Induced-charge Electro-osmotic Flow Research Articles

Induced-charge electrophoresis of a tilted metal nanowire near an insulating wall.

Electric fields are commonly used to control the orientation and motion of microscopic metal particles in aqueous suspensions. For example, metallodielectric Janus spheres are propelled by the induced-charge electro-osmotic flow occurring on their metallic side, the most common case in electrokinetics of exploiting symmetry breaking of surface properties for achieving net particle motion. In this work, we demonstrate that a homogeneous metal rod can translate parallel to a dielectric wall as a result of the hydrodynamic wall-particle interaction arising from the induced-charge electro-osmosis on the rod surface. The applied electric field could be either dc or low-frequency ac. The only requirement for a nonvanishing particle velocity is that the axis of the rod be inclined with respect to the wall, i.e., it cannot be neither parallel nor perpendicular. We show numerical results of the rod velocity as a function of rod orientation and distance to the wall. The maximum particle velocity is found for an orientation of between ∼30^{∘} and ∼50^{∘}, depending on the position and aspect ratio of the cylinder. Particle velocities of up to tens of µm/s are predicted for typical conditions in electrokinetic experiments.

Scattering of Metal Colloids by a Circular Post under Electric Fields.

We consider the scattering of metal colloids in aqueous solutions by an insulating circular post under the action of an AC electric field. We analyze the effects on the particle of several forces of electrical origin: the repulsion between the induced dipole of the particle and its image dipole in the post, the hydrodynamic interaction with the post due to the induced-charge electroosmotic (ICEO) flow around the particle, and the dielectrophoresis arising from the distortion of the applied electric field around the post. The relative influence of these forces is discussed as a function of frequency of the AC field, particle size and distance to the post. We perform numerical simulations of the scattering of the metal colloid by the insulating circular post flowing in a microchannel and subjected to alternating current electric fields. Our simulation results show that the maximum particle deviation is found for an applied electric field parallel to the flow direction. The deviation is also greater at low electric field frequencies, corresponding to the regime in which the ICEO's interaction with the post is predominant over other mechanisms.

Analysis of Sequential Micromixing Driven by Sinusoidally Shaped Induced-Charge Electroosmotic Flow.

Multi-fluid micromixing, which has rarely been explored, typically represents a highly sought-after technique in on-chip biochemical and biomedical assays. Herein, we propose a novel micromixing approach utilizing induced-charge electroosmosis (ICEO) to implement multicomplex mixing between parallel streams. The variations of ICEO microvortices above a sinusoidally shaped floating electrode (SSFE) are first investigated to better understand the microvortex development and the resultant mixing process within a confined channel. On this basis, a mathematical model of the vortex index is newly developed to predict the mixing degree along the microchannel. The negative exponential distribution obtained between the vortex index and mixing index demonstrates an efficient model to describe the mixing performance without solving the coupled diffusion and momentum equations. Specifically, sufficient mixing with a mixing index higher than 0.9 can be achieved when the vortex index exceeds 51, and the mixing efficiency reaches a plateau at an AC frequency close to 100 Hz. Further, a rectangle floating electrode (RFE) is deposited before SSFE to enhance the controlled sequence for three-fluid mixing. One side fluid can fully mix with the middle fluid with a mixing index of 0.623 above RFE in the first mixing stage and achieve entire-channel mixing with a mixing index of 0.983 above SSFE in the second mixing stage, thereby enabling on-demand sequential mixing. As a proof of concept, this work can provide a robust alternative technique for multi-objective issues and structural design related to mixers.

Numerical investigation of field-effect control on hybrid electrokinetics for continuous and position-tunable nanoparticle concentration in microfluidics.

We introduce herein an effective way for continuous delivery and position-switchable trapping of nanoparticles via field-effect control on hybrid electrokinetics (HEK). Flow field-effect transistor exploiting HEK delicately combines horizontal linear electroosmosis and transversal nonlinear electroosmosis of a shiftable flow stagnation line (FSL) on gate terminals under DC-biased AC forcing. The microfluidic nanoparticle concentrator proposed herein makes use of a simple device geometry, in which an individual or a series of planar metal strips serving as gate electrode (GE) are subjected to a hybrid gate voltage signal and arranged in parallel between a pair of 3D driving electrodes. On the application of a DC-biased AC electric field across channel length direction, all the GE are electrochemically polarized, and the action of imposed hybrid electric field on the multiple-frequency bipolar counterions within the composite-induced double layer generates two counter-rotating induced-charge electroosmotic (ICEO) micro-vortices on top of each GE. Symmetry breaking in ICEO flow profile occurs once the gate voltage deviates from natural floating potential of corresponding GE. The gate voltage offset not only results in an additional pump motion of working fluid for enhanced electroosmotic transport but also directly changes the location of FSL where nanoparticles are preferentially collected by field-effect HEK. Our results of field-effect control on HEK are supposed to guide an elaborate design of flexible electrokinetic frameworks embedding coplanar metal strips for a high degree of freedom analyte manipulation in modern micro-total-analytical systems.

Travelling-Wave Electrophoresis, Electro-Hydrodynamics, Electro-Rotation, and Symmetry- Breaking of a Polarizable Dimer in Non-Uniform Fields.

A theoretical framework is presented for calculating the polarization, electro-rotation, travelling-wave dielectrophoresis, electro-hydrodynamics and induced-charge electroosmotic flow fields around a freely suspended conducting dimer (two touching spheres) exposed to non-uniform direct current (DC) or alternating current (AC) electric fields. The analysis is based on employing the classical (linearized) Poisson–Nernst–Planck (PNP) formulation under the standard linearized ‘weak-field’ assumption and using the tangent-sphere coordinate system. Explicit expressions are first derived for the axisymmetric AC electric potential governed by the Robin (mixed) boundary condition applied on the dimer surface depending on the resistance–capacitance circuit (RC) forcing frequency. Dimer electro-rotation due to two orthogonal (out-of-phase) uniform AC fields and the corresponding mobility problem of a polarizable dimer exposed to a travelling-wave electric excitation are also analyzed. We present an explicit solution for the non-linear induced-charge electroosmotic (ICEO) flow problem of a free polarized dimer in terms of the corresponding Stokes stream function determined by the Helmholtz–Smoluchowski velocity slip. Next, we demonstrate how the same framework can be used to obtain an exact solution for the electro-hydrodynamic (EHD) problem of a polarizable sphere lying next to a conducting planar electrode. Finally, we present a new solution for the induced-charge mobility of a Janus dimer composed of two fused spherical colloids, one perfectly conducting and one dielectrically coated. So far, most of the available electrokinetic theoretical studies involving polarizable nano/micro shapes dealt with convex configurations (e.g., spheres, spheroids, ellipsoids) and as such the newly obtained electrostatic AC solution for a dimer provides a useful extension for similar concave colloids and engineered particles.

Breaking electrolyte symmetry in induced-charge electro-osmosis

Abstract

Discharging behavior of confined bipolar electrodes: Coupled electrokinetic and electrochemical dynamics

In this study we numerically investigate the intimately coupled transient electrokinetic and electrochemical dynamics of a nanoconfined bipolar electrode system, using experimental results to guide our analysis. Our recently developed 2D numerical model implements the Poisson-Nernst-Planck-Stokes system of equations to describe nanoscale chemical species transport by advection, migration, and diffusion, as well as the presence of both homogenous and heterogeneous reactions. By eschewing the assumption of electroneutrality and resolving diffuse-charge screening effects, our model uniquely accounts for a wide range of nonlinear transient effects including bipolar electrode (BPE) surface polarization, Faradaic charge accumulation, induced-charge electroosmotic flow, and ion concentration polarization. Using this model, we demonstrate that upon the removal of a polarizing electric field, excess accumulated charge at a BPE surface electrochemically discharges following the capacitive relaxation of diffuse space charge in the electrical double layers (EDLs) surrounding the BPE extremities. These EDLs continue to polarize the BPE as they relax by a process of drift-diffusion, wherein the counter-ionic space charge at each pole promotes a large influx of oppositely charged ions to restore electroneutrality. We numerically reproduced this electrokinetic enhancement effect that was first observed in a recently reported experimental system in which charged fluorophores were used as tracer molecules. Our results also support experimental evidence that, following capacitive EDL relaxation, nanoconfined BPEs can exhibit pseudocapacitance-like discharging behavior that is localized to a single end of the electrode; we experimentally linked this localization to surface oxidation of the anodic BPE pole under the applied field. In addition to providing important insight into the interplay between nanoscale electrokinetic and electrochemical phenomena that govern transient electrode processes, our model and the results presented in this work reinforce the notion that the domain of bipolar electrochemistry constitutes a promising frontier for developing “wirelessly” tunable charge storage and visual detection approaches which exploit both electrokinetic and Faradaic mechanisms.

Efficient particle and droplet manipulation utilizing the combined thermal buoyancy convection and temperature-enhanced rotating induced-charge electroosmotic flow

Efficient granular sample manipulation is crucial for various microfluidic-based applications such as material synthesis and drug delivery. Herein we present a novel method to efficiently manipulate microbeads and droplets using the combined thermal buoyancy convection and temperature-enhanced rotating induced-charge electroosmotic flow. Within the granular fluid, a pair of counter-rotating microvortices is formed above the floating electrode, leading to the formation of a flow stagnation region at the bottom center. Granular samples then can be effectively transported to this region by the Stokes drag, and the concentration performance can be flexibly manipulated by adjusting the energization strategies of the chip. The contributions of fluid convection, dielectrophoresis, thermophoresis, and gravity force to particle migration are first studied and compared, proving that the convection flow and gravity force are mainly responsible for particle migration and deposition respectively. Then the systematic enriching experiments of 4-μm silica particles demonstrate that the particle migration velocity can be highly improved by the combined thermal-electrical field. Finally, the effective concentration of nanocopper particles and the assembly of oil-in-water/water-in-oil-in-water droplets indicate that this approach is capable of manipulating diverse granular samples. Therefore, this strategy can be attractive for lots of microfluidic-based applications because of its high efficiency and simplicity.

Induced charge electroosmotic flow with finite ion size and solvation effects

The most common mathematical models for electrolyte flows are based on the dilute solution assumption, leading to a coupled system of the Nernst–Planck–Poisson drift-diffusion equations for ion transport and the Stokes resp. Navier–Stokes equations for fluid flow of the solvent. In charged boundary layers the dilute solution assumption is in general not valid and volume exclusion and solvation effects have to be taken into account in a thermodynamically consistent way. Whenever boundary layer effects have a dominant impact on the global behavior of a certain electrochemical system, an accurate numerical simulation depends on the correct incorporation of these effects. In this contribution we present a novel numerical solution approach which aims at preserving on the discrete level consistency with basic thermodynamic principles and structural properties like independence of flow velocities from gradient contributions to external forces. We illustrate capabilities of the method by an example of vortex generation due to induced charge electroosmotic forces at an electrode inside a nanochannel.

Electrokinetics of metal cylinders.

We study theoretically the rotation induced on an uncharged metal nanocylinder immersed in an electrolyte by AC electric fields. We consider the rotation of the cylinder when subjected to a rotating electric field (electrorotation) and the orientation of the cylinder in an AC field with constant direction (electro-orientation). The cylinder rotation is due to two mechanisms: the electric field interaction with the induced dipole on the particle and the hydrodynamic stress on the particle originated by the induced-charge electro-osmotic (ICEO) flow around the particle. The cylinder rotation induced by the ICEO mechanism can be calculated by using the Lorentz reciprocal theorem, while the rotation due to the induced dipole is calculated from the cylinder polarizability. We employ 3D numerical computations using finite elements for the general case as well as analytical methods for slender cylinders. Both calculations use the thin-double-layer approximation. We compare the results for slender cylinders of both methods showing good agreement. The electro-orientation (EOr) due to dipole torque aligns the axis of slender cylinders with the applied field, but aligns the axis of short cylinders perpendicularly to the field. The EOr due to ICEO torque always aligns the axis of cylinders with the field. The rotation induced by ICEO torque tends to disappear for frequencies of the applied field much greater than the characteristic frequency for charging the double-layer capacitance of the metal-electrolyte interface.

Asymmetrical Induced Charge Electroosmotic Flow on a Herringbone Floating Electrode and Its Application in a Micromixer.

Enhancing mixing is of significant importance in microfluidic devices characterized by laminar flows and low Reynolds numbers. An asymmetrical induced charge electroosmotic (ICEO) vortex pair generated on the herringbone floating electrode can disturb the interface of two-phase fluids and deliver the fluid transversely, which could be exploited to accomplish fluid mixing between two neighbouring fluids in a microscale system. Herein we present a micromixer based on an asymmetrical ICEO flow induced above the herringbone floating electrode array surface. We investigate the average transverse ICEO slip velocity on the Ridge/Vee/herringbone floating electrode and find that the microvortex generated on the herringbone electrode surface has good potential for mixing the miscible liquids in microfluidic systems. In addition, we explore the effect of applied frequencies and bulk conductivity on the slip velocity above the herringbone floating electrode surface. The high dependence of mixing performance on the floating electrode pair numbers is analysed simultaneously. Finally, we investigate systematically voltage intensity, applied frequencies, inlet fluid velocity and liquid conductivity on the mixing performance of the proposed device. The microfluidic micromixer put forward herein offers great opportunity for fluid mixing in the field of micro total analysis systems.

On the Bipolar DC Flow Field-Effect-Transistor for Multifunctional Sample Handing in Microfluidics: A Theoretical Analysis under the Debye⁻Huckel Limit.

We present herein a novel method of bipolar field-effect control on DC electroosmosis (DCEO) from a physical point of view, in the context of an intelligent and robust operation tool for stratified laminar streams in microscale systems. In this unique design of the DC flow field-effect-transistor (DC-FFET), a pair of face-to-face external gate terminals are imposed with opposite gate-voltage polarities. Diffuse-charge dynamics induces heteropolar Debye screening charge within the diffuse double layer adjacent to the face-to-face oppositely-polarized gates, respectively. A background electric field is applied across the source-drain terminal and forces the face-to-face counterionic charge of reversed polarities into induced-charge electroosmotic (ICEO) vortex flow in the lateral direction. The chaotic turbulence of the transverse ICEO whirlpool interacts actively with the conventional plug flow of DCEO, giving rise to twisted streamlines for simultaneous DCEO pumping and ICEO mixing of fluid samples along the channel length direction. A mathematical model in thin-layer approximation and the low-voltage limit is subsequently established to test the feasibility of the bipolar DC-FFET configuration in electrokinetic manipulation of fluids at the micrometer dimension. According to our simulation analysis, an integrated device design with two sets of side-by-side, but upside-down gate electrode pair exhibits outstanding performance in electroconvective pumping and mixing even without any externally-applied pressure difference. Moreover, a paradigm of a microdevice for fully electrokinetics-driven analyte treatment is established with an array of reversed bipolar gate-terminal pairs arranged on top of the dielectric membrane along the channel length direction, from which we can obtain almost a perfect liquid mixture by using a smaller magnitude of gate voltages for causing less detrimental effects at a small Dukhin number. Sustained by theoretical analysis, our physical demonstration on bipolar field-effect flow control for the microfluidic device of dual functionalities in simultaneous electroconvective pumping and mixing holds great potential in the development of fully-automated liquid-phase actuators in modern microfluidic systems.

Design and Numerical Study of Micropump Based on Induced Electroosmotic Flow

Induced charge electroosmotic flow is a new electric driving mode. Based on the Navier–Stokes equations and the Poisson–Nernst–Planck (PNP) ion transport equations, the finite volume method is adopted to calculate the equations and boundary conditions of the induced charge electroosmotic flow. In this paper, the formula of the induced zeta potential of the polarized solid surface is proposed, and a UDF program suitable for the simulation of the induced charge electroosmotic is prepared according to this theory. At the same time, on the basis of this theory, a cross micropump driven by induced charge electroosmotic flow is designed, and the voltage, electric potential, charge density, and streamline of the induced electroosmotic micropump are obtained. Studies have shown that when the cross-shaped micropump is energized, in the center of the induction electrode near the formation of a dense electric double layer, there exist four symmetrical vortices at the four corners, and they push the solution towards both outlets; it can be found that the average velocity of the solution in the cross-flow microfluidic pump is nonlinear with the applied electric field, which maybe helpful for the practical application of induced electroosmotic flow in the field of micropump.

High efficiency micromixing technique using periodic induced charge electroosmotic flow: A numerical study

Micromixers due to their prominence in Lab-On-a-Chip (LOC), biomanufacturing and chemical engineering applications are of great significances and emphases. In this paper, a 3D transient single phase solver has been developed in the open source code package, OpenFOAM, to investigate mixing efficiency and mixing length of a T-junction micromixer based on AC electroosmotic flow for both Newtonian and non-Newtonian fluids. The mathematical model and the developed solver are validated with existing data in the literature and the effects of substantial parameters such as AC amplitude, period of oscillation and conducting edges are investigated and the optimum range of each parameter are proposed to obtain simultaneously a high mixing efficiency and a relatively short mixing length. Present study shows that by using conducting edges, due to their capability of creating strong vortices, a high mixing efficiency and a short mixing length is achievable.Results show that via implementation of AC electric field as well as conducting edges, the mixing efficiency of 99% in a considerably short mixing length i.e. 20μm even in relatively high flow rates is obtainable. Since the mixing length is depended on the height of microchannel, in order to attain the capability of comparing achieved mixing length with findings of previous studies, a dimensionless parameter, Lm*, is proposed. Comparing of the value of this parameter for the present work and previous studies revealed that the presented micromixer can reduce the dimensionless mixing length up to 60%.

Propulsion of Active Colloids by Self-Induced Field Gradients.

Previously, metallodielectric Janus particles have been shown to travel with their dielectric hemisphere forward under low frequency applied electric fields as a result of asymmetric induced-charge electroosmotic flow. Here, it is demonstrated that at high frequencies, well beyond the charge relaxation time of the electric double layer induced around the particle, rather than the velocity decaying to zero, the Janus particles reverse direction, traveling with their metallic hemisphere forward. It is proposed that such motion is the result of a surface force, arising from localized nonuniform electric field gradients, induced by the dual symmetry-breaking of an asymmetric particle adjacent to a wall, which act on the induced dipole of the particle to drive net motion even in a uniform AC field. Although the field is external, since the driving gradient is induced on the particle level, it may be considered an active colloid. We have thus termed this propulsion mechanism "self-dielectrophoresis", to distinguish from traditional dielectrophoresis where the driving nonuniform field is externally fixed and the particle direction is restricted. It is demonstrated theoretically and experimentally that the critical frequency at which the particle reverses direction can be characterized by a nondimensional parameter which is a function of electrolyte concentration and particle size.

Induced-charge electro-osmotic flow around cylinders with various orientations

Induced-charge electro-osmosis around multiple gold-coated stainless steel rods under various AC electric fields is investigated using the techniques of microparticle image velocimetry and numerical simulation. In this study, the results of interactions between induced electric double layers of two identical conductive cylinders on surrounding fluid are presented. The induced-charge electro-osmosis flow around multiple rods in touch and with one cylinder diameter gap reveals quadrupolar flow structures with four vortices. The induced-charge electro-osmotic flow structure and velocity magnitude also depend on the cylinder geometry and orientation. It is seen that four small vortices develop in the close region of cylinder surface for multiple rods with gap, while the other four large vortices are surrounding them. The distributions of vorticity patterns also strongly depend on cylinder orientation in the close region of cylinder surface.

A novel microfluidic valve controlledby induced charge electro-osmotic flow

In this paper, a novel microfluidic valve by utilizing induced charge electro-osmotic flow (ICEOF) is proposed and analyzed. The key part of the microfluidic valve is a Y-shaped microchannel. A small metal plate is placed at each corner of the junction of the Y-shaped microchannel. When a DC electrical field is applied through the channels, electro-osmotic flows occur in the channels, and two vortices will be formed near each of the metal plates due to the ICEOF. The two vortices behave like virtual ‘blocking columns’ to restrain and direct the flow in the Y-channel. In this paper, effects of the length of the metal plates, the applied voltages, the width of the microchannel, the zeta potential of the non-metal microchannel wall, and the orientation of the branch channels on the flow switching between two outlet channels are numerically investigated. The results show that the flow switching between the two outlet channels can be flexibly achieved by adjusting the applied DC voltages. The critical switching voltage (CSV), under which one outlet channel is closed, decreases with the increase in the metal plate length and the orientation angle of the outlet channels. The CSV, however, increases with the increase in the inlet voltage, the width of the microchannel, and the absolute value of the zeta potential of the non-metal microchannel wall. Compared with other types of micro-valves, the proposed micro-valve is simple in structure without any moving parts. Only a DC power source is needed for its actuation, thus it can operate automatically by controlling the applied voltages.

On utilizing alternating current-flow field effect transistor for flexibly manipulating particles in microfluidics and nanofluidics.

By imposing a biased gate voltage to a center metal strip, arbitrary symmetry breaking in induced-charge electroosmotic flow occurs on the surface of this planar gate electrode, a phenomenon termed as AC-flow field effect transistor (AC-FFET). In this work, the potential of AC-FFET with a shiftable flow stagnation line to flexibly manipulate micro-nano particle samples in both a static and continuous flow condition is demonstrated via theoretical analysis and experimental validation. The effect of finite Debye length of induced double-layer and applied field frequency on the manipulating flexibility factor for static condition is investigated, which indicates AC-FFET turns out to be more effective for achieving a position-controllable concentrating of target nanoparticle samples in nanofluidics compared to the previous trial in microfluidics. Besides, a continuous microfluidics-based particle concentrator/director is developed to deal with incoming analytes in dynamic condition, which exploits a design of tandem electrode configuration to consecutively flow focus and divert incoming particle samples to a desired downstream branch channel, as prerequisite for a following biochemical analysis. Our physical demonstrations with AC-FFET prove valuable for innovative designs of flexible electrokinetic frameworks, which can be conveniently integrated with other microfluidic or nanofluidic components into a complete lab-on-chip diagnostic platform due to a simple electrode structure.

Separation of dielectric Janus particles based on polarizability-dependent induced-charge electroosmotic flow

A new method of sorting dielectric Janus particle is proposed and studied numerically in this paper. The Janus particles are composed of two hemispheres of two different dielectric materials. When the particle is placed in a microchannel under uniform DC electric field along the channel, vortices are induced near the particle. The strengths of the four vortices are determined by the dielectric permittivity of the particle surface, the size of the particle, the external electric field and the orientation of the Janus particle in the electric field. The numerical simulation results show that the dividing line of the Janus particle will align with the channel walls in the uniform electric field. The equilibrium distance between the wall and a particle is determined by the relative polarizability ratio and the size of the Janus particle. Thus Janus particles of the same polarizability ratio and the same size will follow the same streamline; Janus particles of different polarizability ratio and different sizes will have different trajectories. Consequently, by inducing different streamlines into different branch channels, Janus particles can be separated and collected by their polarizability ratios and their sizes.

Trapping and chaining self-assembly of colloidal polystyrene particles over a floating electrode by using combined induced-charge electroosmosis and attractive dipole-dipole interactions.

We propose a novel low-frequency strategy to trap 10 μm colloidal polystyrene (PS) particles of small buoyancy velocity on the surface of a floating electrode, on the basis of combined induced-charge electroosmotic (ICEO) flow and dipole-dipole chaining phenomenon. For field frequencies of 5-50 Hz, much lower than the reciprocal RC time scale, double-layer polarization makes electric field lines pass around the 'insulating' surface of the ideally polarizable floating electrode. Once the long-range ICEO convective micro-vortexes transport particles quickly from the bulk fluid to the electrode surface, neighbouring particles aligned along the local horizontal electric field attract one another by attractive dipolar interactions, and form arrays of particle chains that are almost parallel with the applied electric field. Most importantly, this low-frequency trapping method takes advantage of the dielectrophoretic (DEP) particle-particle interaction to enhance the downward buoyancy force of this dipolar chaining assembly structure, in order to overcome the upward ICEO fluidic drag and realize stable particle trapping around the flow stagnation region. For the sake of comparison, the field frequency is further raised far above the DC limit. At the intermediate frequencies of 200 Hz-2 kHz, this trapping method fails to work, since the normal electric field component emanates from the conducting electrode surface. Besides, at high field frequencies (>3 kHz), particles can be once again effectively trapped at the electrode center, though with a compact (3 kHz) or disordered (10 kHz) 2D packing state on the electrode surface and mainly governed by the short-range negative DEP force field, resulting in requiring a much longer trapping time. To gain a better interpretation of the various particle behaviours observed in experiments, we develop a theoretical framework that takes into account both Maxwell-Wagner interfacial charge relaxation at the particle/electrolyte interface and the field-induced double-layer polarization at the electrode/electrolyte interface, and apply it to quantify the particle-particle electrokinetic interactions. With this simple geometrical configuration of a floating electrode, our results provide a new way to realize trapping of colloidal particles with a small buoyancy velocity under the combined action of ICEO flow and an attractive dipole-dipole interaction.