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.     

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.     

Dynamics of electrical double layer formation at a charged solid surface

A theoretical study of the dynamics of electrical double layer formation near a charged solid surface is presented. A microscopic expression for the time dependent inhomogeneous charge density of an ionic solution next to a newly charged surface is derived by using linear response theory and molecular hydrodynamics. The presence of interionic correlations is included through ionic structure factors. The rate of electrical double layer formation is found to depend rather strongly on ion concentration and on the dielectric constant of the medium. It is also found that the formation of double layer becomes slower with increase in distance from the charged surface.     

Extended space charge in concentration polarization

This paper is concerned with ionic currents from an electrolyte solution into a charge-selective solid, such as, an electrode, an ion-exchange membrane or an array of nano-channels in a micro-fluidic system, and the related viscous fluid flows on the length scales varying from nanometers to millimeters. All systems of this kind have characteristic voltage-current curves with segments in which current nearly saturates at some plateau values due to concentration polarization — formation of solute concentration gradients under the passage of a DC current. A number of seemingly different phenomena occurring in that range, such as anomalous rectification in cathodic copper deposition from a copper sulfate solution, super-fast vortexes near an ion-exchange granule, overlimiting conductance in electrodialysis and the recently observed non-equilibrium electroosmotic instability, result from the formation of an additional extended space charge layer next to that of a classical electrical double layer at the solid/liquid interface. In this paper we review the peculiar features of the non-equilibrium electric double layer and extended space charge and the possibility of their direct probing by harmonic voltage/current perturbations through a linear and non-linear system's response, by the methods of electrical impedance spectroscopy and via the anomalous rectification effect. On the relevant microscopic scales the ionic transport in the direction normal to the interface is dominated by drift-diffusion; hence, the extended space charge related viscous flows remain beyond the scope of this paper.     

Double-layer interaction between parallel solid cylinders partially immersed in an oil/water interface

We consider two identical, parallel, infinitely long solid cylinders at a given separation, lying flat on a plane oil/water interface and both immersed to the same extent in the oil and water phases. The part of the surface of each cylinder in contact with the aqueous phase is charged, forming an electric double layer in a symmetrical aqueous binary electrolyte. The electrical potential in the overlapping electric double layers in the aqueous phase satisfies the Poisson-Boltzmann equation. The potentials within the uncharged interiors of the solid cylinders and in the oil phase satisfy Laplace's equation. The equations for the three potentials are solved simultaneously using the finite element method with Galerkin weighted residuals. The double-layer interaction per unit length of the cylinders is then calculated. Of the numerical results obtained, three deserve special mention. First, a short-range double-layer repulsion, decaying exponentially with separation between the two cylinders, acts through the aqueous electrolyte medium, whereas in the case of an uncharged oil/water interface a weaker, but much longer-ranging, repulsive interaction acts through the oil medium. Second, reasonable estimates of the short-range interaction between cylinders in a planar interface can be obtained from the Derjaguin approximation for thin double layers. Third, in addition to the repulsive force between the cylinders parallel to the oil/water interface, a force normal to the interface acts on the cylinders in the direction of the aqueous electrolyte phase.     

Molecular dynamics and neutron scattering study of the dependence of polyelectrolyte dendrimer conformation on counterion behavior

Atomistic molecular dynamics (MD) simulations and contrast variation small angle neutron scattering (SANS) have been combined to investigate the Generation-5 polyelectrolyte polyamidoamine starburst dendrimer. This work reveals the dendrimer conformational dependence on counterion association at different levels of molecular charge. The accuracy of the simulations is verified through satisfactory comparison between modeled results, such as excess intra-dendrimer scattering length density distribution and hydration level, and their experimental counterparts. While the counterion distributions are not directly measureable with SANS, the spatial distribution of the counterions and their dendrimer association are extracted from the validated MD equilibrium trajectories. It is found that the conformation of the charged dendrimer is strongly dependent on the counterion association. Sensitivity of the distribution of counterions around charged amines to the counterion valency is qualitatively explained by adopting Langmuir adsorption theory. Moreover, via extending the concept of electrical double layer for compact charged colloids, we define an effective radius of a charged dendrimer including the spatial distribution of counterions in its vicinity. Within the same framework, the correlation between the strength of intra-dendrimer electrostatic repulsion and the counterion valency and dynamics is also addressed.     

The Charge of Solid–Liquid Interfaces Measured by X‐Ray Standing Waves and Streaming Current

Measurements of ion distributions at a charged solid–liquid interface using X‐ray standing waves (XSW) are presented. High energy synchrotron radiation (17.48 keV) is used to produce an XSW pattern inside a thin water film on a silicon wafer. The liquid phase is an aqueous solution containing Br and Rb ions. The surface charge is adjusted by titration. Measurements are performed over a pH range from 2.2–9, using the native Si oxide layer and functional (amine) groups as surface charge. The Debye length, indicating the extension of the diffuse layer, could be measured with values varying between 1–4 nm. For functionalized wafers, the pH dependent change from attraction to repulsion of an ion species could be detected, indicating the isoelectric point. In combination with the measurement of the streaming current, the surface charge of the sample could be quantified.     

Liquid friction on charged surfaces: from hydrodynamic slippage to electrokinetics

Hydrodynamic behavior at the vicinity of a confining wall is closely related to the friction properties of the liquid/solid interface. Here we consider, using molecular dynamics simulations, the electric contribution to friction for charged surfaces, and the induced modification of the hydrodynamic boundary condition at the confining boundary. The consequences of liquid slippage for electrokinetic phenomena, through the coupling between hydrodynamics and electrostatics within the electric double layer, are explored. Strong amplification of electro-osmotic effects is revealed, and the nontrivial effect of surface charge is discussed. This work allows us to reconsider existing experimental data, concerning zeta potentials of hydrophobic surfaces and suggests the possibility to generate "giant" electro-osmotic and electrophoretic effects, with direct applications in microfluidics.     

DC-electrokinetic motion of colloidal cylinder(s) in the vicinity of a conducting wall

The boundary effects on DC-electrokinetic behavior of colloidal cylinder(s) in the vicinity of a conducting wall is investigated through a computational model. The contribution of the hydrodynamic drag, gravity, electrokinetic (i.e., electrophoretic and dielectrophoretic), and colloidal forces (i.e., forces due to the electrical double layer and van der Waals interactions) are incorporated in the model. The contribution of electrokinetic and colloidal forces are included by introducing the resulting forces as an external force acting on the particle(s). The colloidal forces are implemented with the prescribed expressions from the literature, and the electrokinetic force is obtained by integrating the corresponding Maxwell stress tensor over the particles' surfaces. The electrokinetic slip-velocity together with the thin electrical double layer assumption is applied on the surfaces. The position and velocity of the particles and the resulting electric and flow fields are obtained and the physical insight for the behavior of the colloidal cylinders are discussed in conjunction with the experimental observations in the literature.     

Structure formation due to antagonistic salts

Antagonistic salts are composed of hydrophilic and hydrophobic ions. In a mixture solvent (water–oil) such ion pairs are preferentially attracted to water or oil, giving rise to a coupling between the charge density and the composition. First, they form a large electric double layer at a water–oil interface, reducing the surface tension and producing mesophases. Here, the cations and anions are loosely bound by the Coulomb attraction across the interface on the scale of the Debye screening length. Second, on solid surfaces, hydrophilic (hydrophobic) ions are trapped in a water-rich (oil-rich) adsorption layer, while those of the other species are expelled from the layer. This yields a solvation mechanism of local charge separation near a solid. In particular, near the solvent criticality, disturbances around solid surfaces can become oscillatory in space. In mesophases, we calculate periodic structures, which resemble those in experiments.     

Ionic Diffusivity, Electrical Conductivity, Membrane and Thermoelectric Potentials in Colloids and Granular Porous Media: A Unified Model

Ionic diffusivity, electrical conductivity, membrane and thermoelectric potentials in isotropic and homogeneous colloidal suspensions, and granular porous media saturated by a binary symmetric 1:1 electrolyte are four interrelated phenomena. The microstructure and the surface properties of the solid grains-water interface influence directly these properties. The ionic diffusivities (and the electrical conductivity, respectively) in colloids and porous media have contributions from diffusion (and electromigration, respectively) through the bulk solution occupying the pores, together with electromigration occurring at the grains-water interface in the electrical double layer. Surface diffusion in porous materials has no contribution from concentration gradients along the grains-water interface. Instead, surface diffusion is envisioned as a purely electromigration process due to the membrane potential. The tortuosities of the transport of anions and cations are equal to the bulk tortuosity of the pore space only at high ionic strength. As the ionic strength decreases, the dominant paths for transport of the ion corresponding to the counterion of the electrical double layer shift from the pore space to the solid grains-water interface. Because anions and cations do not move independently, the membrane potential created by the charge polarization alters the velocity of the anions and influences the mutual diffusivity coefficient of the salt in the porous material. An electric potential of thermal origin is also produced in nonisothermal conditions. The ionic contributions to the electrical conductivity are based on a differential effective medium approach. These ionic contributions to the electrical conductivity are used to derive the ionic diffusivities and the membrane and thermoelectric potentials. The influence of the temperature and the presence, in the pore space, of a second immiscible and nonwetting phase is also considered in this model. Porosity is shown to affect the membrane potential. Several predictions of the model are checked with success by comparing the model to a set of experimental data previously published. Copyright 1999 Academic Press.     

Supercapacitive Swing Adsorption of Carbon Dioxide

An electrical effect, the supercapacitive swing adsorption (SSA) effect is reported, which allows for reversible adsorption and desorption of carbon dioxide by capacitive charge and discharge of electrically conducting porous carbon materials. The SSA effect can be observed when an electrically conducting, nanoporous carbon material is brought into contact with carbon dioxide gas and an aqueous electrolyte. Charging the supercapacitor electrodes initiates the spontaneous organization of electrolyte ions into an electric double layer at the surface of each porous electrode. The presence of this double layer leads to reversible, selective uptake and release of the CO₂ as the supercapacitor is charged and discharged.     

Two-fluid electroosmotic flow in microchannels

This paper presents a mathematical model to describe a two-fluid electroosmotic pumping technique, in which an electrically non-conducting fluid is delivered by the interfacial viscous force of a conducting fluid; the latter is driven by electroosmosis. The electrical potential in the conducting fluid and the analytical solution of the steady two-fluid electroosmotic stratified flow in a rectangular microchannel was presented by assuming a planar interface between the two immiscible fluids. The effects of viscosity ratio, hold-up, concentration, and interfacial zeta potential are analyzed to show the potential feasibility of this technique.     

Complex Ohmic conductance of electrolytes in rectangular microchannels

Motivated by the interest that microelectrolytic systems are gaining in the development of the so-called lab-on-a-chip systems, i.e., miniature microfluidic devices for biochemical analysis, we present an analytical study of Ohmic conduction in rectangular charged microchannels filled with electrolytic solution. The study complements a previous one [M. Campisi et al., J. Chem. Phys. 123, 204724 (2005)], concerning ac electro-osmosis. The problem is framed within the theory of nonequilibrium thermodynamics and is based on the solution of the incompressible Navier-Stokes equation with an electrical body force due to the interaction of the applied electric field with the charged electric double layer (EDL) which forms at the solid-liquid interface. We analyze in detail the dependence of the system complex conductance on the ratio linear dimensions over Debye length with an eye on finite EDL effects, and compare its scaling properties with those of electrokinetic and hydraulic complex conductances.     

Electroosmotic transport of immiscible binary system with a layer of non‐conducting fluid under interfacial slip: The role applied pressure gradient

We investigate the transport of immiscible binary fluid layers, constituted by one conducting (top layer fluid) and another non‐conducting (bottom layer fluid) fluids in a microfluidic channel under the combined influences of an applied pressure gradient and imposed electric field. We solve the transport equation governing the flow dynamics analytically and obtain the closed‐form expressions of the velocity fields. We bring out the alteration in the flow dynamics, mainly attributable to the non‐linear interaction between interfacial slip and the electrical double layer effect over small scales as modulated by the applied pressure gradient. In particular, we show the augmentation in the net volume transport rate through the channel, emerging from an intricate competition among electrical forcing, applied pressure gradient and the viscous resistance as modulated by the interfacial slip. We believe that the results of this study may be of immense consequence for the design of various microfluidic devises, which are often used for the manipulation of two immiscible fluids in different biomedical/biochemical processes.     

Dielectric analysis of macroporous anion-exchange resin beads suspensions

Dielectric measurements were carried out for suspensions of D354 anion-exchange beads dispersed in electrolyte solutions at different concentrations, and distinct Maxwell-Wagner dielectric relaxations were observed around 10(6) Hz. Through fitting the experimental data we obtained the dielectric parameters of the suspensions, and then we calculated the phase parameters from the dielectric parameters and the measured volume fractions by Hanai's method. In light of the present understanding of the interfacial properties, and with the information obtained from the phase parameters, we satisfactorily interpreted the concentration dependences of the dielectric parameters. It is concluded that Hanai's method is an effective tool for obtaining the properties of dispersed particles; the properties of the electrical double layer, which are mainly decided by the properties of the electrolyte solution, predict the dielectric behavior of suspensions with conducting particles. The dielectric relaxation spectroscopy (DRS), based on the M-W mechanism, is also a very sensitive tool for probing the properties of the liquid/solid interface.     

Modeling electrokinetics in ionic liquids

Using direct numerical simulations, we provide a thorough study regarding the electrokinetics of ionic liquids. In particular, modified Poisson–Nernst–Planck equations are solved to capture the crowding and overscreening effects characteristic of an ionic liquid. For modeling electrokinetic flows in an ionic liquid, the modified Poisson‐Nernst‐Planck equations are coupled with Navier–Stokes equations to study the coupling of ion transport, hydrodynamics, and electrostatic forces. Specifically, we consider the ion transport between two parallel charged surfaces, charging dynamics in a nanopore, capacitance of electric double‐layer capacitors, electroosmotic flow in a nanochannel, electroconvective instability on a plane ion‐selective surface, and electroconvective flow on a curved ion‐selective surface. We also discuss how crowding and overscreening and their interplay affect the electrokinetic behaviors of ionic liquids in these application problems.     

Improved theory of cyclical electrical field flow fractionation

Previously reported theories for cyclical electrical field flow fractionation (CyElFFF) are severely limited in that they do not account for diffusion, steric, or electric double layer effects. Experiments have shown that these theories overpredict the retention of particles in CyElFFF. In this work, we present a model for prediction of steric, diffusion, and electrical effects. The electrical double layer effects are treated using a lumped electrical circuit model that accounts for the field shielding by the electrical double layer formed at the electrode-carrier interface. The electrical effects are shown to dominate retention times and outweigh the contributions of diffusion and particle size. Detailed results from the simulations are presented in this work, and a comparison between the theoretical and experimental results obtained from the retentions of polystyrene particle standards is presented in this paper. The models are shown to correctly predict the retention of the polystyrene standards in CyElFFF with a reasonable error, while existing models are shown to have significant failings.     

A singlet reference interation site model theory for solid/liquid interfaces Part II: Electrical double layers

The previously established singlet reference interaction site model (SRISM) theory for the calculation of the fluid structure in the vicinity of a plane impenetrable interface is renormalized for the application to electrical double layers. In combination with the HNC and KH closures, the equations are solved numerically for a 1 M electrolyte solution adjacent to a charged wall with varying surface charge densities. The wall-solvent and wall-ion density distributions as well as the profiles of the electrical field and the electrical potential are compared to computer simulation results. Reasonable agreement is obtained.