Electro-osmotically induced convection at a permselective membrane

On the Dynamical Regimes of Pattern-Accelerated Electroconvection

Recent research has established that electroconvection can enhance ion transport at polarized surfaces such as membranes and electrodes where it would otherwise be limited by diffusion. The onset of such overlimiting transport can be influenced by the surface topology of the ion selective membranes as well as inhomogeneities in their electrochemical properties. However, there is little knowledge regarding the mechanisms through which these surface variations promote transport. We use high-resolution direct numerical simulations to develop a comprehensive analysis of electroconvective flows generated by geometric patterns of impermeable stripes and investigate their potential to regularize electrokinetic instabilities. Counterintuitively, we find that reducing the permeable area of an ion exchange membrane, with appropriate patterning, increases the overall ion transport rate by up to 80%. In addition, we present analysis of nonpatterned membranes, and find a novel regime of electroconvection where a multivalued current is possible due to the coexistence of multiple convective states.

Fouling on ion-exchange membranes: Classification, characterization and strategies of prevention and control

The environmentally friendly ion-exchange membrane (IEM) processes find more and more applications in the modern industries in order to demineralize, concentrate and modify products. Moreover, these processes may be applied for the energy conversion and storage. However, the main drawback of the IEM processes is a formation of fouling, which significantly decreases the process efficiency and increases the process cost. The present review is dedicated to the problematic of IEM fouling phenomena. Firstly, the major types of IEM fouling such as colloidal fouling, organic fouling, scaling and biofouling are discussed along with consideration of the main factors affecting fouling formation and development. Secondly, the review of the possible methods of IEM fouling characterization is provided. This section includes the methods of fouling visualization and characterization as well as methods allowing investigations of characteristics of the fouled IEMs. Eventually, the reader will find the conventional and modern strategies of prevention and control of different fouling types.

Capillarity ion concentration polarization for spontaneous biomolecular preconcentration mechanism

Ionic hydrogel-based ion concentration polarization devices have been demonstrated as platforms to study nanoscale ion transport and to develop engineering applications, such as protein preconcentration and ionic diodes/transistors. Using a microfluidic system composed of a perm-selective hydrogel, we demonstrated a micro/nanofluidic device for the preconcentration of biological samples using a new class of ion concentration polarization mechanism called "capillarity ion concentration polarization" (CICP). Instead of an external electrical voltage source, the capillary force of the perm-selective hydrogel spontaneously generated an ion depletion zone in a microfluidic channel by selectively absorbing counter-ions in a sample solution. We demonstrated a reasonable preconcentration factor (∼100-fold/min) using the CICP device. Although the efficiency was lower than that of conventional electrokinetic ICP operation due to the absence of a drift ion migration, this mechanism was free from the undesirable instability caused by a local amplified electric field inside the ion depletion zone so that the mechanism should be suitable especially for an application where the contents were electrically sensitive. Therefore, this simple system would provide a point-of-care diagnostic device for which the sample volume is limited and a simplified sample handling is demanded.

Morphological instability during steady electrodeposition at overlimiting currents

We present a linear stability analysis of a planar metal electrode during steady electrodeposition. We extend the previous work of Sundstrom and Bark by accounting for the extended space-charge density, which develops at the cathode once the applied voltage exceeds a few thermal voltages. In accordance with Chazalviel's conjecture, the extended space-charge region is found to greatly affect the morphological stability of the electrode. To supplement the numerical solution of the stability problem, we have derived analytical expressions valid in the limit of low and high voltage, respectively.

Theory of the liquid film motor

The liquid film motor is a freely suspended liquid film placed between two capacitively coupled plates that rotates when an electric current is passed through it. Here we propose a theory for its rotation mechanism based on thin film electroconvection. The capacitively coupled plates induce free charges on the surfaces of the film, and the electric field on the film exerts a force that induces rotation. Results of the proposed theory and simulation are in good agreement with the experiments in different properties of the liquid film motor.

Asymmetry-induced electric current rectification in permselective systems

For a symmetric ion permselective system, in terms of geometry and bulk concentrations, the system response is also symmetric under opposite electric field polarity. In this work we derive an analytical solution for the concentration distribution, electric potential, and current-voltage response for a four-layered system comprised of two microchambers connected by two permselective regions of varying properties. It is shown that any additional asymmetry in the system, in terms of the geometry, bulk concentration, or surface charge property of the permselective regions, results in current rectification. Our work is divided into two parts: when both permselective regions have the same surface charge sign and the case of opposite signs. For the same sign case we are able to show that the system behaves as a dialytic battery while accounting for field-focusing effects. For the case of opposite signs (i.e., bipolar membrane), our system exhibits the behavior of a bipolar diode where the magnitude of the rectification can be of order 10^{2}-10^{3}.

Dynamics of microvortices induced by ion concentration polarization

We investigate the coupled dynamics of the local hydrodynamics and global electric response of an electrodialysis system, which consists of an electrolyte solution adjacent to a charge selective membrane under electric forcing. Under a dc electric current, counterions transport through the charged membrane while the passage of co-ions is restricted, thereby developing ion concentration polarization (ICP) or gradients. At sufficiently large currents, simultaneous measurements of voltage drop and flow field reveal several distinct dynamic regimes. Initially, the electrodialysis system displays a steady Ohmic voltage difference (ΔV_{ohm}), followed by a constant voltage jump (ΔV_{c}). Immediately after this voltage increase, microvortices set in and grow both in size and speed with time. After this growth, the resultant voltage levels off around a fixed value. The average vortex size and speed stabilize as well, while the individual vortices become unsteady and dynamic. These quantitative results reveal that microvortices set in with an excess voltage drop (above ΔV_{ohm}+ΔV_{c}) and sustain an approximately constant electrical conductivity, destroying the initial ICP with significantly low viscous dissipation.

Teorell instability in concentration polarization

We investigate the development of electro-osmotic (Teorell) oscillations at a weakly charged microporous membrane without a preimposed transmembrane electrolyte concentration drop. This drop, necessary for the occurrence of oscillations, develops spontaneously as a result of concentration polarization in the solution layers adjacent to the membrane. A three-layer model comprising a membrane flanked by two diffusion layers is proposed and analyzed for galvano- and potentiostatic regimes of operation.

Electroosmotic flow rectification in conical nanopores

Recent experimental work has suggested that electroosmotic flows (EOFs) through conical nanopores exhibit rectification in the opposite sense to the well-studied effect of ionic current rectification. A positive bias voltage generates large EOF and small current, while negative voltages generate small EOF and large current. Here we systematically investigate this effect using finite-element simulations. We find that inside the pore, the electric field and salt concentration are inversely correlated, which leads to the inverse relationship between the magnitudes of EOF and current. Rectification occurs when the pore is driven into states characterized by different salt concentrations depending on the sign of the voltage. The mechanism responsible for this behaviour is concentration polarization, which requires the pore to exhibit the properties of permselectivity and asymmetry.

Probing space charge and resolving overlimiting current mechanisms at the microchannel-nanochannel interface

We present results demonstrating the space charge-mediated transition between classical, diffusion-limited current and surface-conduction dominant over-limiting current in a shallow microchannel-nanochannel device. The extended space charge layer develops at the depleted microchannel-nanochannel entrance at high current and is correlated with a distinctive maximum in the dc resistance. Experimental results for a shallow surface-conduction dominated system are compared with theoretical models, allowing estimates of the effective surface charge at high voltage to be obtained. In comparison to an equilibrium estimate of the surface charge obtained from electrochemical impedance spectroscopy, it is further observed that the effective surface charge appears to change under applied voltage.

Extended space charge near nonideally selective membranes and nanochannels

We demonstrate the role of selectivity variation in the structure of the nonequilibrium extended space charge using one-dimensional analytic and two-dimensional numerical Poisson-Nernst-Planck models for the electro-diffusive transport of a symmetric electrolyte. This provides a deeper understanding of the underlying mechanism behind a previously observed maximum in the resistance-voltage curve for a shallow micro-nanochannel interface device [Schiffbauer, Liel, Leibowitz, Park, and Yossifon, arXiv:1409.4548, Phys. Rev. E (to be published)]. The current study helps to establish a connection between parameters such as the geometry and nanochannel surface charge and the control of selectivity and resistance in the overlimiting current regime.

Thermoelectroconvection near charge-selective surfaces

A new kind of instability caused by Joule heating near charge-selective surfaces (permselective membranes, electrodes, or systems of micro- and nanochannels) is investigated theoretically using a model based on the Rubinstein-Zaltzman approach. A simple relation is derived for the marginal stability curves: Joule heating can either destabilize or stabilize the steady state, depending on the location of the space charge region relative to the gravity vector. For the destabilizing case, the short-wave Rubinstein-Zaltzman instability is replaced by a long-wave thermal instability. The physical mechanism of the thermal instability is found to be very different from Rayleigh-Bénard convection, and is based on a nonuniform distribution of the electrical conductivity in the electrolyte. The study is complemented by numerical investigations both of linear and nonlinear instabilities near a charge-selective surface. There is a good qualitative agreement with the analytics. A possible explanation of the discrepancy between the experimental data and our previous theoretical voltage-current characteristics is highlighted.

Enhanced Ion Current Rectification in 2D Graphene-Based Nanofluidic Devices

Furthering the promise of graphene-based planar nanofluidic devices as flexible, robust, low cost, and facile large-scale alternatives to conventional nanochannels for ion transport, we show how the nonlinear current-voltage (I-V) characteristics and ion current rectification in these platforms can be enhanced by increasing the system asymmetry. Asymmetric cuts made to the 2D multilayered graphene oxide film, for example, introduces further asymmetry to that natively inherent in the structurally symmetric system, which was recently shown to be responsible for its rectification behavior due to diffusion boundary layer fore-aft asymmetry. Supported by good agreement with theory, we attribute the enhancement to the decrease in the limiting current in the positive bias state in which counter-ion trapping occurs within the negatively charged graphene oxide sheets due to increased film permselectivity as its cross-section and surface charge distribution is altered on one end; these effects being shown to be sensitive to the electrolyte pH. Further, we show that an imbalance in the pH or concentration in the microreservoirs flanking the film can also increase asymmetry and hence rectification, in addition to displaying a host of other phenomena associated with the I-V characteristics of typical nanochannel electrokinetic systems.

Flow characterization of electroconvective micromixer with a nanoporous polymer membrane in-situ fabricated using a laser polymerization technique

Electroconvection is known to cause strong convective mixing in a microchannel near a nanoporous membrane or a nanochannel in contact with an electrolyte solution due to the external electric field. This study addresses micromixer behavior subject to electroconvection occurring near a nanoporous membrane in-situ fabricated by a laser polymerization technique on a microfluidic chip. We found that the micromixer behavior can be categorized into three regimes. Briefly, the weak electroconvection regime is characterized by weak mixing performance at a low applied voltage and KCl concentration, whereas the strong electroconvection regime has a high mixing performance when the applied voltage and KCl concentration are moderately high. Finally, the incomplete electroconvection regime has an incomplete electric double-layer overlap in the nanopores of the membrane when the electrolyte concentration is very high. The mixing index reached 0.92 in the strong electroconvection regime. The detailed fabrication methods for the micromixer and characterization results are discussed in this paper.

Coating of Nafion membranes with polyelectrolyte multilayers to achieve high monovalent/divalent cation electrodialysis selectivities

Electrodialysis (ED) membranes typically exhibit modest selectivities between monovalent and divalent ions. This paper reports a dramatic enhancement of the monovalent/divalent cation selectivities of Nafion 115 membranes through coating with multilayer poly(4-styrenesulfonate) (PSS)/protonated poly(allylamine) (PAH) films. Remarkably, K(+)/Mg(2+) ED selectivities reach values >1000, and similar monovalent/divalent cation selectivities occur with feed solutions containing K(+) and Ca(2+). For comparison, the corresponding K(+)/Mg(2+) selectivity of bare Nafion 115 is only 1.8 ± 0.1. However, with 0.01 M KNO3 and 0.01 M Mg(NO3)2 in the source phase, as the applied current density increases from 1.27 to 2.54 mA cm(-2), the K(+)/Mg(2+) selectivities of coated membranes decrease from >1000 to 22. Water-splitting at strongly overlimiting current densities may lead to a local pH increase close to the membrane surface and alter film permeability or allow passage of Mg(OH)x species to decrease selectivity. When the source phase contains 0.1 M KNO3 and 0.1 M Mg(NO3)2, the K(+) transference number approaches unity and the K(+)/Mg(2+) selectivity is >20,000, presumably because the applied current is below the limiting value for K(+) and H(+) transport is negligible at this high K(+) concentration. The high selectivities of these membranes may enable electrodialysis applications such as purification of salts that contain divalent or trivalent ions.

Equilibrium electroconvective instability

Since its prediction 15 years ago, hydrodynamic instability in concentration polarization at a charge-selective interface has been attributed to nonequilibrium electro-osmosis related to the extended space charge which develops at the limiting current. This attribution had a double basis. On the one hand, it has been recognized that neither equilibrium electro-osmosis nor bulk electroconvection can yield instability for a perfectly charge-selective solid. On the other hand, it has been shown that nonequilibrium electro-osmosis can. The first theoretical studies in which electro-osmotic instability was predicted and analyzed employed the assumption of perfect charge selectivity for the sake of simplicity and so did the subsequent studies of various time-dependent and nonlinear features of electro-osmotic instability. In this Letter, we show that relaxing the assumption of perfect charge selectivity (tantamount to fixing the electrochemical potential of counterions in the solid) allows for the equilibrium electroconvective instability. In addition, we suggest a simple experimental test for determining the true, either equilibrium or nonequilibrium, origin of instability in concentration polarization.

Experimental verification of overlimiting current by surface conduction and electro-osmotic flow in microchannels

Direct evidence is provided for the transition from surface conduction (SC) to electro-osmotic flow (EOF) above a critical channel depth (d) of a nanofluidic device. The dependence of the overlimiting conductance (OLC) on d is consistent with theoretical predictions, scaling as d(-1) for SC and d(4/5) for EOF with a minimum around d=8  μm. The propagation of transient deionization shocks is also visualized, revealing complex patterns of EOF vortices and unstable convection with increasing d. This unified picture of surface-driven OLC can guide further advances in electrokinetic theory, as well as engineering applications of ion concentration polarization in microfluidics and porous media.

An electrokinetic study on tunable 3D nanochannel networks constructed by spatially controlled nanoparticle assembly

This paper proposes a novel method to form ion-selective nanochannel networks between two microfluidic channels using geometrically controlled in situ self-assembled nanoparticles. We present a thorough experimental and theoretical analysis of nanoscale electrokinetics using the proposed microplatform. The nano-interstices between these assembled nanoparticles serve as the nanopores of ion-selective membranes with equivalent pore size. Its inherent characteristics (compared with the conventional one-dimensional nanochannels) are a high ionic flux and a low fluidic resistance because these nanopore clusters have a role as collective three-dimensional nanochannel networks, which result in a highly efficient performance beneficial for various applications. Another uniqueness of our system is that the electrical characteristics (such as ion transport through the nanochannel networks and the decrease in the limiting current region) can be tuned quantitatively or even optimized by changing the geometry of the microchannel and the pH condition of the working solution or by appropriately selecting the size and materials of the assembled nanoparticles. The correlation between these tuning parameters and nanoscale electrokinetics is deeply investigated with carefully designed experiments and their mechanism is thoroughly examined by a theoretical study. We expect that the presented system and methodology can contribute to opening new application fields, such as biomolecule separation/filtering/accumulation/analysis, bioelectronics, and energy generation.

Real-time dual-loop electric current measurement for label-free nanofluidic preconcentration chip

An electrokinetic trapping (EKT)-based nanofluidic preconcentration device with the capability of label-free monitoring trapped biomolecules through real-time dual-loop electric current measurement was demonstrated. Universal current-voltage (I-V) curves of EKT-based preconcentration devices, consisting of two microchannels connected by ion-selective channels, are presented for functional validation and optimal operation; universal onset current curves indicating the appearance of the EKT mechanism serve as a confirmation of the concentrating action. The EKT mechanism and the dissimilarity in the current curves related to the volume flow rate (Q), diffusion coefficient (D), and diffusion layer (DL) thickness were explained by a control volume model with a five-stage preconcentration process. Different behaviors of the trapped molecular plug were categorized based on four modes associated with different degrees of electroosmotic instability (EOI). A label-free approach to preconcentrating (bio)molecules and monitoring the multibehavior molecular plug was demonstrated through real-time electric current monitoring, rather than through the use of microscope images.

Enhanced conductivity of monovalent cation exchange membranes with chitosan/PANI composite modification

The application of electrodialysis (ED) for desalination requires the use of natural seawater or river water, in which the presence of multivalent ions is inevitable.

Ion concentration polarization on paper-based microfluidic devices and its application to preconcentrate dilute sample solutions

Microfluidic paper-based analytical devices (μPADs) are a promising solution for a wide range of point-of-care applications. The feasibility of inducing ion concentration polarization (ICP) on μPADs has thus far attracted little attention. Accordingly, this study commences by demonstrating the ICP phenomenon in a μPAD with a Nafion ion-selective membrane. We are the first to measure the current-voltage curve on a Nafion-coated μPAD in order to indicate that the ion depletion occurs and the ICP is triggered when the current reaches the limiting current. The ICP effect is then exploited to preconcentrate fluorescein on μPADs incorporating straight and convergent channels. By an optimal geometric design, it is shown that the convergent channel results in a greater preconcentration effect than the straight channel. Specifically, a 20-fold enhancement in the sample concentration is achieved after 130 s given an initial concentration of [Formula: see text] M and an external potential of 50 V. By contrast, the straight channel yields only a 10-fold improvement in the concentration after 180 s. Further, the practical feasibility of the proposed convergent-channel μPAD is demonstrated using fluorescein isothiocyanate labeled bovine serum albumin. The experimental results show that a 15-fold enhancement of the initial sample concentration ([Formula: see text] M) is obtained after 120 s given an external potential of 50 V.

Bridging the gap between an isolated nanochannel and a communicating multipore heterogeneous membrane

To bridge the gap between single and isolated pore systems to multipore systems, such as membranes and electrodes, we studied an array of nanochannels with varying interchannel spacing that controlled the degree of channel communication. Instead of treating them as individual channels connected in parallel or an assembly like a homogeneous membrane, this study resolves the pore-pore interaction. We found that increased channel isolation leads to current intensification, whereas at high voltages electroconvective effects control the degree of communication via suppression of the diffusion layer growth.

Energy from CO2 using capacitive electrodes - a model for energy extraction cycles

A model is presented for the process of harvesting electrical energy from CO2 emissions using capacitive cells. The principle consists of controlling the mixing process of a concentrated CO2 gas stream with a dilute CO2 gas stream (as, for example, exhaust gas and air), thereby converting part of the released mixing energy into electrical energy. The model describes the transient reactive transport of CO2 gas absorbed in water or in monoethanolamine (MEA) solutions, under the assumption of local chemical equilibrium. The model combines the selective transport of ions through ion-exchange membranes, the accumulation of charge in the porous carbon electrodes and the coupling between the ionic current and the produced electrical current and power. We demonstrate that the model can be used to calculate the energy that can be extracted by mixing concentrated and dilute CO2 containing gas streams. Our calculation results for the process using MEA solutions have various counterintuitive features, including: 1. When dynamic equilibrium is reached in the cyclical process, the electrical charge in the anode is negative both during charging and discharging; 2. Placing an anion-exchange membrane (AEM) in the system is not required, the energy per cycle is just as large with or without an AEM.

Multiphysics simulation of ion concentration polarization induced by nanoporous membranes in dual channel devices

Many microfluidic devices have been utilizing ion concentration polarization (ICP) phenomena by using a permselective, nanoporous membrane with electric fields for a variety of preconcentration applications. However, numerical analyses on the ICP phenomena have not drawn sufficient attention, although they are an intriguing and interdisciplinary research area. In this work, we propose a 2-D model and present numerical simulation results on the ICP, which were obtained by solving three coupled governing equations: Nernst-Planck, Navier-Stokes, and Poisson. With improved boundary conditions and assumptions, we demonstrated that the simulation results not only are consistent with other experimental results but also make it possible to thoroughly understand the ICP phenomena. In addition, we demonstrated that the preconcentration of analytes can be simulated and quantified in terms of concentration enhancement factors (CEFs) that were related to many factors, such as ionic concentration distribution, electric fields, and flow fields including vortex flows across the membrane. Furthermore, we demonstrated that a high electrophoretic mobility (EPM) of counterions in the membrane plays the most important role in producing accurate simulation results while the effect of the charge density of the membrane is relatively insignificant. Hence, it is believed that the model and simulation results would provide good guidelines to better develop microfluidic preconcentration devices based on the ICP phenomena.

Spatiotemporal pH dynamics in concentration polarization near ion-selective membranes

We present a detailed analysis of the transient pH dynamics for a weak, buffered electrolyte subject to voltage-driven transport through an ion-selective membrane. We show that pH fronts emanate from the concentration polarization zone next to the membrane and that these propagating fronts change the pH in the system several units from its equilibrium value. The analysis is based on a 1D model using the unsteady Poisson-Nernst-Planck equations with nonequilibrium chemistry and without assumptions of electroneutrality or asymptotically thin electric double layers. Nonequilibrium chemical effects, especially for water splitting, are shown to be important for the dynamical and spatiotemporal evolution of the pH fronts. Nonetheless, the model also shows that at steady state the assumption of chemical equilibrium can still lead to good approximations of the global pH distribution. Moreover, our model shows that the transport of the hydronium ion in the extended space charge region is governed by a balance between electromigration and water self-ionization. On the basis of this observation, we present a simple model showing that the net flux of the hydronium ion is proportional to the length of the extended space charge region and the water self-ionization rate. To demonstrate these effects in practice, we have adopted the experiment of Mai et al. (Mai, J.; Miller, H.; Hatch, A. V. Spatiotemporal Mapping of Concentration Polarization Induced pH Changes at Nanoconstrictions. ACS Nano 2012, 6, 10206) as a model problem, and by including the full chemistry and transport, we show that the present model can capture the experimentally observed pH fronts. Our model can, among other things, be used to predict and engineer pH dynamics, which can be essential to the performance of membrane-based systems for biochemical separation and analysis.

Three-dimensional coherent structures of electrokinetic instability

A direct numerical simulation of the three-dimensional elektrokinetic instability near a charge-selective surface (electric membrane, electrode, or system of micro- or nanochannels) has been carried out and analyzed. A special finite-difference method has been used for the space discretization along with a semi-implicit 31/3-step Runge-Kutta scheme for the integration in time. The calculations employ parallel computing. Three characteristic patterns, which correspond to the overlimiting currents, are observed: (a) two-dimensional electroconvective rolls, (b) three-dimensional regular hexagonal structures, and (c) three-dimensional structures of spatiotemporal chaos, which are a combination of unsteady hexagons, quadrangles, and triangles. The transition from (b) to (c) is accompanied by the generation of interacting two-dimensional solitary pulses.

Electrokinetic instability near charge-selective hydrophobic surfaces

The influence of the texture of a hydrophobic surface on the electro-osmotic slip of the second kind and the electrokinetic instability near charge selective surfaces (permselective membranes, electrodes, or systems of microchannels and nanochannels) is investigated theoretically using a simple model based on the Rubinstein-Zaltzman approach. A simple formula is derived to evaluate the decrease in the instability threshold due to hydrophobicity. The study is complemented by numerical investigations both of linear and nonlinear instabilities near a hydrophobic membrane surface. Theory predicts a significant enhancement of the ion flux to the surface and shows a good qualitative agreement with the available experimental data.

Rectification of Ion Current in Nanopores Depends on the Type of Monovalent Cations: Experiments and Modeling

Rectifying nanopores feature ion currents that are higher for voltages of one polarity compared to the currents recorded for corresponding voltages of the opposite polarity. Rectification of nanopores has been found to depend on the pore opening diameter and distribution of surface charges on the pore walls as well as pore geometry. Very little is known, however, on the dependence of ionic rectification on the type of transported ions of the same charge. We performed experiments with single conically shaped nanopores in a polymer film and recorded current-voltage curves in three electrolytes: LiCl, NaCl, and KCl. Rectification degrees of the pores, quantified as the ratio of currents recorded for voltages of opposite polarities, were the highest for KCl and the lowest for LiCl. The experimental observations could not be explained by a continuum modeling based on the Poisson-Nernst-Planck equations. All-atom molecular dynamics simulations revealed differential binding between Li⁺, Na⁺, and K⁺ ions and carboxyl groups on the pore walls, resulting in changes to both the effective surface charge of the nanopore and cation mobility within the pore.

Lattice Boltzmann scheme for electrolytes by an extended Maxwell-Stefan approach

This paper presents an extended multicomponent lattice Boltzmann model for the simulation of electrolytes. It is derived by means of a finite discrete velocity model and its discretization. The model recovers momentum and mass transport according to the incompressible Navier-Stokes equation and Maxwell-Stefan formulation, respectively. It includes external driving forces (e.g., electric field) on diffusive and viscous scales, concentration-dependent Maxwell-Stefan diffusivities, and thermodynamic factors. The latter take into account nonideal diffusion behavior, which is essential as electrolytes involve charged species and therefore nonideal long and short-range interactions among the molecules of the species. Furthermore, we couple our scheme to a finite element method to include electrostatic interactions on the macroscopic level. Numerical experiments show the validity of the presented model.

Transport-limited water splitting at ion-selective interfaces during concentration polarization

We present an analytical model of salt- and water-ion transport across an ion-selective interface based on an assumption of local equilibrium of the water-dissociation reaction. The model yields current-voltage characteristics and curves of water-ion current versus salt-ion current, which are in qualitative agreement with experimental results published in the literature. The analytical results are furthermore in agreement with direct numerical simulations. As part of the analysis, we find approximate solutions to the classical problem of pure salt transport across an ion-selective interface. These solutions provide closed-form expressions for the current-voltage characteristics, which include the overlimiting current due to the development of an extended space-charge region. Finally, we discuss how the addition of an acid or a base affects the transport properties of the system and thus provide predictions accessible to further experimental tests of the model.

Effect of geometry on concentration polarization in realistic heterogeneous permselective systems

This study extends previous analytical solutions of concentration polarization occurring solely in the depleted region, to the more realistic geometry consisting of a three-dimensional (3D) heterogeneous ion-permselective medium connecting two opposite microchambers (i.e., a three-layer system). Under the local electroneutrality approximation, the separation of variable methods is used to derive an analytical solution of the electrodiffusive problem for the two opposing asymmetric microchambers. The assumption of an ideal permselective medium allows for the analytic calculation of the 3D concentration and electric potential distributions as well as a current-voltage relation. It is shown that any asymmetry in the microchamber geometries will result in current rectification. Moreover, it is demonstrated that for non-negligible microchamber resistances, the conductance does not exhibit the expected saturation at low concentrations but instead shows a continuous decrease. The results are intended to facilitate a more direct comparison between theory and experiments, as now the voltage drop is across a realistic 3D and three-layer system.

Nanometer-thick lateral polyelectrolyte micropatterns induce macrosopic electro-osmotic chaotic fluid instabilities

Electro-convective vortices in ion concentration polarization under shear flow have been of practical relevance for desalination processes using electrodialysis. The phenomenon has been scientifically disregarded for decades, but is recently embraced by a growing fluid dynamics community due its complex superposition of multi-scale gradients in electrochemical potential and space charge interacting with emerging complex fluid momentum gradients. While the visualization, quantification and fundamental understanding of the often-chaotic fluid dynamics is evolving rapidly due to sophisticated simulations and experimentation, little is known whether these instabilities can be induced and affected by chemical topological heterogeneity in surface properties. In this letter, we report that polyelectrolyte layers applied as micropatterns on ion exchange membranes induce and facilitate the electro-osmotic fluid instabilities. The findings stimulate a variety of fundamental questions comparable to the complexity of today's turbulence research.

Effects of three-dimensional geometric field focusing on concentration polarization in a heterogeneous permselective system

The current study extends previous two-dimensional (2D) analysis of concentration polarization to account for three-dimensional effects in realistic heterogeneous ion-permselective systems, e.g., microchamber-nanoslot devices. An analytical solution of the electrodiffusive problem, decoupled from electroconvection along with the local electroneutrality approximation, was obtained using the separation of variables technique. It is able to account for the previously neglected effects of microchamber and nanoslot heights on concentration polarization in terms of concentration profiles, limiting current, and current-voltage curves. The resultant heterogeneity in the third dimension adds to that already existing in the 2D in plane problem to further increase geometric field-focusing effects. As a result the currents no longer scale linearly with the nanoslot area, but rather depend on its shape and relative size compared to that of the nonconducting region (i.e., level of heterogeneity). This is turn leads to pronounced current density intensification with increased system heterogeneity found to be in qualitative agreement with previously reported experiments in which both microchamber and nanoslot geometries were varied.

Microfluidic systems with ion-selective membranes

When integrated into microfluidic chips, ion-selective nanoporous polymer and solid-state membranes can be used for on-chip pumping, pH actuation, analyte concentration, molecular separation, reactive mixing, and molecular sensing. They offer numerous functionalities and are hence superior to paper-based devices for point-of-care biochips, with only slightly more investment in fabrication and material costs required. In this review, we first discuss the fundamentals of several nonequilibrium ion current phenomena associated with ion-selective membranes, many of them revealed by studies with fabricated single nanochannels/nanopores. We then focus on how the plethora of phenomena has been applied for transport, separation, concentration, and detection of biomolecules on biochips.