Deionization shocks in microstructures

Brain-inspired computing with fluidic iontronic nanochannels

The brain's remarkable and efficient information processing capability is driving research into brain-inspired (neuromorphic) computing paradigms. Artificial aqueous ion channels are emerging as an exciting platform for neuromorphic computing, representing a departure from conventional solid-state devices by directly mimicking the brain's fluidic ion transport. Supported by a quantitative theoretical model, we present easy-to-fabricate tapered microchannels that embed a conducting network of fluidic nanochannels between a colloidal structure. Due to transient salt concentration polarization, our devices are volatile memristors (memory resistors) that are remarkably stable. The voltage-driven net salt flux and accumulation, that underpin the concentration polarization, surprisingly combine into a diffusionlike quadratic dependence of the memory retention time on the channel length, allowing channel design for a specific timescale. We implement our device as a synaptic element for neuromorphic reservoir computing. Individual channels distinguish various time series, that together represent (handwritten) numbers, for subsequent in silico classification with a simple readout function. Our results represent a significant step toward realizing the promise of fluidic ion channels as a platform to emulate the rich aqueous dynamics of the brain.

Theoretical Analysis of the Influence of Spacers on Salt Ion Transport in Electromembrane Systems Considering the Main Coupled Effects

This article considers a theoretical analysis of the influence of the main coupled effects and spacers on the transfer of salt ions in electromembrane systems (EMS) using a 2D mathematical model of the transfer process in a desalting channel with spacers based on boundary value problems for the coupled system of Nernst-Planck-Poisson and Navier-Stokes equations. The basic patterns of salt ion transport have been established, taking into account diffusion, electromigration, forced convection, electroconvection, dissociation/recombination reactions of water molecules, as well as spacers located inside the desalting channel. It has been shown that spacers and taking into account the dissociation/recombination reaction of water molecules significantly change both the formation and development of electroconvection. This article confirms the fact of the exaltation of the limiting current studied by Harkatz, where it is shown that the current (flux) of salt ions increases when the dissociation reaction begins by a certain value called the exaltation current, which is proportional to the flow of water dissociation products. A significant combined effect of electroconvection and dissociation/recombination reactions as well as the spacer system in the desalting channel on the transport of salt ions are shown. The complex, nonlinear, and non-stationary interaction of all the main effects of concentration polarization and spacers in the desalting channel are also considered in the work.

Selective and Chemical-Free Removal of Toxic Heavy Metal Cations from Water Using Shock Ion Extraction

Electrochemical methods are known to have attractive features and capabilities when used for ion separations and water purification. In this study, we developed a new process called shock ion extraction (shock IX) for selective and chemical-free removal of toxic heavy metals from water. Shock IX is a hybrid process that combines shock electrodialysis (shock ED) and ion exchange using an ion exchange resin wafer (IERW), and this method can be thought of functionally as an electrochemically assisted variation of traditional ion exchange. In particular, shock IX exhibits greater ion removal and selectivity for longer periods of time, compared to the use of ion exchange alone. The use of an IERW in shock ED also increases multivalent ion selectivity, reduces energy consumption, and improves the hydrodynamics and scalability of the system.

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.

Interfacial Resistive Switching by Multiphase Polarization in Ion-Intercalation Nanofilms

Nonvolatile resistive-switching (RS) memories promise to revolutionize hardware architectures with in-memory computing. Recently, ion-interclation materials have attracted increasing attention as potential RS materials for their ion-modulated electronic conductivity. In this Letter, we propose RS by multiphase polarization (MP) of ion-intercalated thin films between ion-blocking electrodes, in which interfacial phase separation triggered by an applied voltage switches the electron-transfer resistance. We develop an electrochemical phase-field model for simulations of coupled ion-electron transport and ion-modulated electron-transfer rates and use it to analyze the MP switching current and time, resistance ratio, and current-voltage response. The model is able to reproduce the complex cyclic voltammograms of lithium titanate (LTO) memristors, which cannot be explained by existing models based on bulk dielectric breakdown. The theory predicts the achievable switching speeds for multiphase ion-intercalation materials and could be used to guide the design of high-performance MP-based RS memories.

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.

Electroosmotic flow: From microfluidics to nanofluidics

Electroosmotic flow (EOF), a consequence of an imposed electric field onto an electrolyte solution in the tangential direction of a charged surface, has emerged as an important phenomenon in electrokinetic transport at the micro/nanoscale. Because of their ability to efficiently pump liquids in miniaturized systems without incorporating any mechanical parts, electroosmotic methods for fluid pumping have been adopted in versatile applications—from biotechnology to environmental science. To understand the electrokinetic pumping mechanism, it is crucial to identify the role of an ionically polarized layer, the so‐called electrical double layer (EDL), which forms in the vicinity of a charged solid–liquid interface, as well as the characteristic length scale of the conducting media. Therefore, in this tutorial review, we summarize the development of electrical double layer models from a historical point of view to elucidate the interplay and configuration of water molecules and ions in the vicinity of a solid–liquid interface. Moreover, we discuss the physicochemical phenomena owing to the interaction of electrical double layer when the characteristic length of the conducting media is decreased from the microscale to the nanoscale. Finally, we highlight the pioneering studies and the most recent works on electro osmotic flow devoted to both theoretical and experimental aspects.

Theory of shock electrodialysis II: Mechanisms of selective ion removal

Shock electrodialysis (shock ED), an emerging nonlinear electrokinetic process for water treatment, has recently showed its capability to selectively remove multivalent cations from electrolyte mixtures. However, the mechanisms have not been understood yet. Based on the depth-averaged model developed in the first-part of the series paper for planer shock ED system, this work focuses on the mechanisms of selective ion removal. We first assume plug feed flow and do scaling analysis, and identify three possible mechanisms of selective removal of multivalent cations: smaller concentration left behind deionization zone, affinity to the charged surface where non-slip boundary slows down the velocity, and stronger push-back by streaming potential. Then we use numerical simulations to prove our hypothesis and show additional contribution from electroosmotic flow. Simulation results show that Mg is more removed from Na-Mg-Cl mixture at overlimiting current, which is qualitatively consistent with experiment results in literature.

Desalination Performance Assessment of Scalable, Multi-Stack Ready Shock Electrodialysis Unit Utilizing Anion-Exchange Membranes

Incumbent electromembrane separation processes, including electrodialysis (ED) and electrodeionization (EDI), provide competitive techniques for desalination, selective separation, and unique solutions for ultra-pure water production. However, most of these common electrochemical systems are limited by concentration polarization and the necessity for multistep raw water pre-treatment. Shock electrodialysis (SED) utilizes overlimiting current to produce fresh, deionized water in a single step process by extending ion depleted zones that propagate through a porous medium as a sharp concentration gradient or a shock wave. So far, SED has been demonstrated on small scale laboratory units using cation-exchange membranes. In this work, we present a scalable and multi-stack ready unit with a large, 5000 mm² membrane active area designed and constructed at the Technical University of Liberec in cooperation with MemBrain s.r.o. and Mega a.s. companies (Czechia). We report more than 99% salt rejection using anion-exchange membranes, depending on a dimensionless parameter that scales the constant applied current by the limiting current. It is shown that these parameters are most probably associated with pore size and porous media chemistry. Further design changes need to be done to the separator, the porous medium, and other functional elements to improve the functionality and energy efficiency.

Breakdown of electroneutrality in nanopores

Ion transport in extremely narrow nanochannels has gained increasing interest in recent years due to unique physical properties at the nanoscale and the technological advances that allow us to study them. It is tempting to approach this confined regime with the theoretical tools and knowledge developed for membranes and microfluidic devices, and naively apply continuum models, such as the Poisson-Nernst-Planck and Navier-Stokes equations. However, it turns out that some of the most basic principles we take for granted in larger systems, such as the complete screening of surface charge by counter-ions, can break down under extreme confinement. We show that in a truly one-dimensional system of ions interacting with three-dimensional electrostatic interactions, the screening length is exponentially large, and can easily exceed the macroscopic length of a nanotube. Without screening, electroneutrality breaks down within the nanotube, with fundamental consequences for ion transport and electrokinetic phenomena. In this work, we build a general theoretical framework for electroneutrality breakdown in nanopores, focusing on the most interesting case of a one-dimensional nanotube, and show how it provides an elegant interpretation for the peculiar scaling observed in experimental measurements of ionic conductance in carbon nanotubes.

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).

Electrodialytic Processes: Market Overview, Membrane Phenomena, Recent Developments and Sustainable Strategies

In the context of preserving and improving human health, electrodialytic processes are very promising perspectives. Indeed, they allow the treatment of water, preservation of food products, production of bioactive compounds, extraction of organic acids, and recovery of energy from natural and wastewaters without major environmental impact. Hence, the aim of the present review is to give a global portrait of the most recent developments in electrodialytic membrane phenomena and their uses in sustainable strategies. It has appeared that new knowledge on pulsed electric fields, electroconvective vortices, overlimiting conditions and reversal modes as well as recent demonstrations of their applications are currently boosting the interest for electrodialytic processes. However, the hurdles are still high when dealing with scale-ups and real-life conditions. Furthermore, looking at the recent research trends, potable water and wastewater treatment as well as the production of value-added bioactive products in a circular economy will probably be the main applications to be developed and improved. All these processes, taking into account their principles and specificities, can be used for specific eco-efficient applications. However, to prove the sustainability of such process strategies, more life cycle assessments will be necessary to convince people of the merits of coupling these technologies.

Reasons for the Formation and Properties of Soliton-Like Charge Waves in Membrane Systems When Using Overlimiting Current Modes

The study of ion transport in membrane systems in overlimiting current modes is an important problem of physical chemistry and has an important application value. The influence of the space charge on the transport of salt ions under overlimiting current modes was first studied in the work of Rubinstein and Shtilman and later in the works of many authors. The purpose of this research is to study, using the method of mathematical modeling, the reasons of formation and properties of the local maximum (minimum) space charge in membrane systems under overlimiting current conditions. It is shown that, in the diffusion layer of the cation-exchange membrane (CEM), the local maximum of the space charge appears due to the limited capacity (exchange capacity) of the membrane at a given potential jump, i.e., the local maximum of space charge appears due to the presence of a local minimum of space charge at the surface of the CEM. The local maximum of the space charge moves as a single soliton-like wave into the depth of the solution. Unlike real solitons, this charged wave changes its size and shape, albeit quite slowly. In the section of the desalination channel, the situation is completely different. First, the space charge of the anion-exchange membrane (AEM) has a negative value, so we should be talking about the local minimum (or the maximum of the absolute value of the charge). However, this is an insignificant clarification. Secondly, the space charge waves of different signs begin to interact, which leads to a new effect, namely the effect of the breakdown of the space charge. The dependence of the local maximum on the input parameters—the cation diffusion coefficient, the growth rate of the potential jump, and the initial and boundary concentrations—is studied.

Biomolecule-guided cation regulation for dendrite-free metal anodes

Lithium (Li) or zinc (Zn) metal anodes have attracted interest for battery research due to their high theoretical capacities and low redox potentials. However, uncontrollable dendrite growth, especially under high current (>4 mA cm^-2), precludes reversable cycling in Li or Zn metal batteries with a high-loading (>4 mAh cm^-2), precludes reversable cycling in Li or Zn metal batteries with high-loading (>4 mAh cm^-2) cathode. We report a cation regulation mechanism to address this failure. Collagen hydrolysate coated on absorbed glass mat (CH@AGM) can simultaneously induce a deionization shock inside the separator and spread cations on the anode to promote uniform electrodeposition. Employing 24 mAh cm^-2 cathodes, Li and Zn metal batteries with CH@AGM delivered 600 cycles with a Coulombic efficiency of 99.7%. In comparison, pristine Li and Zn metal batteries only survive for 10 and 100 cycles, respectively. This approach enabled 400 cycles in a 200 Ah-class Zn metal battery, which suggests a scalable method to achieve dendrite-free anodes in various batteries.

Continuous Separation of Radionuclides from Contaminated Water by Shock Electrodialysis

The increasing popularity of nuclear energy necessitates development of new methods to treat water that becomes contaminated with radioactive substances. Because this polluted water comprises several dissolved species (not all of which are radioactive), selective accumulation of the radionuclides is desirable to minimize the volume of nuclear waste and to facilitate its containment or disposal. In this article, we use shock electrodialysis to selectively, continuously, and efficiently remove cobalt and cesium from a feed of dissolved lithium, cobalt, cesium, and boric acid. This formulation models the contaminated water commonly found in light-water reactors and in other nuclear processes. In a three-pass process, a consistent trade-off is observed between the recovery of decontaminated water and the percentage of cobalt removed, which offers flexibility in operating the system. For example, 99.5% of cobalt can be removed with a water recovery of 43%, but up to 66% of the water can be recovered if deionization of cobalt is allowed to drop to 98.3%. In general, the energy consumed during this process (ranging between 1.76 and 4.8 kW h m^-3) is low because only charged species are targeted and virtually no energy is expended removing boric acid, the most abundant species in solution.

Electrochemical impedance of electrodiffusion in charged medium under dc bias

An immobile charged species provides a charged medium for transport of charge carriers that is exploited in many applications, such as permselective membranes, doped semiconductors, biological ion channels, as well as porous media and microchannels with surface charges. In this paper, we theoretically study the electrochemical impedance of electrodiffusion in a charged medium by employing the Nernst-Planck equation and the electroneutrality condition with a background charge density. The impedance response is obtained under different dc bias conditions extending above the diffusion-limiting bias. We find a transition in the impedance behavior around the diffusion-limiting bias and present an analytical approximation for a weakly charged medium under an overlimiting bias.

Effect of surface conduction-induced electromigration on current monitoring method for electroosmotic flow measurement

Current monitoring method for measurement of EOF in microchannels involves measurement of time-varying current while an electrolyte displaces another electrolyte having different conductivity due to EOF. The basic premise of the current monitoring method is that an axial gradient in conductivity of a binary electrolyte in a microchannel advects only due to EOF. In the current work, using theory and experiments, we show that this assumption is not valid for low concentration electrolytes and narrow microchannels wherein surface conduction is comparable with bulk conduction. We show that in presence of surface conduction, a gradient in conductivity of binary electrolyte not only advects with EOF but also undergoes electromigration. This electromigration phenomenon is nonlinear and is characterized by propagation of shock and rarefaction waves in ion concentrations. Consequently, in presence of surface conduction, the current-time relationships for forward and reverse displacement in the current monitoring method are asymmetric and the displacement time is also direction dependent. To quantify the effect of surface conduction, we present analytical expressions for current-time relationship in the regime when surface conduction is comparable to bulk conduction. We validate these relations with experimental data by performing a series of current monitoring experiments in a glass microfluidic chip at low electrolyte concentrations. The experimentally validated analytical expressions for current-time relationships presented in this work can be used to correctly estimate EOF using the current monitoring method when surface conduction is not negligible.

Dynamics of driftless preconcentration using ion concentration polarization leveraged by convection and diffusion

Over the past several decades, separation and preconcentration methods of (bio)molecules have been actively developed for various biomedical and chemical processes such as disease diagnostics, point of care test and environmental monitoring. Among the great developments of the electrokinetic method in a micro/nanofluidic platform is the ion concentration polarization (ICP) phenomenon, in which a target molecule is accumulated near a permselective nanoporous membrane under an applied electric field. ICP method has been actively studied due to its easy implementation and high preconcentration/separation efficiency. However, the dynamic behavior of preconcentrated analytes has not yet been fully studied, especially driftless migration, where the applied electric field is orthogonal to the direction of the drift migration. Here, we demonstrate anomalous shapes of preconcentrated analytes (either plug or dumbbell shape) and the morphologies were analytically modeled by the leverage of convection and diffusion migration. This model was experimentally verified with various lengths of DNA and the limiting cases (convection-free environment in paper-based microfluidic device and extremely low diffusivity of red blood cells) were also shown to confirm the model. Thus, this study not only provides an insight into the fundamental electrokinetic dynamics of molecules in an ICP platform but also plays a guiding role for the design of a nanofluidic preconcentrator for a lab on a chip application.

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.

Transient response of nonideal ion-selective microchannel-nanochannel devices

We report evidence of variation in ion selectivity of a fabricated microchannel-nanochannel device resulting in the appearance of a distinct local maximum in the overlimiting chronopotentiometric response. In this system consisting of shallow microchannels joined by a nanochannel, viscous shear at the microchannel walls suppresses the electro-osmotic instability and prevents any associated contribution to the nonmonotonic response. Thus, this response is primarily electrodiffusive. Numerical simulations indicate that concentration polarization develops not only within the microchannel but also within the nanochannel itself, with a local voltage maximum in the chronopotentiometric response correlated with interfacial depletion and having the classic i^{-2} Sands time dependence. Furthermore, the occurrence of the local maxima is correlated with the change in selectivity due to internal concentration polarization. Understanding the transient nonideal permselective response is essential for obtaining fundamental insight and for optimizing efficient operation of practical fabricated nanofluidic and membrane devices.

Surface Conduction in a Microchannel

Ionic current through a microchannel has drawn significant attention not only for fundamental electrokinetic research but also for the development of novel micro/nanofluidic applications. Among various ion transport mechanisms, surface conduction, which is a predominant mechanism in micro/nanofluidic devices, has been theoretically characterized based on two-dimensional analysis. However, its infinite axis assumption has become a barrier for direct application in practical micro/nanochannel networks. In this work, we conducted rigorous experiments to include all of the three-dimensional length scales. There, L/ A, the perimeter to area ratio of the microchannel cross-section, came up as a single parameter to quantitatively interpret the surface conductive ion transportation. Overlimiting conductance of microchannel devices increased with larger perimeter, which is equivalent to specific surface area, even with the same cross sectional area. Finally, a micro/nanofluidic diode with a different L/ A value on its forward and reverse channel was demonstrated as a simple application. The analysis presented could provide a practical guideline to design a micro/nanofluidic application.

Half-Cell Ion Concentration Polarization on Nafion-Coated Electrode

On ion-selective membranes, cation/anion-selective transport under electric field initiates ion concentration polarization (ICP); ion concentration increases at one side of the membrane (ion enrichment), whereas it decreases at the other side (ion depletion). This polarization always occurs as the pair of ion enrichment and ion depletion. Departing from such pair generation, we demonstrate that only half of ICP (either ion enrichment or ion depletion) can be solitary on a Nafion-coated electrode. Current-voltage-time responses and conductance measurement capture this half-cell ICP with qualitative in situ pH/ion concentration visualization. In this half-cell, ion depletion hinders an ion flux, whereas ion enrichment facilitates the flux, so a diode-like current rectification is observed even in high-voltage regime (<±200 V) with a rectification factor up to 500. The results in this work give us deeper understanding about ICP on the electrodes and also open the possibility to use half-cell ICP as a high-voltage ionic diode and related sensing/energy applications.

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.

Electrokinetic Control of Viscous Fingering

We present a theory of the interfacial stability of two immiscible electrolytes under the coupled action of pressure gradients and electric fields in a Hele-Shaw cell or porous medium. Mathematically, our theory describes a phenomenon of "vector Laplacian growth," in which the interface moves in response to the gradient of a vector-valued potential function through a generalized mobility tensor. Physically, we extend the classical Saffman-Taylor problem to electrolytes by incorporating electrokinetic (EK) phenomena. A surprising prediction is that viscous fingering can be controlled by varying the injection ratio of electric current to flow rate. Beyond a critical injection ratio, stability depends only upon the relative direction of flow and current, regardless of the viscosity ratio. Possible applications include porous materials processing, electrically enhanced oil recovery, and EK remediation of contaminated soils.

Multiscale Model for Electrokinetic Transport in Networks of Pores, Part II: Computational Algorithms and Applications

The first part of this two-article series presented a robust mathematical model for the fast and accurate prediction of electrokinetic phenomena in porous networks with complex topologies. In the second part of this series, we first present a numerical algorithm that can efficiently solve the model equations. We then demonstrate that the resulting framework is capable of capturing a wide range of transport phenomena in microstructures by considering a hierarchy of canonical problems with increasing complexity. The developed framework is validated against direct numerical simulations of deionization shocks in micropore-membrane junctions and concentration polarization in micro- and nanochannel systems. We demonstrate that for thin pores subject to concentration gradients our model consistently captures correct induced osmotic pressure, which is a macroscopic phenomena originally derived from thermodynamic principles but here is naturally predicted through microscopic electrostatic interactions. Moreover, we show that the developed model captures current rectification phenomena in a conical nanopore subject to an axial external electric field. Finally, we provide discussions on examples involving stationary and moving deionization shocks in micropore nanopore T-junctions as well as induced-flow loops when pores of varying sizes are connected in parallel.

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.

Electrohydrodynamic instability of ion-concentration shock wave in electrophoresis

Capillary electrophoresis techniques often involve ion-concentration shock waves in an electrolyte solution, propagating under the effect of an external electric field. These shock waves are characterized by self-sharpening gradients in ion concentrations and electrical conductivity that are collinear with the electric field. The coupling of electric field and fluid motion at the shock interface sometimes leads to an undesirable electrohydrodynamic (EHD) instability. Using linear stability analysis, we describe the motion of small-amplitude disturbances of an electrophoretic shock wave. Our analysis shows that the EHD instability results due to the competition between destabilizing electroviscous flow and stabilizing electromigration of the shock wave. The ratio of timescales corresponding to electroviscous flow and electromigration yields a threshold criterion for the onset of instability. We present a validation of this threshold criterion with published experimental data and also describe the physical mechanism underlying the EHD instability of the electrophoretic shock wave.

Theory of linear sweep voltammetry with diffuse charge: Unsupported electrolytes, thin films, and leaky membranes

Linear sweep and cyclic voltammetry techniques are important tools for electrochemists and have a variety of applications in engineering. Voltammetry has classically been treated with the Randles-Sevcik equation, which assumes an electroneutral supported electrolyte. In this paper, we provide a comprehensive mathematical theory of voltammetry in electrochemical cells with unsupported electrolytes and for other situations where diffuse charge effects play a role, and present analytical and simulated solutions of the time-dependent Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions for a 1:1 electrolyte and a simple reaction. Using these solutions, we construct theoretical and simulated current-voltage curves for liquid and solid thin films, membranes with fixed background charge, and cells with blocking electrodes. The full range of dimensionless parameters is considered, including the dimensionless Debye screening length (scaled to the electrode separation), Damkohler number (ratio of characteristic diffusion and reaction times), and dimensionless sweep rate (scaled to the thermal voltage per diffusion time). The analysis focuses on the coupling of Faradaic reactions and diffuse charge dynamics, although capacitive charging of the electrical double layers is also studied, for early time transients at reactive electrodes and for nonreactive blocking electrodes. Our work highlights cases where diffuse charge effects are important in the context of voltammetry, and illustrates which regimes can be approximated using simple analytical expressions and which require more careful consideration.

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).

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.

Stabilizing electrodeposition in elastic solid electrolytes containing immobilized anions

Ion transport-driven instabilities in electrodeposition of metals that lead to morphological instabilities and dendrites are receiving renewed attention because mitigation strategies are needed for improving rechargeability and safety of lithium batteries. The growth rate of these morphological instabilities can be slowed by immobilizing a fraction of anions within the electrolyte to reduce the electric field at the metal electrode. We analyze the role of elastic deformation of the solid electrolyte with immobilized anions and present theory combining the roles of separator elasticity and modified transport to evaluate the factors affecting the stability of planar deposition over a wide range of current densities. We find that stable electrodeposition can be easily achieved even at relatively high current densities in electrolytes/separators with moderate polymer-like mechanical moduli, provided a small fraction of anions are immobilized in the separator.

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.

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.