Coupled concentration polarization and electroosmotic circulation near micro/nanointerfaces: Taylor-Aris model of hydrodynamic dispersion and limits of its applicability

Differential Impact of Surface Conduction and Electroosmotic Flow on Ion Transport Enhancement by Microscale Auxiliary Structures

Our research investigates the impact of auxiliary structures on ion transport in electrochemical systems such as batteries and microscale desalination units, whose importance for sustainable development has increased dramatically in recent decades. The electrochemical systems typically feature ion-selective surfaces, such as electrodes and ion exchange membranes, where ion depletion can cause performance issues including metal dendrite formation and flow instability. Recent research has shown that auxiliary structures in these electrochemical systems can enhance ion transfer near ion-selective surfaces, thereby resolving the instability problem and improving the energy conversion efficiency of the system. Our study leverages recent advancements in nanoscale electrokinetics to model these auxiliary structures as pillar arrays near an ion exchange membrane in a microchannel. We examine how these structures enhance ion transports relative to the characteristic length scale of microchannel depth and pillars' proximity to the ion-selective surface. Results show that the effect of the pillars varies significantly with their placement. Specifically, in deeper microchannels, where electrokinetic convection is stronger, the closer the auxiliary structure is to the ion-selective membrane, the better the ion transfer. However, in the thinner microchannel, the proximity of the auxiliary structure to the ion selective membrane has a less significant correlation with the ion transfer. Therefore, this finding highlights the importance of spatial arrangement of the auxiliary structures in improving the performance of electrochemical devices. Conclusively, this study can help to better understand energy conversion systems such as fuel cells, salinity gradient power generation systems, and electrochemical desalination systems, where auxiliary structures can be used in the vicinity of ion-selective surfaces. Especially, our fundamental electrokinetic study provides an effective means for designing the efficient electrochemical platforms utilizing micro/nanofluidics.

Electrochemical Methods for Water Purification, Ion Separations, and Energy Conversion

Agricultural development, extensive industrialization, and rapid growth of the global population have inadvertently been accompanied by environmental pollution. Water pollution is exacerbated by the decreasing ability of traditional treatment methods to comply with tightening environmental standards. This review provides a comprehensive description of the principles and applications of electrochemical methods for water purification, ion separations, and energy conversion. Electrochemical methods have attractive features such as compact size, chemical selectivity, broad applicability, and reduced generation of secondary waste. Perhaps the greatest advantage of electrochemical methods, however, is that they remove contaminants directly from the water, while other technologies extract the water from the contaminants, which enables efficient removal of trace pollutants. The review begins with an overview of conventional electrochemical methods, which drive chemical or physical transformations via Faradaic reactions at electrodes, and proceeds to a detailed examination of the two primary mechanisms by which contaminants are separated in nondestructive electrochemical processes, namely electrokinetics and electrosorption. In these sections, special attention is given to emerging methods, such as shock electrodialysis and Faradaic electrosorption. Given the importance of generating clean, renewable energy, which may sometimes be combined with water purification, the review also discusses inverse methods of electrochemical energy conversion based on reverse electrosorption, electrowetting, and electrokinetic phenomena. The review concludes with a discussion of technology comparisons, remaining challenges, and potential innovations for the field such as process intensification and technoeconomic optimization.

Theory of shock electrodialysis I: Water dissociation and electrosmotic vortices

Shock electrodialysis (shock ED), an emerging electrokinetic process for water purification, leverages the new physics of deionization shock waves in porous media. In previous work, a simple leaky membrane model with surface conduction can explain the propagation of deionization shocks in a shock ED system, but it cannot quantitatively predict the deionization and conductance (which determines the energy consumption), and it cannot explain the selective removal of ions in experiments. This two-part series of work establishes a more comprehensive model for shock ED, which applies to multicomponent electrolytes and any electrical double layer thickness, captures the phenomena of electroosmosis, diffusioosmosis, and water dissociation, and incorporates more realistic boundary conditions. In this paper, we will present the model details and show that hydronium transport and electroosmotic vortices (at the inlet and outlet) play important roles in determining the deionization and conductance in shock ED. We also find that the results are quantitatively consistent with experimental data in the literature. Finally, the model is used to investigate design strategies for scale up and optimization.

Novel ionic separation mechanisms in electrically driven membrane processes

Electromembrane processes including electrodialysis (ED) and related processes are usually limited by diffusion transport of ions from a bulk solution to ion exchange membranes. The diffusion limited current (DLC) occurs when the concentration at membrane surfaces vanishes and approaches zero. Increasing the applied potential difference above this point has no substantial effect on ion transport and causes operational problems such as low current efficiency, high energy consumption, and mineral scaling. However, it is evident from numerous studies that operating at overlimiting current (OLC) is possible and allows one to enhance the mass transfer of an electromembrane process. While OLC is sometimes possible by electrochemical means, such as water splitting or current induced membrane discharge, it has been found that exotic ion transport mechanisms, such as ion concentration polarization in micro/nanofluidic system, deionization shock waves, and ionic bridges, can provide novel electrokinetic means of achieving OLC. In this paper, these novel ionic separation mechanisms and their role in enhanced current transfer are reviewed in the context of emerging electromembrane processes, such as shock ED and electrodeionization (EDI).

Water Desalination by Flow-Electrode Capacitive Deionization in Overlimiting Current Regimes

Since flow-electrodes do not have a maximum allowable charge capacity, a high salt removal rate in flow-electrode capacitive deionization (FCDI) can be achieved theoretically by simply increasing the applied voltage. However, present attempts to run FCDI at high voltages are unsatisfactory because of the instability of the module occurring in the overlimiting current regimes. To implement FCDI in the overlimiting current regimes (namely, OLC-FCDI), in this work, we analyzed the voltage-current (V-I) characteristics of several FCDI units. We confirmed that a continuous, rapid, and stable desalination performance of OLC-FCDI can be attained when the employed FCDI unit possesses a linear V-I characteristic (only one ohmic regime), which is distinct from the three V-I regimes in electrodialysis (ohmic, limiting current, and water splitting regimes) and the two in membrane capacitive deionization (ohmic and water splitting regimes). Notably, the linearV-I characteristic of FCDI requires continuous charge percolation near the boundaries of ion-exchange membranes. Effective methods include increasing the carbon content in the flow-electrodes and introducing electrical (carbon cloth) or ionic (ion-exchange resins) conductive intermediates in the solution compartment, which result in corresponding upgraded FCDI units exhibiting extremely high salt removal rates (>100 mg m^-2 s^-1), good cycling stability, and rapid seawater desalination performance under typical OLC-FCDI operation condition (27-40 g L^-1 NaCl, 500 mA). This study can guide future research of FCDI in terms of flow-electrode preparation and device configuration optimization.

Surface conduction and electroosmotic flow around charged dielectric pillar arrays in microchannels

Dielectric microstructures have been reported to have a negative influence on permselective ion transportation because ions do not migrate in areas where the structures are located. However, the structure can promote the transportation if the membrane is confined to a microscopic scale. In such a scale where the area to volume ratio is significantly large, the primary driving mechanisms of the ion transportation transition from electro-convective instability (EOI) to surface conduction (SC) and electroosmotic flow (EOF). Here, we provide rigorous evidence on how the SC and EOF around the dielectric microstructures can accelerate the ion transportation by multi-physics simulations and experimental visualizations. The microstructures further polarize the ion distribution by SC and EOF so that ion carriers can travel to the membrane more efficiently. Furthermore, we verified, for the first time, that the arrangements of microstructures have a critical impact on the ion transportation. While convective flows are isolated in the crystal pillar configuration, the flows show an elongated pattern and create an additional path for ion current in the aligned pillar configuration. Therefore, the fundamental findings of the electrokinetic effects on the dielectric microstructures suggest an innovative application in micro/nanofluidic devices with high mass transport efficiency.

Novel Electrochemical Flow Sensor Based on Sensing the Convective-Diffusive Ionic Concentration Layer

Presented is a novel flow sensor based on electrochemical sensing of the ionic concentration-polarization (CP) layer developed within a microchannel-ion permselective membrane device. To demonstrate the working principle of the electrochemical flow sensor, the effect of advection on the transient and steady-state ionic concentration-polarization (CP) phenomenon in microchannel-Nafion membrane systems is studied. In particular, we focused on the local impedance, measured using an array of electrode pairs embedded at the bottom of the microchannel, as well as the total current across the permselective medium, as two approaches for estimating the flow. We examined both a stepwise application of CP under steady-state flow and a stepwise application of flow under steady-state CP.

High-performance bioanalysis based on ion concentration polarization of micro-/nanofluidic devices

Micro-/nanofluidics has received considerable attention over the past two decades, which allows efficient biomolecule trapping and preconcentration due to ion concentration polarization (ICP) within nanostructures. The rich scientific content related to ICP has been widely exploited in different applications including protein concentration, biomolecules sensing and detection, cell analysis, and water purification. Compared to pure microfluidic devices, micro-/nanofluidic devices show a highly efficient sample enrichment capacity and nonlinear electrokinetic flow feature. These two unique characterizations make the micro-/nanofluidic systems promising in high-performance bioanalysis. This review provides a comprehensive description of the ICP phenomenon and its applications in bioanalysis. Perspectives are also provided for future developments and directions of this research field.

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.

Effect of advection on transient ion concentration-polarization phenomenon

Here, we studied the effect of advection on the transient ion concentration-polarization phenomenon in microchannel-membrane systems. Specifically, the temporal evolution of the depletion layer in a system that supports net flow rates with varying Péclet values was examined. Experiments complemented with simplified analytical one-dimensional semi-infinite modeling and numerical simulations demonstrated either suppression or enhancement of the depletion layer propagation against or with the direction of the net flow, respectively. Of particular interest was the third-species fluorescent dye ion concentration-polarization dynamics which was further explained using two-dimensional numerical simulations that accounted for the device complex geometry.

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.

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.

Dendrite Suppression by Shock Electrodeposition in Charged Porous Media

It is shown that surface conduction can stabilize electrodeposition in random, charged porous media at high rates, above the diffusion-limited current. After linear sweep voltammetry and impedance spectroscopy, copper electrodeposits are visualized by scanning electron microscopy and energy dispersive spectroscopy in two different porous separators (cellulose nitrate, polyethylene), whose surfaces are modified by layer-by-layer deposition of positive or negative charged polyelectrolytes. Above the limiting current, surface conduction inhibits growth in the positive separators and produces irregular dendrites, while it enhances growth and suppresses dendrites behind a deionization shock in the negative separators, also leading to improved cycle life. The discovery of stable uniform growth in the random media differs from the non-uniform growth observed in parallel nanopores and cannot be explained by classic quasi-steady "leaky membrane" models, which always predict instability and dendritic growth. Instead, the experimental results suggest that transient electro-diffusion in random porous media imparts the stability of a deionization shock to the growing metal interface behind it. Shock electrodeposition could be exploited to enhance the cycle life and recharging rate of metal batteries or to accelerate the fabrication of metal matrix composite coatings.

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.

Analysis of electrolyte transport through charged nanopores

We revisit the classical problem of flow of electrolyte solutions through charged capillary nanopores or nanotubes as described by the capillary pore model (also called "space charge" theory). This theory assumes very long and thin pores and uses a one-dimensional flux-force formalism which relates fluxes (electrical current, salt flux, and fluid velocity) and driving forces (difference in electric potential, salt concentration, and pressure). We analyze the general case with overlapping electric double layers in the pore and a nonzero axial salt concentration gradient. The 3×3 matrix relating these quantities exhibits Onsager symmetry and we report a significant new simplification for the diagonal element relating axial salt flux to the gradient in chemical potential. We prove that Onsager symmetry is preserved under changes of variables, which we illustrate by transformation to a different flux-force matrix given by Gross and Osterle [J. Chem. Phys. 49, 228 (1968)JCPSA60021-960610.1063/1.1669814]. The capillary pore model is well suited to describe the nonlinear response of charged membranes or nanofluidic devices for electrokinetic energy conversion and water desalination, as long as the transverse ion profiles remain in local quasiequilibrium. As an example, we evaluate electrical power production from a salt concentration difference by reverse electrodialysis, using an efficiency versus power diagram. We show that since the capillary pore model allows for axial gradients in salt concentration, partial loops in current, salt flux, or fluid flow can develop in the pore. Predictions for macroscopic transport properties using a reduced model, where the potential and concentration are assumed to be invariant with radial coordinate ("uniform potential" or "fine capillary pore" model), are close to results of the full model.

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}.

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.

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.

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.

Over-limiting current and control of dendritic growth by surface conduction in nanopores

Understanding over-limiting current (faster than diffusion) is a long-standing challenge in electrochemistry with applications in desalination and energy storage. Known mechanisms involve either chemical or hydrodynamic instabilities in unconfined electrolytes. Here, it is shown that over-limiting current can be sustained by surface conduction in nanopores, without any such instabilities, and used to control dendritic growth during electrodeposition. Copper electrodeposits are grown in anodized aluminum oxide membranes with polyelectrolyte coatings to modify the surface charge. At low currents, uniform electroplating occurs, unaffected by surface modification due to thin electric double layers, but the morphology changes dramatically above the limiting current. With negative surface charge, growth is enhanced along the nanopore surfaces, forming surface dendrites and nanotubes behind a deionization shock. With positive surface charge, dendrites avoid the surfaces and are either guided along the nanopore centers or blocked from penetrating the membrane.

Concentration polarization, surface currents, and bulk advection in a microchannel

We present a comprehensive analysis of salt transport and overlimiting currents in a microchannel during concentration polarization. We have carried out full numerical simulations of the coupled Poisson-Nernst-Planck-Stokes problem governing the transport and rationalized the behavior of the system. A remarkable outcome of the investigations is the discovery of strong couplings between bulk advection and the surface current; without a surface current, bulk advection is strongly suppressed. The numerical simulations are supplemented by analytical models valid in the long channel limit as well as in the limit of negligible surface charge. By including the effects of diffusion and advection in the diffuse part of the electric double layers, we extend a recently published analytical model of overlimiting current due to surface conduction.

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.

Overlimiting current and shock electrodialysis in porous media

Most electrochemical processes, such as electrodialysis, are limited by diffusion, but in porous media, surface conduction and electroosmotic flow also contribute to ionic flux. In this article, we report experimental evidence for surface-driven overlimiting current (faster than diffusion) and deionization shocks (propagating salt removal) in a porous medium. The apparatus consists of a silica glass frit (1 mm thick with a 500 nm mean pore size) in an aqueous electrolyte (CuSO4 or AgNO3) passing ionic current from a reservoir to a cation-selective membrane (Nafion). The current-voltage relation of the whole system is consistent with a proposed theory based on the electroosmotic flow mechanism over a broad range of reservoir salt concentrations (0.1 mM to 1.0 M) after accounting for (Cu) electrode polarization and pH-regulated silica charge. Above the limiting current, deionized water (≈10 μM) can be continuously extracted from the frit, which implies the existence of a stable shock propagating against the flow, bordering a depleted region that extends more than 0.5 mm across the outlet. The results suggest the feasibility of shock electrodialysis as a new approach to water desalination and other electrochemical separations.

Over-limiting currents and deionization "shocks" in current-induced polarization: local-equilibrium analysis

The problem is considered theoretically of dynamics of current-induced concentration polarization of interfaces between ideally perm-selective and non-ideally perm-selective ("leaky") ion-exchange media in binary electrolyte solutions under galvanostatic conditions and at negligible volume flow. In contrast to the previous studies, the analysis is systematically carried out in terms of local thermodynamic equilibrium in the approximation of local electric neutrality in virtual solution. For macroscopically homogeneous media, this enables one to obtain model-independent results in quadratures for the stationary state as well as an approximate scaling-form solution for the transient response to the step-wise increase in electric-current density. These results are formulated in terms of such phenomenological properties of the "leaky" medium as ion transport numbers, diffusion permeability to salt and specific chemical capacity. An easy-to-solve numerically 1D PDE is also formulated in the same terms. A systematic parametric study is carried out within the scope of fine-pore model of "leaky" medium in terms of such properties as volumetric concentration of fixed electric charges and diffusivities of ions of symmetrical electrolyte. While previous studies paid principal attention to the shape and propagation rate of the so-called deionization "shocks", we also consider in detail the time evolution of voltage drop and interface salt concentration. Our analysis confirms the previously predicted pattern of propagating deionization "shocks" within the "leaky" medium but also reveals several novel features. In particular, we demonstrate that the deionization-shock pattern is really pronounced only at intermediate ratios of fixed-charge concentration to the initial salt concentration and at quite high steady-state voltages where the model used in this and previous studies is applicable only at relatively early stages of concentration-polarization process.

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.

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.