The effect of step height on the performance of three-dimensional ac electro-osmotic microfluidic pumps

Recent numerical and experimental studies have investigated the increase in efficiency of microfluidic ac electro-osmotic pumps by introducing nonplanar geometries with raised steps on the electrodes. In this study, we analyze the effect of the step height on ac electro-osmotic pump performance. AC electro-osmotic pumps with three-dimensional electroplated steps are fabricated on glass substrates and pumping velocities of low ionic strength electrolyte solutions are measured systematically using a custom microfluidic device. Numerical simulations predict an improvement in pump performance with increasing step height, at a given frequency and voltage, up to an optimal step height, which qualitatively matches the trend observed in experiment. For a broad range of step heights near the optimum, the observed flow is much faster than with existing planar pumps (at the same voltage and minimum feature size) and in the theoretically predicted direction of the "fluid conveyor belt" mechanism. For small step heights, the experiments also exhibit significant flow reversal at the optimal frequency, which cannot be explained by the theory, although the simulations predict weak flow reversal at higher frequencies due to incomplete charging. These results provide insight to an important parameter for the design of nonplanar electro-osmotic pumps and clues to improve the fundamental theory of ACEO.     

Removal of iron (III) oxide particles from a quartz plate by liquid flow

The detachment of submicron particles of iron (III) oxide from a quartz plate in aqueous solutions was investigated by using a well-defined flow of electro-osmosis in comparison with the ordinary flow of water without electrokinetic effect. A rectangular quartz cell was used for removal experiments. Zeta potentials of the particles and the plate were determined by electrophoresis and electro-osmosis, respectively. When the iron (III) oxide particles adhering to the quartz plate were removed by the electro-osmotic flow or the ordinary (Poiseuille) flow, the removal efficiency increased with increasing hydrodynamic force. The removal efficiency by electro-osmotic flow was almost the same as that by ordinary flow under the condition of the same magnitude of applied hydrodynamic force. The values of volume flow rate for the removal efficiency of 0.5 for the electro-osmotic flow was extremely small compared with that for the ordinary flow, showing the effectiveness of particle removal by electrokinetic effect of electro-osmosis. The kinetic analysis of the particle removal process showed that it was characterized by two different rate constants, the rate constant of the rapid process and that of the slow process. The rate constant of slow process increased with increasing electro-osmotic velocity. This shows that the electro-osmotic flow acts as a mechanical force to overcome the energy barrier in the removal process. The rate constant increased with increasing surfactant concentration and this trend became more noticeable as electro-osmotic velocity increased. It is concluded from this result that the effect of surfactant on particle removal is enhanced by the mechanical force in removal processes.     

Electroviscous effects on pressure-driven flow of dilute electrolyte solutions in small microchannels

A fundamental understanding of the flow characteristics of electrolyte solutions in microchannels is critical to the design and control of microfluidic devices. Experimental studies have shown that the electroviscous effect is appreciable for a dilute solution in a small microchannel. However, the experimentally observed electroviscous effects cannot be predicted by the traditional theoretical model, which involves the use of the Boltzmann distribution for the ionic concentration field. It has been found that the Boltzmann distribution is not applicable to systems with dilute electrolyte solutions in small microchannels because it violates the ion number conservation condition. A new theoretical model is developed in this paper using the Nernst equation and the ion number conservation, instead of the Boltzmann distribution, to obtain the ionic concentration field. The ionic concentration field, electrical potential field, and flow field in small microchannels are studied using the model developed here. In order to verify this model, the model-predicted dP/dx (applied pressure gradient) Re (Reynolds number) relationship is compared with the experimentally determined dP/dx approximately Re relationship. Strong agreement between the model predictions and the experimental results supports this model.     

Influence of atomistic physics on electro-osmotic flow: an analysis based on density functional theory

Molecular density profiles and charge distributions determined by density functional theory (DFT) are used in conjunction with the continuum Navier-Stokes equations to compute electro-osmotic flows in nanoscale channels. The ion species of the electrolyte are represented as centrally charged hard spheres, and the solvent is treated as a dense fluid of neutral hard spheres having a uniform dielectric constant. The model explicitly accounts for Lennard-Jones interactions among fluid and wall molecules, hard sphere repulsions, and short range electrical interactions, as well as long range Coulombic interactions. Only the last of these interactions is included in classical Poisson-Boltzmann (PB) modeling of the electric field. Although the proposed DFT approach is quite general, the sample calculations presented here are limited to symmetric monovalent electrolytes. For a prescribed surface charge, this DFT model predicts larger counterion concentrations near charged channel walls, relative to classical PB modeling, and hence smaller concentrations in the channel center. This shifting of counterions toward the walls reduces the effective thickness of the Debye layer and reduces electro-osmotic velocities as compared to classical PB modeling. Zeta potentials and fluid speeds computed by the DFT model are as much as two or three times smaller than corresponding PB results. This disparity generally increases with increasing electrolyte concentration, increasing surface charge density and decreasing channel width. The DFT results are found to be comparable to those obtained by molecular dynamics simulation, but require considerably less computing time.     

Electro-osmotic flows in a microchannel with patterned hydrodynamic slip walls

We present an analysis of the electro-osmotic flow of electrolytic solutions in a microchannel with patterned hydrodynamic slippage on channel walls. A set of governing equations is formulated to account for the effects of small variations in hydrodynamic slippage over the microchannel walls on the electro-osmotic flow. These equations are then solved analytically by using the perturbation method. Two frequently encountered surface patterns, (i) cosine wave variation and (ii) square wave variation in slip length, are considered in our analyses. The results show that patterned slippage over microchannel walls can induce complex flow patterns (such as vortical flows) in otherwise plug-like electro-osmotic flows, which suggests potential applications of such flows in microfluidic mixers.     

Determining zeta Potential and Surface Conductance by Monitoring the Current in Electro-osmotic Flow

In this paper we have outlined a simple procedure for determining zeta potential, zeta(0), and surface conductance, lambda(s), based on current monitoring in electro-osmosis. In these experiments, the average velocity was determined by measuring the amount of time required to completely displace a solution by another solution in the capillary tube. The average velocity during electro-osmosis was found to be independent of capillary size, although it was dependent on the electrolyte concentration and applied electrical field. The measured values of the zeta potential, zeta(0), were found to be independent of capillary size and the applied field, while zeta(0) is strongly dependent on the electrolyte concentration. Calculations of the specific surface conductivity lambda(s) based on current measurements reveal a relationship between lambda(s) and capillary size, in agreement with the results reported in the literature. Copyright 2000 Academic Press.     

A linear analysis of the effect of Faradaic currents on traveling-wave electroosmosis

Net fluid flow of electrolytic solutions induced by a traveling-wave potential applied to an array of co-planar interdigitated microelectrodes has been reported. At low applied voltages the flow is driven in the direction of the traveling-wave potential, as expected by linear and weakly nonlinear theoretical studies. The flow is driven at the surfaces of the electrodes by electrical forces acting in the diffuse electrical double layer. The pumping mechanism has been analyzed theoretically under the assumption of perfectly polarizable electrodes. Here we extend these studies to include the effect of Faradaic currents on the electroosmotic slip velocity generated at the electrode/electrolyte interface. We integrate the electrokinetic equations under the thin-double-layer and low-potential approximations. Finally, we analyze the pumping of electrolyte induced by a traveling-wave signal applied to a microelectrode array using this linear model.     

Electrokinetic flow in a capillary with a charge-regulating surface polymer layer

An analytical study of the steady electrokinetic flow in a long uniform capillary tube or slit is presented. The inside wall of the capillary is covered by a layer of adsorbed or covalently bound charge-regulating polymer in equilibrium with the ambient electrolyte solution. In this solvent-permeable and ion-penetrable surface polyelectrolyte layer, ionogenic functional groups and frictional segments are assumed to distribute at uniform densities. The electrical potential and space charge density distributions in the cross section of the capillary are obtained by solving the linearized Poisson-Boltzmann equation. The fluid velocity profile due to the application of an electric field and a pressure gradient through the capillary is obtained from the analytical solution of a modified Navier-Stokes/Brinkman equation. Explicit formulas for the electroosmotic velocity, the average fluid velocity and electric current density on the cross section, and the streaming potential in the capillary are also derived. The results demonstrate that the direction of the electroosmotic flow and the magnitudes of the fluid velocity and electric current density are dominated by the fixed charge density inside the surface polymer layer, which is determined by the regulation characteristics such as the dissociation equilibrium constants of the ionogenic functional groups in the surface layer and the concentration of the potential-determining ions in the bulk solution.     

Electrokinetic studies on testosterone/aqueous electrolyte interface : Part 1. Electro-osmosis,electrophoresis, streaming potential and streaming current

The electrical properties of testosterone interfaces were investigated. For this purpose, measurements of electro-osmosis, hydrodynamic permeation, streaming potential and streaming currents of metabolically important solutions of the electrolytes NaCl, KCl and MgCl₂ (in the concentration range 10^?4?10^?3 mol/l) across a testosterone plug were carried out. Electrophoretic mobility of testosterone particles suspended in these electrolyte solutions was also studied. The data were analysed from the viewpoint of nonequilibrium thermodynamics. Phenomenological coefficients were evaluated from the linear transport equations and Saxen's relationship was verified. Dependence of phenomenological coefficients on electrolyte concentration was examined. Electro-osmotic and electrophoretic transport coefficients were found to vary linearly with concentration, whereas hydrodynamic permeation and membrane conductance coefficients show non-linear variation. The results are explained on the basis of structural modifications occurring during the passage of the permeating species through the membrane. The nature of the electrical double layer formed at the testosterone/solution interface was ascertained on the basis of the direction of electro-osmotic permeation and electrophoretic migration of testosterone particles.Zeta potentials were estimated in order to obtain a plausible picture of the electrical double layer at the testosterone/solution interfaces. Dependence of zeta potentials on concentration was examined and membrane parameters calculated. The double layer thickness was estimated, which reveals that the diffuse double layer is more compact in the case of MgCl₂ than in that of KCl.     

Lattice Poisson-Boltzmann simulations of electro-osmotic flows in microchannels

This paper presents the numerical results of electro-osmotic flows in micro- and nanofluidics using a lattice Poisson-Boltzmann method (LPBM) which combines a potential evolution method on discrete lattices to solve the nonlinear Poisson equation (lattice Poisson method) with a density evolution method on discrete lattices to solve the Boltzmann-BGK equation (lattice Boltzmann method). In an electrically driven osmotic flow field, the flow velocity increases with both the external electrical field strength and the surface zeta potential for flows in a homogeneous channel. However, for a given electrical field strength and zeta potential, electrically driven flows have an optimal ionic concentration and an optimum width that maximize the flow velocity. For pressure-driven flows, the electro-viscosity effect increases with the surface zeta potential, but has an ionic concentration that yields the largest electro-viscosity effect. The zeta potential arrangement has little effect on the electro-viscosity for heterogeneous channels. For flows driven by both an electrical force and a pressure gradient, various zeta potential arrangements were considered for maximize the mixing enhancement with a less energy dissipation.     

The effect of partial charge transfer on the electrochemical turbulent noise

Theoretical analysis of the effect of electrode potential on the spectral density of random alternating current emerged in electrochemical cell under the action of turbulent pulsations of the electrolyte solution velocity is carried out. An impedance model of metal electrode dissolution reaction, including two adsorption stages, is suggested, with allowance for the oxidized ion diffusion in electrolyte solution. It is known that in terms of the Ershler-Randles model, at low frequencies the experimentally measured slope of bilogarithmic frequency dependence of spectral density equals 3, which is characteristic of the diffusion control; at high frequencies the slope equals 4, which is characteristic of the kinetic control. It is shown that for the model of impedance of the two-stage adsorption oxidation process, in the middle segment of the spectrum the local slope must decrease down to 2, provided the first oxidation stage, which proceeds within the inner electrical double layer, is slow; the local slope must increase up to 6 (or 5, for diffusion control), provided the second oxidation stage (the partially oxidized ion desorption to solution) is slow. The “height” and “width” of the slope local changes appeared explicitly depending on the parameters of the partial charge transfer. This makes the turbulent noise method somewhat superior to the impedance method in the studying of the above-specified reaction type.     

Communication: The phoretic drift of a charged particle animated by a direct ionic current

A charged colloidal particle which is suspended in an electrolyte solution drifts due to an external voltage application. For direct currents, particle motion is affected by two separate mechanisms: electro-osmotic slip associated with the electric field and chemi-osmotic slip associated with the inherent salt concentration gradient in the solution. These two mechanisms are interrelated and are of comparable magnitude. Their combined effect is demonstrated for cation-exchange electrodes using a weak-current approximation. The linkage between the two mechanisms results in an effectively modified mobility, whose dependence on the particle zeta potential is nonlinear. At small potentials, the electro-osmotic mechanism dominates and the particle migrates according to the familiar Smoluchowski mobility, linear in the electric field. At large zeta potentials, chemiosmosis becomes dominant: for positively charged particles, it tends to arrest motion, leading to mobility saturation; for negatively charged particles, it enhances the drift, effectively leading to a shifted linear dependence of the mobility on the zeta potential, with twice the Smoluchowski slope.     

Particle Interactions in Diffusiophoresis and Electrophoresis of Colloidal Spheres with Thin but Polarized Double Layers

The diffusiophoretic and electrophoretic motions of two colloidal spheres in the solution of a symmetrically charged electrolyte are analyzed using a method of reflections. The particles are oriented arbitrarily with respect to the electrolyte gradient or the electric field, and they are allowed to differ in radius and in zeta potential. The thickness of the electric double layers surrounding the particles is assumed to be small relative to the radius of each particle and to the gap width between the particles, but the effect of polarization of the mobile ions in the diffuse layer is taken into account. A slip velocity of fluid and normal fluxes of solute ions at the outer edge of the thin double layer are used as the boundary conditions for the fluid phase outside the double layers. The method of reflections is based on an analysis of the electrochemical potential and fluid velocity disturbances produced by a single dielectric sphere placed in an arbitrarily varying electrolyte gradient or electric field. The solution for two-sphere interactions is obtained in expansion form correct to O(r(12)(-7)), where r(12) is the distance between the particle centers. Our analytical results are found to be in good agreement with the available numerical solutions obtained using a boundary collocation method. On the basis of a model of statistical mechanics, the results of two-sphere interactions are used to analytically determine the first-order effect of the volume fraction of particles of each type on the mean diffusiophoretic and eletrophoretic velocities in a bounded suspension. For a suspension of identical spheres, the mean diffusiophoretic velocity can be decreased or increased as the volume fraction of the particles is increased, while the mean electrophoretic velocity is reduced with the increase in the particle concentration. Generally speaking, the particle interaction effects can be quite significant in typical situations. Copyright 2000 Academic Press.     

Finite element analysis as a tool for crossflow membrane filter simulation

Finite element analysis (FEA) is a very powerful tool in analyzing many engineering problems. In this study, FEA was used to simulate the development of concentration polarization in ultrafiltration of protein solutions. A miniature crossflow membrane filter was developed to verify the FEA models. Polysulfone membrane disks (47 mm) were used in this study. Bovine serum albumin (BSA) solutions of different concentrations were pumped across the membrane flow channel. The crossflow velocity of the feed solution was carefully controlled at the laminar region. With the flow velocities within the flow channel estimated by a perturbation solution, the protein concentration on the membrane surface and the mass transfer coefficient were accurately predicted by FEA. This simulation method may provide a useful tool in engineering analysis and design of a membrane filtration process.     

Direct analysis of inorganic anions in samples with high salt content by capillary zone electrophoresis

Trace-level inorganic anions in seawater are separated efficiently by capillary zone electrophoresis using direct UV detection. The carrier electrolyte is 50 mM borate at pH 9.3 and contained 1.5M NaCl. This buffer solution is adopted to prevent interference from high concentrations of the chloride ion in seawater. No electro-osmotic flow reverser is used to shorten the analysis time. The experimental conditions such as the concentration of NaCl in the carrier electrolyte, capillary inner diameter, applied current, and temperature are optimized. Linear plots are obtained in the concentration range of 0.1 to 20 microg/mL. The quantitation limits of the anions are in the order of 0.02 to 0.1 microg/mL. The proposed method may be applicable to the determination of inorganic anions in other environmental samples and effluents of a power plant.     

A quantitative model for the formation of adsorption-entanglement layers

The formation of thick adsorption-entanglement layers at foreign surfaces during the flow of high molecular weight polymer solutions is now well documented. This paper presents a quantitative model which describes the formation of such layers in terms of the polymer molecular weight and radius of gyration, the solution concentration and the local flow velocity. The model is tested against experiments using capillary flow of atactic polystyrene solutions. The agreement between theory and experiment is very good.     

AC electrokinetics of conducting microparticles: A review

This paper reviews both theory and experimental observation of the AC electrokinetic properties of conducting microparticles suspended in an aqueous electrolyte. Applied AC electric fields interact with the induced charge in the electrical double layer at the metal particle–electrolyte interface. In general, particle motion is governed by both the electric field interacting with the induced dipole on the particle and also the induced-charge electro-osmotic (ICEO) flow around the particle. The importance of the RC time for charging the double layer is highlighted. Experimental measurements of the AC electrokinetic behaviour of conducting particles (dielectrophoresis, electro-rotation and electro-orientation) are compared with theory, providing a comprehensive review of the relative importance of particle motion due to forces on the induced dipole compared with motion arising from induced-charge electro-osmotic flow. In addition, the electric-field driven assembly of conducting particles is reviewed in relation to their AC electrokinetic properties and behaviour.     

Numerical analysis of electroosmotic flow in dense regular and random arrays of impermeable, nonconducting spheres

We present a numerical scheme for analyzing steady-state isothermal electroosmotic flow (EOF) in three-dimensional random porous media, involving solution of the coupled Poisson, Nernst-Planck, and Navier-Stokes equations. While traditional finite-difference methods were used to resolve the Poisson-Nernst-Planck problem, the (electro)hydrodynamics has been addressed with high efficiency using the lattice-Boltzmann method. The developed model allows simulation of electrokinetic transport under most general conditions, including arbitrary value and distribution of electrokinetic potential at the solid-liquid interface, electrolyte composition, and pore space morphology. The approach provides quantitative information on a spatial distribution of simulated velocities. This feature was utilized to characterize EOF fields in regular and random, confined and bulk packings of hard (i.e., impermeable, nonconducting) spheres. Important aspects of pore space morphology (sphere size distribution), surface heterogeneity (mismatch in electrokinetic potentials at confining wall and sphere surface), and fluid phase properties (electrical double layer thickness) were investigated with respect to their influence on the EOF dynamics over microscopic and macroscopic spatial domains. Most important is the observation of a generally nonuniform pore-level EOF velocity profile in the sphere packings (even in the thin double layer limit) which is caused by pore space morphology and which is in contrast to the pluglike velocity distribution in a single, straight capillary under the same conditions.     

Application of magnetohydrodynamic actuation to continuous flow chemistry

Continuous flow microreactors with an annular microchannel for cyclical chemical reactions were fabricated by either bulk micromachining in silicon or by rapid prototyping using EPON SU-8. Fluid propulsion in these unusual microchannels was achieved using AC magnetohydrodynamic (MHD) actuation. This integrated micropumping mechanism obviates the use of moving parts by acting locally on the electrolyte, exploiting its inherent conductive nature. Both silicon and SU-8 microreactors were capable of MHD actuation, attaining fluid velocities of the order of 300 microm s(-1) when using a 500 mM KCl electrolyte. The polymerase chain reaction (PCR), a thermocycling process, was chosen as an illustrative example of a cyclical chemistry. Accordingly, temperature zones were provided to enable a thermal cycle during each revolution. With this approach, fluid velocity determines cycle duration. Here, we report device fabrication and performance, a model to accurately describe fluid circulation by MHD actuation, and compatibility issues relating to this approach to chemistry.     

毛细管区带电泳技术快速分离检测爆炸残留物中的无机离子

利用间接紫外毛细管区带电泳方法完成了对爆炸残留物中7种无机离子(K+,NH+4,NO-2,NO-3,SO2-4,ClO-3,ClO-4)的分离检测。阳离子测定采用的缓冲体系为10 mmol/L吡啶（pH 4.5）-3 mmol/L冠醚,K+和NH+4在2.6 min内达到基线分离,检出限分别为0.25 mg/L和0.10 mg/L(S/N=3)。阴离子测定采用的缓冲体系为40 mmol/L硼酸-1.8 mmol/L重铬酸钾-2 mmol/L硼酸钠（pH 8.6）,氢氧化四甲铵为电渗流改性剂,5种阴离子在4.6 min内达到基线分离,检出限为0.10～1.85 mg/L。该方法已成功地应用于实际爆炸物样品种类的判定分析,取得了很好的结果。