Electro-osmotically induced convection at a permselective membrane

Charge polarization, local electroneutrality breakdown and eddy formation due to electroosmosis in varying-section channels

We characterize the dynamics of an electrolyte embedded in a varying-section channel under the action of a constant external electrostatic field. By means of molecular dynamics simulations we determine the stationary density, charge and velocity profiles of the electrolyte. Our results show that when the Debye length is comparable to the width of the channel bottlenecks a concentration polarization along with two eddies sets inside the channel. Interestingly, upon increasing the external field, local electroneutrality breaks down and charge polarization sets leading to the onset of net dipolar field. This novel scenario, that cannot be captured by the standard approaches based on local electroneutrality, opens the route for the realization of novel micro and nano-fluidic devices.

Overlimiting current due to electro-diffusive amplification of the second Wien effect at a cation-anion bipolar membrane junction

Numerical simulations are presented for the transient and steady-state response of a model electrodiffusive cell with a bipolar ion-selective membrane under electric current. The model uses a continuum Poisson-Nernst-Planck theory including source terms to account for the catalytic second Wien effect between ionogenic groups in the membranes and resolves the Debye layers at interfaces. The resulting electric field at the membrane junction is increased by as much as four orders of magnitude in comparison to the field external to the membrane. This leads to a significant amplification of the second Wien effect, creating an increased ionic flux due to the catalytic decomposition of water. The effect also induces an exaltation effect wherein the salt ion flux undergoes a concomitant increase as well. The interplay of effects results in a unique over-limiting current mechanism due to concentration polarization internal, rather than external, to the membranes. In addition to the case of two equal but oppositely charged membranes under the standard simplifying assumption of equal ionic diffusivities, two variations on this model are studied. Asymmetric diffusivities, representative of the actual mobility difference in dissociated water ions, and the effect of the membrane charge density ratio were also considered. The latter elucidates an overlimiting current shift mechanism for DNA adsorption on anion-selective membranes proposed by Slouka et al. [Langmuir 29, 8275 (2013)]. The former provides more realistic picture of multi-ion transport and demonstrates a surprising steady-state effect due to the asymmetry in the diffusivity of hydroxide and hydronium.

1D Mathematical Modelling of Non-Stationary Ion Transfer in the Diffusion Layer Adjacent to an Ion-Exchange Membrane in Galvanostatic Mode

The use of the Nernst–Planck and Poisson (NPP) equations allows computation of the space charge density near solution/electrode or solution/ion-exchange membrane interface. This is important in modelling ion transfer, especially when taking into account electroconvective transport. The most solutions in literature use the condition setting a potential difference in the system (potentiostatic or potentiodynamic mode). However, very often in practice and experiment (such as chronopotentiometry and voltammetry), the galvanostatic/galvanodynamic mode is applied. In this study, a depleted stagnant diffusion layer adjacent to an ion-exchange membrane is considered. In this article, a new boundary condition is proposed, which sets a total current density, i, via an equation expressing the potential gradient as an explicit function of i. The numerical solution of the problem is compared with an approximate solution, which is obtained by a combination of numerical solution in one part of the diffusion layer (including the electroneutral region and the extended space charge region, zone (I) with an analytical solution in the other part (the quasi-equilibrium electric double layer (EDL), zone (II). It is shown that this approach (called the “zonal” model) allows reducing the computational complexity of the problem tens of times without significant loss of accuracy. An additional simplification is introduced by neglecting the thickness of the quasi-equilibrium EDL in comparison to the diffusion layer thickness (the “simplified” model). For the first time, the distributions of concentrations, space charge density and current density along the distance to an ion-exchange membrane surface are computed as functions of time in galvanostatic mode. The calculation of the transition time, τ, for an ion-exchange membrane agree with an experiment from literature. It is suggested that rapid changes of space charge density, and current density with time and distance, could lead to lateral electroosmotic flows delaying depletion of near-surface solution and increasing τ.

Deciphering ion concentration polarization-based electrokinetic molecular concentration at the micro-nanofluidic interface: theoretical limits and scaling laws

The electrokinetic molecular concentration (EMC) effect at the micro-nanofluidic interface, which enables million-fold preconcentration of biomolecules, is one of the most compelling yet least understood nanofluidic phenomena. Despite the tremendous interests in EMC and the substantial efforts devoted, the detailed mechanism of EMC remains an enigma so far owing to its high complexity, which gives rise to the significant scientific controversies outstanding for over a decade and leaves the precise engineering of EMC devices infeasible. We report a series of experimental and theoretical new findings that decipher the mechanism of EMC. We demonstrate the first elucidation of two separate operating regimes of EMC, and establish the first theoretical model that analytically yet concisely describes the system. We further unveil the dramatically different scaling behaviors of EMC in the two regimes, thereby clarifying the long-lasting controversies. We believe this work represents important progress towards the scientific understanding of EMC and related nano-electrokinetic systems, and would enable the rational design and optimization of EMC devices for a variety of applications.

A Multiwell-Based Detection Platform with Integrated PDMS Concentrators for Rapid Multiplexed Enzymatic Assays

We report an integrated system for accelerating assays with concentrators in a standard 12-well plate (ISAAC-12) and demonstrate its versatility for rapid detection of matrix metalloproteinase (MMP)-9 expression in the cell culture supernatant of breast cancer cell line MDA-MB-231 by accelerating the enzymatic reaction and end-point signal intensity via electrokinetic preconcentration. Using direct printing of a conductive ion-permselective polymer on a polydimethylsiloxane (PDMS) channel, the new microfluidic concentrator chip can be built without modifying the underlying substrate. Through this decoupling fabrication strategy, our microfluidic concentrator chip can easily be integrated with a standard multiwell plate, the de facto laboratory standard platform for high-throughput assays, simply by reversible bonding on the bottom of each well. It increases the reaction rate of enzymatic assays by concentrating the enzyme and the reaction product inside each well simultaneously for rapid multiplexed detection.

Electrothermal based active control of ion transport in a microfluidic device with an ion-permselective membrane

The ability to induce regions of high and low ionic concentrations adjacent to a permselective membrane or a nanochannel subject to an externally applied electric field (a phenomenon termed concentration-polarization) has been used for a broad spectrum of applications ranging from on-chip desalination, bacteria filtration to biomolecule preconcentration. But these applications have been limited by the ability to control the length of the diffusion layer that is commonly indirectly prescribed by the fixed geometric and surface properties of a nanofluidic system. Here, we demonstrate that the depletion layer can be dynamically varied by inducing controlled electrothermal flow driven by the interaction of temperature gradients with the applied electric field. To this end, a series of microscale heaters, which can be individually activated on demand are embedded at the bottom of the microchannel and the relationship between their activation and ionic concentration is characterized. Such spatio-temporal control of the diffusion layer can be used to enhance on-chip electro-dialysis by producing shorter depletion layers, to dynamically reduce the microchannel resistance relative to that of the nanochannel for nanochannel based (bio)sensing, to generate current rectification reminiscent of a diode like behavior and control the location of the preconcentrated plug of analytes or the interface of brine and desalted streams.

Direct numerical simulation of continuous lithium extraction from high Mg2+/Li+ ratio brines using microfluidic channels with ion concentration polarization

A novel ion concentration polarization-based microfluidic device is proposed for continuous extraction of Li+ from high Mg2+/Li+ ratio brines. With simultaneous application of the cross-channel voltage that drives electroosmotic flow and the cross-membrane voltage that induces ion depletion, Li+ is concentrated much more than other cations in front of the membrane in the microchannel. The application of external pressure produces a fluid flow that drags a portion of Li+ (and Na+) to flow through the microchannel, while keeping most of Mg2+ (and K+) blocked, thus implementing continuous Li+ extraction. Two-dimensional numerical simulation using a microchannel of 120 µm length and 4 µm height and a model, highly concentrated brine, shows that the system may produce a continuous flow rate of 1.72 mm/s, extracting 25.6% of Li+, with a Li+/Mg2+ flux ratio of 2.81×103, at a pressure of 100 Pa and cross-membrane voltage of 100 times of thermal voltages (25.8 mV). Fundamental mechanisms of the system are elaborated and effects of the cross-membrane voltage and the external pressure are analyzed. These results and findings provide clear guidance for the understanding and designing of microfluidic devices not only for Li+ extraction, but also for other ionic or molecular separations.

Enhanced ion transport using geometrically structured charge selective interfaces

A microfluidic platform containing charged hydrogels is used to investigate the effect of geometry on charge transport in electrodialysis applications. The influence of heterogeneity on ion transport is determined by electrical characterization and fluorescence microscopy of three different hydrogel geometries. We found that electroosmotic transport of ions towards the hydrogel is enhanced in heterogeneous geometries, as a result of the inhomogeneous electric field in these systems. This yields higher ionic currents for equal applied potentials when compared to homogeneous geometries. The contribution of electroosmotic transport is present in all current regimes, including the Ohmic regime. We also found that the onset of the overlimiting current occurs at lower potentials due to the increased heterogeneity in hydrogel shape, owing to the non-uniform electric field distribution in these systems. Pinning of ion depletion and enrichment zones is observed in the heterogeneous hydrogel systems, due to electroosmotic flows and electrokinetic instabilities. Our platform is highly versatile for the rapid investigation of the effects of membrane topology on general electrodialysis characteristics, including the formation of ion depletion zones on the micro-scale and the onset of the overlimiting current.

Stability of two layers dielectric-electrolyte microflow subjected to an alternating external electric field

The stability of the electroosmotic flow of the two-phase system electrolyte-dielectric with a free interface in the microchannel under an external electric field is examined theoretically. The mathematical model includes the Nernst-Plank equations for the ion concentrations. The linear stability of the 1D nonstationary solution with respect to the small, periodic perturbations along the channel, is studied. Two types of instability have been highlighted. The first is known as the long-wave instability and is connected with the distortion of the free charge on the interface. In the long-wave area, the results are in good agreement with the ones obtained theoretically and experimentally in the literature. The second type of instability is a short-wave and mostly connected with the disturbance of the electrolyte conductivity. The short-wave type of instability has not been found previously in the literature and constitutes the basis and the strength of the present work. It is revealed that with the increase of the external electric field frequency, the 1D flow is stabilized. The dependence of the flow on the other parameters of the system is qualitatively the same as for the constant electric field.

Stabilizing electrochemical interfaces in viscoelastic liquid electrolytes

Electrodeposition is a widely practiced method for creating metal, colloidal, and polymer coatings on conductive substrates. In the Newtonian liquid electrolytes typically used, the process is fundamentally unstable. The underlying instabilities have been linked to failure of microcircuits, dendrite formation on battery electrodes, and overlimiting conductance in ion-selective membranes. We report that viscoelastic electrolytes composed of semidilute solutions of very high-molecular weight neutral polymers suppress these instabilities by multiple mechanisms. The voltage window ΔV in which a liquid electrolyte can operate free of electroconvective instabilities is shown to be markedly extended in viscoelastic electrolytes and is a power-law function, ΔV : η^1/4, of electrolyte viscosity, η. This power-law relation is replicated in the resistance to ion transport at liquid/solid interfaces. We discuss consequences of our observations and show that viscoelastic electrolytes enable stable electrodeposition of many metals, with the most profound effects observed for reactive metals, such as sodium and lithium. This finding is of contemporary interest for high-energy electrochemical energy storage.

Confined Electroconvective Vortices at Structured Ion Exchange Membranes

In this paper, we investigate electroconvective ion transport at cation exchange membranes with different geometry square-wave structures (line undulations) experimentally and numerically. Electroconvective microvortices are induced by strong concentration polarization once a threshold potential difference is applied. The applied potential required to start and sustain electroconvection is strongly affected by the geometry of the membrane. A reduction in the resistance of approximately 50% can be obtained when the structure size is similar to the mixing layer (ML) thickness, resulting in confined vortices with less lateral motion compared to the case of flat membranes. From electrical, flow, and concentration measurements, ion migration, advection, and diffusion are quantified, respectively. Advection and migration are dominant in the vortex ML, whereas diffusion and migration are dominant in the stagnant diffusion layer. Numerical simulations, based on Poisson-Nernst-Planck and Navier-Stokes equations, show similar ion transport and flow characteristics, highlighting the importance of membrane topology on the resulting electrokinetic and electrohydrodynamic behavior.

Force fields of charged particles in micro-nanofluidic preconcentration systems

Electrokinetic concentration devices based on the ion concentration polarization (ICP) phenomenon have drawn much attention due to their simple setup, high enrichment factor, and easy integration with many subsequent processes, such as separation, reaction, and extraction etc. Despite significant progress in the experimental research, fundamental understanding and detailed modeling of the preconcentration systems is still lacking. The mechanism of the electrokinetic trapping of charged particles is currently limited to the force balance analysis between the electric force and fluid drag force in an over-simplified one-dimensional (1D) model, which misses many signatures of the actual system. This letter studies the particle trapping phenomena that are not explainable in the 1D model through the calculation of the two-dimensional (2D) force fields. The trapping of charged particles is shown to significantly distort the electric field and fluid flow pattern, which in turn leads to the different trapping behaviors of particles of different sizes. The mechanisms behind the protrusions and instability of the focused band, which are important factors determining overall preconcentration efficiency, are revealed through analyzing the rotating fluxes of particles in the vicinity of the ion-selective membrane. The differences in the enrichment factors of differently sized particles are understood through the interplay between the electric force and convective fluid flow. These results provide insights into the electrokinetic concentration effect, which could facilitate the design and optimization of ICP-based preconcentration systems.

Enabling electrical biomolecular detection in high ionic concentrations and enhancement of the detection limit thereof by coupling a nanofluidic crystal with reconfigurable ion concentration polarization

The regulation effect of surface charges on the transport of electrons in nanomaterials and ions in nanofluidic devices has been widely used to develop highly sensitive and label-free electrical biosensors. The intrinsic limitation to the clinical application of surface charge-effect nano-electrical biosensors is that they usually do not function in physiological conditions normally with high ionic concentrations (∼160 mM), in which the surface charges are screened within a short distance (<1 nm at 160 mM). In this work, we developed a general strategy that enables surface charge-effect electrical biomolecular detection in physiological conditions with an integrated mechanism for enhancement of the limit of detection (LOD) by in situ preconcentration of target molecules during incubation and creation of a transient low ionic concentration environment during the signal read-out step using reconfigurable ion concentration polarization (ICP). We demonstrated the effectiveness of this strategy in a simple nanofluidic biosensor named a nanofluidic crystal (NFC), which can be prepared within hours and without expensive equipment. Our results indicate that the ion depletion effect of ICP could lower the ionic concentration by at least 200 fold and provide a stable ionic environment for over 15 s, enabling electrical detection of proteins and DNAs in serum and urine with LODs of 1-10 nM. We further reconfigured the device to preconcentrate target biomolecules before detection using the enrichment effect of ICP, obtaining LODs of 10-100 pM for proteins and DNAs in physiological conditions. By overcoming the inherent constraint on buffer conditions and the issues regarding fabrication, we believe that this work represents significant progress towards the practical application of surface charge-effect nano-electrical biosensors in point-of-care diagnostics and clinical medicine.

Nanofluidic crystals: nanofluidics in a close-packed nanoparticle array

With various promising applications demonstrated, nanofluidics has been of broad research interest in the past decade. As nanofluidics matures from a proof of concept towards practical applications, it faces two major barriers: expensive nanofabrication and ultra-low throughput. To date, the only material that enables nanofabrication-free, high-throughput, yet precisely controllable nanofluidic systems is the close-packed nanoparticle array, i.e. nanofluidic crystals. Recently, significant progress in nanofluidics has been made using nanofluidic crystals, including high-current ionic diodes, high-power energy harvesters, efficient biomolecular separation, and facile biosensors. Nanofluidic crystals are seen as a key to applying nanofluidic concepts to real-world applications. In this review, we introduce the key concepts and models in nanofluidic crystals, summarize the fabrication methods, and discuss the various applications of nanofluidic crystals in depth, highlighting their advantages in terms of simple fabrication, low cost, flexibility, and high throughput. Finally, we provide our perspectives on the future of nanofluidic crystals and their potential impacts.

A concentration-independent micro/nanofluidic active diode using an asymmetric ion concentration polarization layer

Over the past decade, nanofluidic diodes that rectify ionic currents (i.e. greater current in one direction than in the opposite direction) have drawn significant attention in biomolecular sensing, switching and energy harvesting devices. To obtain current rectification, conventional nanofluidic diodes have utilized complex nanoscale asymmetry such as nanochannel geometry, surface charge density, and reservoir concentration. Avoiding the use of sophisticated nano-asymmetry, micro/nanofluidic diodes using microscale asymmetry have been recently introduced; however, their diodic performance is still impeded by (i) low (even absent) rectification effects at physiological concentrations over 100 mM and strong dependency on the bulk concentration, and (ii) the fact that they possess only passive predefined rectification factors. Here, we demonstrated a new class of micro/nanofluidic diode with an ideal perm-selective nanoporous membrane based on ion concentration polarization (ICP) phenomenon. Thin side-microchannels installed near a nanojunction served as mitigators of the amplified electrokinetic flows generated by ICP and induced convective salt transfer to the nanoporous membrane, leading to actively controlled micro-scale asymmetry. Using this device, current rectifications were successfully demonstrated in a wide range of electrolytic concentrations (10^-5 M to 3 M) as a function of the fluidic resistance of the side-microchannels. Noteworthily, it was confirmed that the rectification factors were independent from the bulk concentration due to the ideal perm-selectivity. Moreover, the rectification of the presenting diode was actively controlled by adjusting the external convective flows, while that of the previous diode was passively determined by invariant nanoscale asymmetry.

Multiscale Model for Electrokinetic Transport in Networks of Pores, Part I: Model Derivation

We present an efficient and robust numerical model for the simulation of electrokinetic phenomena in porous media and microstructure networks considering a wide range of applications including energy conversion, deionization, and microfluidic-based lab-on-a-chip systems. Coupling between fluid flow and ion transport in these networks is governed by the Poisson-Nernst-Planck-Stokes equations. These equations describe a wide range of phenomena that can interact in a complex fashion when coupled in networks involving multiple pores with variable properties. Capturing these phenomena by direct simulation of the governing equations in multidimensions is prohibitively expensive. We present here a reduced-order model that treats a network of many pores via solutions to 1D equations. Assuming that each pore in the network is long and thin, we derive a 1D model describing the transport in the pore's longitudinal direction. We take into account the cross-sectional nonuniformity of potential and ion concentration fields in the form of area-averaged coefficients in different flux terms representing fluid flow, electric current, and ion fluxes. These coefficients are obtained from the solutions to the Poisson-Boltzmann equation and are tabulated against dimensionless surface charge and dimensionless thickness of the electric double layer (EDL). Although similar models have been attempted in the past, distinct advantages of the present framework include a fully conservative discretization with zero numerical leakage, fully bounded area-averaged coefficients without any singularity in the limit of infinitely thick EDLs, a flux discretization that exactly preserves equilibrium conditions, and extension to a general network of pores with multiple intersections. In part II of this two-article series, we present a numerical implementation of this model and demonstrate its applications in predicting a wide range of electrokinetic phenomena in microstructures.

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.

Merging Ion Concentration Polarization between Juxtaposed Ion Exchange Membranes to Block the Propagation of the Polarization Zone

The ion concentration polarization (ICP) phenomenon is one of the most prevailing methods to preconcentrate low-abundance biological samples. The ICP induces a noninvasive region for charged biomolecules (i.e., the ion depletion zone), and targets can be preconcentrated on this region boundary. Despite the high preconcentration performances with ICP, it is difficult to find the operating conditions of non-propagating ion depletion zones. To overcome this narrow operating window, we recently developed a new platform for spatiotemporally fixed preconcentration. Unlike preceding methods that only use ion depletion, this platform also uses the opposite polarity of the ICP (i.e., ion enrichment) to stop the propagation of the ion depletion zone. By confronting the enrichment zone with the depletion zone, the two zones merge together and stop. In this paper, we describe a detailed experimental protocol to build this spatiotemporally defined ICP platform and characterize the preconcentration dynamics of the new platform by comparing them with those of the conventional device. Qualitative ion concentration profiles and current-time responses successfully capture the different dynamics between the merged ICP and the stand-alone ICP. In contrast to the conventional one that can fix the preconcentration location at only ~5 V, the new platform can produce a target-condensed plug at a specific location in the broad ranges of operating conditions: voltage (0.5-100 V), ionic strength (1-100 mM), and pH (3.7-10.3).

Influence of anion hydration status on selective properties of a commercial anion exchange membrane electrochemically impregnated with polyaniline deposits

There is currently great interest in the use of polyaniline (PAni) to impart particular properties to anion exchange membranes, employed in several fields.

Morphology-Directed Selective Production of Ethylene or Ethane from CO2 on a Cu Mesopore Electrode

The electrocatalytic conversion of CO₂ to value-added hydrocarbons is receiving significant attention as a promising way to close the broken carbon-cycle. While most metal catalysts produce C₁ species, such as carbon monoxide and formate, the production of various hydrocarbons and alcohols comprising more than two carbons has been achieved using copper (Cu)-based catalysts only. Methods for producing specific C₂ reduction outcomes with high selectivity, however, are not available thus far. Herein, the morphological effect of a Cu mesopore electrode on the selective production of C₂ products, ethylene or ethane, is presented. Cu mesopore electrodes with precisely controlled pore widths and depths were prepared by using a thermal deposition process on anodized aluminum oxide. With this simple synthesis method, we demonstrated that C₂ chemical selectivity can be tuned by systematically altering the morphology. Supported by computational simulations, we proved that nanomorphology can change the local pH and, additionally, retention time of key intermediates by confining the chemicals inside the pores.

Modes of electrokinetic instability for imperfect electric membranes

The direct transition to overlimiting current bypassing the stage of limiting currents is considered for imperfect membranes. Instability of the quiescent steady-state one-dimensional solution, which is the result of a balance of diffusion and electromigration, is investigated on the basis of the full Nernst-Planck-Poisson-Stokes system and a simplified quasielectroneutral system. A three-layer geometry, electrolyte-porous membrane-electrolyte, is considered. The usual assumption of a constant electrochemical potential along the membrane surface is removed from consideration. The effect of bulk and surface effects on the instability and transition to the overlimiting currents is evaluated for a different membrane selectivity. It becomes clear that for sufficiently small fixed charge concentration (large ion concentration in the electrolyte), the monotonic instability is replaced by an oscillatory one. The dependence of instability on the membrane porosity is found to be weak.

Observation and experimental investigation of confinement effects on ion transport and electrokinetic flows at the microscale

Electrokinetic effects adjacent to charge-selective interfaces (CSI) have been experimentally investigated in microfluidic platforms in order to gain understanding on underlying phenomena of ion transport at elevated applied voltages. We experimentally investigate the influence of geometry and multiple array densities of the CSI on concentration and flow profiles in a microfluidic set-up using nanochannels as the CSI. Particle tracking obtained under chronoamperometric measurements show the development of vortices in the microchannel adjacent to the nanochannels. We found that the direction of the electric field and the potential drop inside the microchannel has a large influence on the ion transport through the interface, for example by inducing immediate wall electroosmotic flow. In microfluidic devices, the electric field may not be directed normal to the interface, which can result in an inefficient use of the CSI. Multiple vortices are observed adjacent to the CSI, growing in size and velocity as a function of time and dependent on their location in the microfluidic device. Local velocities inside the vortices are measured to be more than 1.5 mm/s. Vortex speed, as well as flow speed in the channel, are dependent on the geometry of the CSI and the distance from the electrode.

Competition between diffusion and electroconvection at an ion-selective surface in intensive current regimes

Considering diffusion near a solid surface and simplifying the shape of concentration profile in diffusion-dominated layer allowed Nernst and Brunner to propose their famous equation for calculating the solute diffusion flux. Intensive (overlimiting) currents generate electroconvection (EC), which is a recently discovered interfacial phenomenon produced by the action of an external electric field on the electric space charge formed near an ion-selective interface. EC microscale vortices effectively mix the depleted solution layer that allows the reduction of diffusion transport limitations. Enhancement of ion transport by EC is important in membrane separation, nano-microfluidics, analytical chemistry, electrode kinetics and some other fields. This paper presents a review of the actual understanding of the transport mechanisms in intensive current regimes, where the role of diffusion declines in the profit of EC. We analyse recent publications devoted to explore the properties of different zones of the diffusion layer. Visualization of concentration profile and fluid current lines are considered as well as mathematical modelling of the overlimiting transfer.

Effect of field-focusing and ion selectivity on the extended space charge developed at the microchannel-nanochannel interface

We present results demonstrating the effect of varying microchannel depth and bulk conductivity on the space charge-mediated transition between classical, diffusion-limited current and over-limiting current in microchannel-nanochannel devices. The extended space charge layer develops at the depleted microchannel-nanochannel entrance when the limiting current is exceeded and is correlated with a distinctive maximum in the dc resistance. This maximum is shown to be affected by the microchannel depth, via field-focusing, and solution conductivity. In particular, we observe that upon their increase, the maximum becomes flatter and shifts to higher voltages.

Pseudo 1-D Micro/Nanofluidic Device for Exact Electrokinetic Responses

Conventionally, a 1-D micro/nanofluidic device, whose nanochannel bridged two microchannels, was widely chosen in the fundamental electrokinetic studies; however, the configuration had intrinsic limitations of the time-consuming and labor intensive tasks of filling and flushing the microchannel due to the high fluidic resistance of the nanochannel bridge. In this work, a pseudo 1-D micro/nanofluidic device incorporating air valves at each microchannel was proposed for mitigating these limitations. High Laplace pressure formed at liquid/air interface inside the microchannels played as a virtual valve only when the electrokinetic operations were conducted. The identical electrokinetic behaviors of the propagation of ion concentration polarization layer and current-voltage responses were obtained in comparison with the conventional 1-D micro/nanofluidic device by both experiments and numerical simulations. Therefore, the suggested pseudo 1-D micro/nanofluidic device owned not only experimental conveniences but also exact electrokinetic responses.

Induced-charge electrokinetics, bipolar current, and concentration polarization in a microchannel-Nafion-membrane system

The presence of a floating electrode array located within the depletion layer formed due to concentration polarization across a microchannel-membrane interface device may produce not only induced-charge electro-osmosis (ICEO) but also bipolar current resulting from the induced Faradaic reaction. It has been shown that there exists an optimal thickness of a thin dielectric coating that is sufficient to suppress bipolar currents but still enables ICEO vortices that stir the depletion layer, thereby affecting the system's current-voltage response. In addition, the use of alternating-current electro-osmosis by activating electrodes results in further enhancement of the fluid stirring and opens new routes for on-demand spatiotemporal control of the depletion layer length.

Numerical simulation of electrochemical desalination

We present an effective numerical approach to simulate electrochemically mediated desalination of seawater. This new membraneless, energy efficient desalination method relies on the oxidation of chloride ions, which generates an ion depletion zone and local electric field gradient near the junction of a microchannel branch to redirect sea salt into the brine stream, consequently producing desalted water. The proposed numerical model is based on resolution of the 3D coupled Navier-Stokes, Nernst-Planck, and Poisson equations at non-uniform spatial grids. The model is implemented as a parallel code and can be employed to simulate mass-charge transport coupled with surface or volume reactions in 3D systems showing an arbitrarily complex geometrical configuration.

Enhanced Salt Removal by Unipolar Ion Conduction in Ion Concentration Polarization Desalination

Chloride ion, the majority salt in nature, is ∼52% faster than sodium ion (DNa+ = 1.33, DCl- = 2.03[10(-9)m(2)s(-1)]). Yet, current electrochemical desalination technologies (e.g. electrodialysis) rely on bipolar ion conduction, removing one pair of the cation and the anion simultaneously. Here, we demonstrate that novel ion concentration polarization desalination can enhance salt removal under a given current by implementing unipolar ion conduction: conducting only cations (or anions) with the unipolar ion exchange membrane stack. Combining theoretical analysis, experiment, and numerical modeling, we elucidate that this enhanced salt removal can shift current utilization (ratio between desalted ions and ions conducted through electrodes) and corresponding energy efficiency by the factor ∼(D- - D+)/(D- + D+). Specifically for desalting NaCl, this enhancement of unipolar cation conduction saves power consumption by ∼50% in overlimiting regime, compared with conventional electrodialysis. Recognizing and utilizing differences between unipolar and bipolar ion conductions have significant implications not only on electromembrane desalination, but also energy harvesting applications (e.g. reverse electrodialysis).

Capillarity ion concentration polarization as spontaneous desalting mechanism

To overcome a world-wide water shortage problem, numerous desalination methods have been developed with state-of-the-art power efficiency. Here we propose a spontaneous desalting mechanism referred to as the capillarity ion concentration polarization. An ion-depletion zone is spontaneously formed near a nanoporous material by the permselective ion transportation driven by the capillarity of the material, in contrast to electrokinetic ion concentration polarization which achieves the same ion-depletion zone by an external d.c. bias. This capillarity ion concentration polarization device is shown to be capable of desalting an ambient electrolyte more than 90% without any external electrical power sources. Theoretical analysis for both static and transient conditions are conducted to characterize this phenomenon. These results indicate that the capillarity ion concentration polarization system can offer unique and economical approaches for a power-free water purification system.