Electro-osmotically induced convection at a permselective membrane

Effect of concentration polarization on permselectivity

In this paper, the variation of permselectivity in the course of concentration polarization is systematically analyzed for a three-layer membrane system consisting of a nonperfectly permselective ion exchange membrane, homogeneous or heterogeneous, flanked by two diffusion layers of a binary univalent electrolyte. For a heterogeneous membrane, an ionic transport model is proposed, which is amenable to analytical treatment. In this model, assuming a constant fixed charge in the membrane and disregarding water splitting, the entire transport problem is reduced to solution of a single algebraic equation for the counterion transport number. It is concluded that for both types of membrane the concentration polarization may significantly affect the permselectivity of the system through the effects of the induced nonuniformity of the coion diffusion flux in the membrane (convexity of the coion concentration profile) and varying membrane-solution interface concentration. While the former is significant for low membrane fixed charge density, for a heterogeneous membrane, the latter might be considerably affected by the flux focusing effect at the permeable membrane segments.

Hydrodynamic flow in the vicinity of a nanopore induced by an applied voltage

Continuum simulation is employed to study ion transport and fluid flow through a nanopore in a solid-state membrane under an applied potential drop. The results show the existence of concentration polarization layers on the surfaces of the membrane. The nonuniformity of the ionic distribution gives rise to an electric pressure that drives vortical motion in the fluid. There is also a net hydrodynamic flow through the nanopore due to an asymmetry induced by the membrane surface charge. The qualitative behavior is similar to that observed in a previous study using molecular dynamic simulations. The current-voltage characteristics show some nonlinear features but are not greatly affected by the hydrodynamic flow in the parameter regime studied. In the limit of thin Debye layers, the electric resistance of the system can be characterized using an equivalent circuit with lumped parameters. Generation of vorticity can be understood qualitatively from elementary considerations of the Maxwell stresses. However, the flow strength is a strongly nonlinear function of the applied field. Combination of electrophoretic and hydrodynamic effects can lead to ion selectivity in terms of valences and this could have some practical applications in separations.

Laser interferometry analysis of ciprofloxacin and ampicillin diffusion from liposomal solutions to water phase

The paper presents experimental investigations of diffusion of antibiotics (ciprofloxacin or ampicillin) into the water phase from mixtures of neutral or negatively charged liposomes, and antibiotic-liposome interactions. Using the laser interferometry technique, the amounts and fluxes of released antibiotics, concentration field evolution, and the velocity of the concentration boundary layer's "growth" were determined. To avoid the limitations of membranes, a measurement system without the artificial boundary of phases with a free water-solution interface has been proposed. It was found that the diffusion of anionic and neutral liposomes into the water phase was insignificant and mainly the diffusion of antibiotics was measured. Differences in the diffusion kinetics of ciprofloxacin and ampicillin from liposomal solutions to the water phase were observed. Ampicillin diffused more efficiently than ciprofloxacin regardless of the liposomal solution type. Moreover, the amount of ampicillin and ciprofloxacin released from the anionic liposomal phase was higher than that from the neutral one. Our results confirm that ciprofloxacin at neutral pH shows little tendency to bind neutral liposomes. Additionally, it was also observed that ciprofloxacin disrupts negatively charged liposomes as a final effect of antibiotic-lipid interactions.

Shear flow of an electrically charged fluid by ion concentration polarization: scaling laws for electroconvective vortices

We consider electroconvective fluid flows initiated by ion concentration polarization (ICP) under pressure-driven shear flow, a scenario often found in many electrochemical devices and systems. Combining scaling analysis, experiment, and numerical modeling, we reveal unique behaviors of ICP under shear flow: a unidirectional vortex structure, its height selection, and vortex advection. Determined by both the external pressure gradient and the electric body force, the dimensionless height of the sheared electroconvective vortex is shown to scale as (ϕ(2)/U(HP))(1/3), which is a clear departure from the previous diffusion-drift model prediction. To the best of our knowledge, this is the first microscopic characterization of ion concentration polarization under shear flow, and it firmly establishes electroconvection as the mechanism for an overlimiting current in realistic, large-area ion exchange membrane systems such as electrodialysis. The new scaling law has significant implications on the optimization of electrodialysis and other electrochemical systems.

Multi-vortical flow inducing electrokinetic instability in ion concentration polarization layer

In this work, we investigated multiple vortical flows inside the ion concentration polarization (ICP) layer that forms due to a coupling of applied electric fields and the semipermeable nanoporous junction between microchannels. While only a primary vortex near perm-selective membrane is traditionally known to lead to electrokinetic instability, multiple vortexes induced by the primary vortex were found to play a major role in the electrokinetic instability. The existence of multiple vortexes was directly confirmed by experiments using particle tracers and interdigitated electrodes were used to measure the local concentration profile inside the ICP layer. At larger applied electric fields, we observed aperiodic fluid motion due to electrokinetic instabilities which develop from a coupling of applied electric fields and electrical conductivity gradients induced by the ICP. The electrokinetic instability at micro-nanofluidic interfaces is important in the development of various electro-chemical-mechanical applications such as fuel cells, bio-analytical preconcentration methods, water purification/desalination and the fundamental study of ion electromigration through nanochannels and nonporous perm-selective membranes.

Role of electro-osmosis in the impedance response of microchannel-nanochannel interfaces

The influence of net fluid flow on the low-frequency ac response of a microchannel-nanochannel interface under dc bias is studied theoretically using a simple 1D model based on the Poisson-Nernst-Planck-Stokes equations. The model describes cross-sectional averaged transport wherein the electro-osmotic flow is controlled by the magnitude of the dc bias and captures essential features of the problem related to the micro-nano interface, specifically geometric focusing effects and nanochannel control of the net fluid flow. This model predicts behavior which differs from that predicted by a purely electrodiffusive formulation. The high-frequency edge of the Warburg branch of the complex impedance plot has a slope which deviates from the π/4 Warburg value, decreasing with increasing bias, and there are corresponding changes in the overall phase as seen in the Bode plots. This can be attributed to a streaming contribution to the capacitive reactance of the device as well an increase in the conductance of the depleted region, both due to net fluid flow. The increase in conductance, corresponding to reduced interfacial depletion, also permits dc currents above the classical electrodiffusive limit.

Direct numerical simulation of electroconvective instability and hysteretic current-voltage response of a permselective membrane

We present a systematic, multiscale, fully detailed numerical modeling for dynamics of fluid flow and ion transport covering Ohmic, limiting, and overlimiting current regimes in conductance of ion-selective membrane. By numerically solving the Poisson-Nernst-Planck-Navier-Stokes equations, it is demonstrated that the electroconvective instability, arising from the electric field acting upon the extended space charge layer, and the induced strong vortical fluid flow are the dominant factors of the overlimiting current in the planar membrane system. More importantly, at the transition between the limiting and the overlimiting current regimes, hysteresis of electric current is identified. The hysteresis demonstrates the important role of the electroconvective flow in enhancing of current in electrolyte systems with ion-selective membrane.

Competition between Dukhin's and Rubinstein's electrokinetic modes

The combined effect of two modes of electroconvection, i.e., (a) the electro-osmotic flow of the second kind induced by a curved membrane surface and (b) electrokinetic instability, is studied numerically. Both physical mechanisms are responsible for electric current enhancement to the surface, and these modes are strongly nonlinearly coupled. For the limiting regimes, their resonant interaction near the threshold of instability with a corresponding resonantly amplified current enhancement is found. For the overlimiting regimes, inside the unstable region, their interaction becomes more complex with negative "sideband" and positive "subharmonic" resonant interactions. Wall corrugation can still be in resonance with the unstable modes. At some wave numbers of corrugation, these two mechanisms compete and electrokinetic instability can even be completely suppressed by the wall corrugation.

Current-induced membrane discharge

Possible mechanisms for overlimiting current (OLC) through aqueous ion-exchange membranes (exceeding diffusion limitation) have been debated for half a century. Flows consistent with electro-osmotic instability have recently been observed in microfluidic experiments, but the existing theory neglects chemical effects and remains to be quantitatively tested. Here, we show that charge regulation and water self-ionization can lead to OLC by "current-induced membrane discharge" (CIMD), even in the absence of fluid flow, in ion-exchange membranes much thicker than the local Debye screening length. Salt depletion leads to a large electric field resulting in a local pH shift within the membrane with the effect that the membrane discharges and loses its ion selectivity. Since salt co-ions, H(+) ions, and OH(-) ions contribute to OLC, CIMD interferes with electrodialysis (salt counterion removal) but could be exploited for current-assisted ion exchange and pH control. CIMD also suppresses the extended space charge that leads to electro-osmotic instability, so it should be reconsidered in both models and experiments on OLC.

Ion concentration polarization near microchannel-nanochannel interfaces: effect of pH value

This study investigates the effect of the pH value on the ion concentration polarization phenomenon and the nonlinear current-voltage characteristics of a hybrid soda-lime glass micro/nanochannel for a constant KCl salt concentration of about 1 mM. The experimental results show that the electrical conductance of the nanochannel in the Ohmic regime and the critical threshold voltage of the limiting current are both dependent on the pH value of the salt solution when the electrical double layer thickness is considerable in the nanochannel. Specifically, the nanochannel conductance increases and the critical threshold voltage for the limiting current decreases as the pH value is increased. It also suggests that a higher pH value induces a higher surface charge density on the nanochannel walls, and therefore increases both the ionic conductance and the counter-ion flux within the nanochannel.

Electrokinetic instability in microchannels

The effect of geometric confinement on electroconvective instability due to nonequilibrium electro-osmotic slip at the interface of an electrolytic fluid and charge-selective solid is studied. It is shown that the topology of the marginal stability curves and the behavior of the critical parameters depend strongly on both channel geometry and dimensionless Debye length at low voltages for sufficiently deep channels, corresponding to the Rubinstein-Zaltzman instability mechanism, but that stability is governed almost entirely by channel depth for narrow channels at higher voltages. For shallow channels, it is shown that above a transition threshold, determined by both channel depth and Debye length, the low-voltage instability is completely suppressed.

Numerical study on the bulk instability of constant-current conduction in cation-exchange membranes

Numerical simulation of two-dimensional bulk instability of the one-dimensional conduction state in an electrolyte confined between a pair of cation-exchange membranes subjected to an external voltage is conducted under an assumption of constant current. By employing variable grids, we resolve the problem of sensitive dependence of the numerical solutions to the grid refinement in particular at a current close to the limiting value. In fact, the full range of parameters, i.e., Schmidt number, Peclet number, diffusivity ratio, and current, is considered in this study in obtaining the stability chart. It turns out that the Schmidt number exerts almost no influence on the results. From the neutral curves in the chart of the parameter space (current versus diffusivity ratio, i.e., cation diffusivity divided by anion diffusivity) we confirm that the system tends to be unstable at high Peclet numbers, high currents, and low diffusivity ratios. As the diffusivity ratio is increased the instability mode switches from the monotonic to the oscillatory type, and the critical diffusivity ratio for the switching is found to be decreased as the Peclet number decreases. At the switching, no jump in the neutral curves is found, contrary to the earlier result, because the wave number is set free to change in this study. The stability chart obtained in this study represents the true boundaries in discriminating the stable from the unstable parameter sets because the critical eigenvalues constituting the chart are sought for the entire possible range of the wave numbers and the frequencies.

Evolution with time of hydrophobicity and microrelief of a cation-exchange membrane surface and its impact on overlimiting mass transfer

Surface properties were measured together with electrochemical characteristics of a CMX (Neosepta, Tokuyama Corp.) cation-exchange membrane. Relative hydrophobicity was controlled by the contact angle; XPS and SEM were used for characterizing chemical composition and microrelief of the surface, respectively. Voltammetry, chronopotentiometry, and mass transfer rate measurements were made as well. A "fresh" membrane and samples after 10, 25, 100, and 150 h of operation in an electrodialysis cell at an overlimiting current equal to 3 theoretical limiting currents, in a 0.02 M NaCl solution, were characterized. Some electrochemical properties were also measured for a Neosepta cation-exchange membrane, aged 2 years, in an industrial food process. It was found that the hydrophobicity of the CMX membrane has increased after the first 10 h of operation; more and more cavities of the dimension of the order of 1 μm have appeared with time testifying electrochemical erosion of the surface. The limiting current density (i(lim)) and the overlimiting transfer rate through the CMX membrane increased with time of its operation under overlimiting current. In the case of new CMX, i(lim) was very close to the theoretical value i(lim)(theor) calculated by the Lévêque equation. After 10 h of operation, i(lim) increased by 5%, and after 25, 100, and 150 h, the increase was by 30%, 70%, and 100%, respectively. Similarly, the mass transfer rate was found to increase up to 5 times (when desalting 0.005 M NaCl under 3 V) in comparison with the theoretical value. The ensemble of data was explained by the hypothesis that the passage of intensive current produces erosion of the ion-exchange polymer forming a continuous phase in CMX. This erosion results in exposure at the surface of the other constituent of CMX: small (about 100 nm) particles of relatively hydrophobic polyvinylchloride. Increasing surface hydrophobicity facilitates the slip of electroconvective vortexes along the surface. Besides, the geometry of the cavities gives rise to appearing tangential electric force applied to the extended space charge density at cavity's walls. As the local limiting current density within a cavity is lower than at the flat surface, electroconvective vortices arise at current densities lower than i(lim)(theor). With time, the number and the size of cavities increase (apparently, due to paired electroconvective vortices occurring inside them) that seems the main reason for overlimiting transfer increase.

Enhancing Ion Transfer in Overlimiting Electrodialysis of Dilute Solutions by Modifying the Surface of Heterogeneous Ion-Exchange Membranes

The desalination of dilute NaCl solutions with heterogeneous Russian commercial and modified ion-exchange membranes was studied in a laboratory cell imitating desalination channels of large-scale electrodialysers. The modification was made by casting a thin film of a Nafion-type material on the surface of cation-exchange membrane, and by processing with a strong polyelectrolyte the surface of anion-exchange membrane. It was shown that the modifications resulted in an increase of mass transfer coefficient and in a decrease in water splitting rate, both by up to 2 times. The effect of mass transfer growth is explained by higher surface hydrophobicity of the modified membrane that enhances electroconvection. The decrease in water splitting rate in the case of cation-exchange membrane is due to homogenization of its surface layer. In the case of anion-exchange membrane the effect is due to grafting of quaternary ammonium bases onto the original membrane surface layer. The suppression of water splitting favors development of electroconvection. In turn, intensive electroconvection contributes to deliver salt ions to membrane surface and thus reduces water splitting.

Deionization shocks in microstructures

Salt transport in bulk electrolytes is limited by diffusion and advection, but in microstructures with charged surfaces (e.g., microfluidic devices, porous media, soils, or biological tissues) surface conduction and electro-osmotic flow also contribute to ionic fluxes. For small applied voltages, these effects lead to well known linear electrokinetic phenomena. In this paper, we predict some surprising nonlinear dynamics that can result from the competition between bulk and interfacial transport at higher voltages. When counterions are selectively removed by a membrane or electrode, a "deionization shock" can propagate through the microstructure, leaving in its wake an ultrapure solution, nearly devoid of coions and colloidal impurities. We elucidate the basic physics of deionization shocks and develop a mathematical theory of their existence, structure, and stability, allowing for slow variations in surface charge or channel geometry. Via asymptotic approximations and similarity solutions, we show that deionization shocks accelerate and sharpen in narrowing channels, while they decelerate and weaken, and sometimes disappear, in widening channels. These phenomena may find applications in separations (deionization, decontamination, biological assays) and energy storage (batteries, supercapacitors) involving electrolytes in microstructures.

Overlimiting current in a microchannel

We revisit the classical problem of diffusion-limited ion transport to a membrane (or electrode) by considering the effects of charged sidewalls. Using simple mathematical models and numerical simulations, we identify three basic mechanisms for overlimiting current in a microchannel: (i) surface conduction carried by excess counterions, which dominates for very thin channels, (ii) convection by electro-osmotic flow on the sidewalls, which dominates for thicker channels, and (iii) transitions to electro-osmotic instability on the membrane end in very thick channels. These intriguing electrokinetic phenomena may find applications in biological separations, water desalination, and electrochemical energy storage.

Linear and nonlinear evolution and diffusion layer selection in electrokinetic instability

In the present work, four nontrivial stages of electrokinetic instability are identified by direct numerical simulation (DNS) of the full Nernst-Planck-Poisson-Stokes system: (i) a stage of the influence of the initial conditions (milliseconds); (ii) one-dimensional (1D) self-similar evolution (milliseconds-seconds); (iii) a primary instability of the self-similar solution (seconds); (iv) a nonlinear stage with secondary instabilities. The self-similar character of evolution at moderately large times is confirmed. Rubinstein and Zaltzman instability and noise-driven nonlinear evolution toward overlimiting regimes in ion-exchange membranes are numerically simulated and compared with theoretical and experimental predictions. The primary instability which happens during this stage is found to arrest a self-similar growth of the diffusion layer. It also specifies its characteristic length as was first experimentally predicted by Yossifon and Chang [G. Yossifon and H.-C. Chang, Phys. Rev. Lett. 101, 254501 (2008)]. A novel principle for the characteristic wave-number selection from the broadband initial noise is established.

Intensive current transfer in membrane systems: modelling, mechanisms and application in electrodialysis

Usually in electrochemical systems, the direct current densities not exceeding the limiting current density are applied. However, the recent practice of electrodialysis evidences the interest of other current modes where either the imposed direct current is over the limiting one or a non-constant asymmetrical (such as pulsed) current is used. The paper is devoted to make the mechanisms of mass transfer under these current regimes more clear. The theoretical background for mathematical modelling of mass transfer at overlimiting currents is described. Four effects providing overlimiting current conductance are examined. Two of them are related to water splitting: the appearance of additional charge carriers (H(+) and OH(-) ions) and exaltation effect. Two others are due to coupled convection partially destroying the diffusion boundary layer: gravitational convection and electroconvection. These effects result from formation of concentration gradients (known as concentration polarization) caused by the current flowing under conditions where ionic transport numbers are different in the membrane and solution. Similar effects take place not only in electrodialysis membrane systems, but in electrode ones, in electrophoresis and electrokinetic micro- and nanofluidic devices such as micropumps. The relation of these effects to the properties of the membrane surface (the chemical nature of the fixed groups, the degree of heterogeneity and hydrophobicity, and the geometrical shape of the surface) is analyzed. The interaction between the coupled effects is studied, and the conditions under which one or another effect becomes dominant are discussed. The application of intensive current modes in electrodialysis, the state-of-the-art and perspectives, are considered. It is shown that the intensive current modes are compatible with new trends in water treatment oriented towards Zero Liquid Discharge (ZLD) technologies. The main idea of these hybrid schemes including pressure- and electro-driven processes as well as conventional methods is to provide the precipitation of hardness salts before the membrane modules and that of well dissolved salts after.

Concentration polarization of interface and non-linear electrokinetic phenomena

The review addresses the peculiarities of concentration polarization caused by an electric current passing through conducting and around nonconducting charged materials. The conditions of emergence of an induced space charge of large density and thickness behind an electrical double layer, leading to strong non-linearity of electroosmosis and electrophoresis, are analyzed. Basic findings about concentration polarization, its theoretical modeling and experimental investigations, as well as its influence on electrokinetic phenomena and mass transfer through ion-exchange materials are discussed from the point of view of the fundamental knowledge about polarization processes and from the perspective of their practical application. The analysis focuses on the main properties of concentration polarization, electroosmotic flow of liquid around single fixed particles and through the system of particles, and electrophoresis of particles suspended in aqueous medium and current through flat, spherical and cylindrical interfaces and membranes with heterogeneous conductivity. The paper also presents the general ideas of concentration polarization and non-linear electrokinetic phenomena in case of nonconducting particles and their dependence on particle surface electroconductivity. Existing theoretical models describing polarization of nonconducting particles at high and low Peclet numbers are analyzed, with appropriate experimental data being provided to validate the theory. A joint analysis of polarization of conducting and nonconducting particles completes the review.

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.

Strongly nonlinear dynamics of electrolytes in large ac voltages

We study the response of a model microelectrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes, ignoring any transverse instability or fluid flow. We analyze the resulting one-dimensional problem by matched asymptotic expansions in the limit of thin double layers and extend previous work into the strongly nonlinear regime, which is characterized by two features--significant salt depletion in the electrolyte near the electrodes and, at very large voltage, the breakdown of the quasiequilibrium structure of the double layers. The former leads to the prediction of "ac capacitive desalination" since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion layers. The latter is associated with transient diffusion limitation, which drives the formation and collapse of space-charge layers, even in the absence of any net Faradaic current through the cell. We also predict that steric effects of finite ion sizes (going beyond dilute-solution theory) act to suppress the strongly nonlinear regime in the limit of concentrated electrolytes, ionic liquids, and molten salts. Beyond the model problem, our reduced equations for thin double layers, based on uniformly valid matched asymptotic expansions, provide a useful mathematical framework to describe additional nonlinear responses to large ac voltages, such as Faradaic reactions, electro-osmotic instabilities, and induced-charge electrokinetic phenomena.

Changing nanoslot ion flux with a dynamic nanocolloid ion-selective filter: secondary overlimiting currents due to nanocolloid-nanoslot interaction

Nanocolloids trapped at the depleted side (anodic) of a fluidic nanoslot entrance are shown to sensitively regulate dc ion transport through the nanoslot, such that a second limiting-overlimiting transition occurs in its nonlinear current-voltage characteristics. The nanocolloids, brought to the entrance by electro-osmosis, are not stationary but are confined to closed circular and toroidal streamlines, driven by a back-pressure corner vortex and an orthogonal electroconvection vortex instability. The transition from the corner vortex to a complex torus with both vortical motions coincides with the first overlimiting transition, while electrostatic interaction of nanocolloids in these vortices with the nanoslot entrance drives the second limiting transition.

Dynamics of 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 nanochannels in a microfluidic system. 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, superfast vortexes near an ion-exchange granule, overlimiting conductance in electrodialysis and the recently observed nonequilibrium electro-osmotic instability, result from formation of an additional extended space charge layer next to that of a classical electrical double layer at the solid/liquid interface or, rather, from the peculiar features of the extended space charge distinguishing it from that of a common diffuse electrical double layer. In this paper we discuss the nature and origin of the extended space charge and analyze its peculiar steady state and time-dependent properties important for understanding nonequilibrium electrokinetic phenomena in ionic systems.

Eliminating the limiting-current phenomenon by geometric field focusing into nanopores and nanoslots

A peculiar and undesirable current-voltage characteristic of nanoporous membranes is that it exhibits a voltage window with a near-constant limiting-current density when bulk ions near one surface of the membrane are depleted. We show both theoretically and experimentally that this interval disappears for an isolated circular nanopore (or narrow nanoslot) because radial field focusing at the pore entrance enhances the depletion effect and drives an ejecting hydrodynamic vortex pair that amplifies ion flux into the nanopore. This vortex pair is distinct from the vortex arrays that appear in front of a wide nanoslot or a nanoporous membrane with small inter-nanopore separation. It hence suggests that an optimal pore radius/separation ratio exists for maximum current density across a membrane.

Nanofluidic concentration devices for biomolecules utilizing ion concentration polarization: theory, fabrication, and applications

Recently, a new type of electrokinetic concentration devices has been developed in a microfluidic chip format, which allows efficient trapping and concentration of biomolecules by utilizing ion concentration polarization near nanofluidic structures. These devices have drawn much attention not only due to their potential application in biomolecule sensing, but also due to the rich scientific content related to ion concentration polarization, the underlying physical phenomenon for the operation of these electrokinetic concentration devices. This tutorial review provides an introduction to the scientific and engineering advances achieved, in-depth discussion about several interesting applications of these unique concentration devices, and their current limitations and challenges.

Stabilization of ion concentration polarization using a heterogeneous nanoporous junction

We demonstrate a recycled ion-flux through heterogeneous nanoporous junctions, which induce stable ion concentration polarization with an electric field. The nanoporous junctions are based on integration of ionic hydrogels whose surfaces are negatively or positively charged for cationic or anionic selectivity, respectively. Such heterogeneous junctions can be matched up in a way to achieve continuous ion-flux operation for stable concentration gradient or ionic conductance. Furthermore, the combined junctions can be used to accumulate ions on a specific region of the device.

Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions

The venerable theory of electrokinetic phenomena rests on the hypothesis of a dilute solution of point-like ions in quasi-equilibrium with a weakly charged surface, whose potential relative to the bulk is of order the thermal voltage (kT/e approximately 25 mV at room temperature). In nonlinear electrokinetic phenomena, such as AC or induced-charge electro-osmosis (ACEO, ICEO) and induced-charge electrophoresis (ICEP), several V approximately 100 kT/e are applied to polarizable surfaces in microscopic geometries, and the resulting electric fields and induced surface charges are large enough to violate the assumptions of the classical theory. In this article, we review the experimental and theoretical literatures, highlight discrepancies between theory and experiment, introduce possible modifications of the theory, and analyze their consequences. We argue that, in response to a large applied voltage, the "compact layer" and "shear plane" effectively advance into the liquid, due to the crowding of counterions. Using simple continuum models, we predict two general trends at large voltages: (i) ionic crowding against a blocking surface expands the diffuse double layer and thus decreases its differential capacitance, and (ii) a charge-induced viscosity increase near the surface reduces the electro-osmotic mobility; each trend is enhanced by dielectric saturation. The first effect is able to predict high-frequency flow reversal in ACEO pumps, while the second may explain the decay of ICEO flow with increasing salt concentration. Through several colloidal examples, such as ICEP of an uncharged metal sphere in an asymmetric electrolyte, we show that nonlinear electrokinetic phenomena are generally ion-specific. Similar theoretical issues arise in nanofluidics (due to confinement) and ionic liquids (due to the lack of solvent), so the paper concludes with a general framework of modified electrokinetic equations for finite-sized ions.

Asymptotic current-voltage relations for currents exceeding the diffusion limit

We consider the one-dimensional transport of ions into a perm-selective solid. Direct attempts to evaluate the current-voltage characteristics for currents exceeding the diffusion limit are frustrated by the appearance of nonconverging integrals. We describe how to overcome this obstacle using a regularization scheme.