation of the electroosmotic flow in a column of an aqueous solution surrounded by an immiscible liquid. While governing equations in this case are the same as that in the electroosmotic flow through a microchannel with solid walls, the main difference is the types of interfacial boundary conditions. The effects of electric double layer (EDL) and surface charge (SC) are considered to apply the most realistic model for the velocity boundary condition at the interface of the two fluids. Effects on the flow field of ?-potential and viscosity ratio of the two fluids were investigated. Similar to the electroosmotic flow in microchannels, an approximately flat velocity profile exists in the aqueous solution. In the immiscible fluid phase, the velocity decreases to zero from the interface toward the immiscible fluid phase. The velocity in both phases increases with ?-potential at the interface of the two fluids. The higher values of ?-potential also increase the slip velocity at the interface of the two fluids. For the same applied electric field and the same ?-potential at the interface of the two fluids, the more viscous immiscible fluid, the slower the system moves. The viscosity of the immiscible fluid phase also affects the flatness of the velocity profile in the aqueous solution.     

Water molecule clusters measured at water/air interfaces using atomic force microscopy

During the tip approach to hydrophobic surfaces like the water/air interface, the measured interaction force reveals a strong attraction with a range of approximately 250 nm at some points along the interface. The range of this force is approximately 100 times larger than the measured for gold (approximately 3 nm) and 10 times larger than the one for hydrophobic silicon surfaces (approximately 25 nm). At other points the interface exerts a medium range repulsive force growing stepwise as the tip approaches the interface plane, consequently the hydrophobic force is a strong function of position. To explain these results we propose a model where the force on the tip is associated with the exchange of a small volume of the interface with a dielectric permittivity epsilon(int) by the tip with a dielectric permittivity epsilon(tip). By assuming a oscillatory spatial dependence for the dielectric permittivity it is possible to fit the measured force profiles. This dielectric spatial variation was associated with the orientation of the water molecules arrangement in the interfacial region. Small nanosized hydrogen-bond connected cages of water molecules present in bulk water at the interface are oriented by the interfacial electric field generated by the water molecules broken bonds, one broken hydrogen bond out of every four. This interfacial field orients small clusters formed by approximately 100 water molecules into larger clusters (approximately 100 nm). In the limit of small (less than 5 nm thick) water molecule cages we have modeled the static dielectric permittivity (epsilon) as the average response of those cages. In these regions the dielectric permittivity for water/air interfaces decreases monotonically from the bulk value epsilon approximately 80 to approximately 2 at the interface. For regions filled with medium size cages, the tip senses the structure of each cage and the static dielectric permittivity is matched to the geometrical features of these cages sized approximately 25 to 40 nm. Interfacial electric energy density values were calculated using the electric field intensity and the dielectric permittivity obtained by the fitting of the experimental points. The integration of the electric energy density along the interfacial region gives a value of 0.072 J m(-2) for interfacial energy density for points where the hydrophobic force has a range of approximately 250 nm. Regions formed by various clusters result in lower values of the interfacial energy density.     

外部电场下水分子间静电相互作用的分子动力学研究

本文利用分子动力学模拟探讨了不同外电场下,液态水的分子间作用及分子排布的变化. 在不同外电场下,O…O原子间的径向分布函数差别很小,但是单个水分子的偶极矩的取向变化却很大. 当外电场为0时,单个水分子偶极取向的范围很宽（30-150度）. 与此同时,本文给出了局域诱导电场随着位置的变化关系图. 当外加电场增强时,局域的诱导电场强度也随之增加. 由于电场下偶极矩有序性的增加,局域诱导的静电相互作用能显著增加. 计算结果表明,相对介电常数随着电场强度的增加而呈现指数衰减的变化形式. 这一变化趋势可以用来理解不同电化学环境下,静电相互作用和局域诱导电场的变化.     

Dielectrophoretic assembly of metallodielectric Janus particles in AC electric fields

"Janus" particles with two hemispheres of different polarizability or charge demonstrate a multitude of interesting effects in external electric fields. We reported earlier how particles with one metallic hemisphere and one dielectric hemisphere self-propel in low-frequency alternating current (AC) electric fields. Here, we demonstrate the assembly of such Janus particles driven by AC electric fields at frequencies above 10 kHz. We investigated the relation between field-induced dielectrophoretic force, field distribution, and structure of the assemblies. The phase space for electric field intensity and frequency was explored for particle concentrations large enough to form a monolayer on a glass surface between two gold electrodes. A rich variety of metallodielectric particle structures and dynamics were uncovered, which are very different from those obtained from directed assembly of plain dielectric or plain conductive particles under the action of fields of similar frequency and intensity. The metallodielectric particles assemble into new types of chain structures, where the metallized halves of neighboring particles align into lanes along the direction of the electric field, while the dielectric halves face in alternating direction. The staggered chains may assemble in various orientations to form different types of two-dimensional metallodielectric crystals. The experimental results on the formation of staggered chains are interpreted by means of numerical simulations of the electric energy of the system. The assembly of Janus metallodielectric particles may find applications in liquid-borne microcircuits and materials with directional electric and heat transfer.     

A polarizable continuum model for molecules at diffuse interfaces

In this work we illustrate an extension of the polarizable continuum model to describe solvation effects on molecules at the interface between two fluid phases (liquid/liquid, liquid/vapor). This extension goes beyond the naive picture of the interface as a plane dividing two distinct dielectrics, commonly employed in continuum models. The main feature of the model is the use of a diffuse interface with an electric permittivity depending on the position. This characteristic clearly allows the study of simple interfaces as well as more complex membrane or multilayer structures. Moreover the smooth variation of the permittivity in the diffuse interface, in contrast to the sharp boundary between two regions, overcomes the numerical divergences due to charges placed at the boundary. The implementation of the model relies on the integral equation formalism, which allows one to calculate the reaction field acting on a molecule immersed in a dielectric environment once the proper Green's function is known. In the present case, such a Green's function is obtained numerically, allowing a large flexibility in the choice of the dielectric permittivity profile. The applications have been selected with the aim of illustrating the capabilities of the model; its present limitations are also discussed.     

Considerations on ultra-high frequency electric field effects on oxygen vacancy concentration in oxide thin films

Atomistic simulations employing dynamic charge transfer between atoms are used to investigate ultra-thin oxide growth on Al(100) metal substrates in the presence of an ac electric field. In the range of 1-10 GHz frequencies, the enhancement in oxidation kinetics by ～12% over natural oxidation can be explained by the Cabrera-Mott mechanism. At field frequencies approaching 0.1-1 THz, however, we observe a dramatic lowering of the kinetics of oxygen incorporation by ～35% compared to the maximum oxidation achieved, which results in oxygen non-stoichiometry near the oxide-gas interface (O/Al ≈ 1.0). This is attributed to oxygen desorption from the oxide surface. These results suggest a general strategy to tune oxygen concentration at oxide surfaces using ac electric fields that could be of interest in diverse fields related to surface chemistry and applications such as tunnel barriers, thin dielectrics and oxide interfaces.     

Electrophoresis of a colloidal sphere in a spherical cavity with arbitrary zeta potential distributions

An analytical study is presented for the quasi-steady electrophoretic motion of a dielectric sphere situated at the center of a spherical cavity when the surface potentials are arbitrarily nonuniform. The applied electric field is constant, and the electric double layers adjacent to the solid surfaces are assumed to be much thinner than the particle radius and the gap width between the surfaces. The presence of the cavity wall causes three basic effects on the particle velocity: (1) the local electric field on the particle surface is enhanced or reduced by the wall; (2) the wall increases the viscous retardation of the moving particle; and (3) a circulating electroosmotic flow of the suspending fluid exists because of the interaction between the electric field and the charged wall. The Laplace and Stokes equations are solved analytically for the electric potential and velocity fields, respectively, in the fluid phase, and explicit formulas for the electrophoretic and angular velocities of the particle are obtained. To apply these formulas, one has to calculate only the monopole, dipole, and quadrupole moments of the zeta-potential distributions at the particle and cavity surfaces. It is found that the contribution from the electroosmotic flow developing from the interaction of the imposed electric field with the thin double layer adjacent to the cavity wall and the contribution from the wall-corrected electrophoretic driving force to the particle velocities can be superimposed as a result of the linearity of the problem.