On the Dynamical Regimes of Pattern-Accelerated Electroconvection

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.

Research on Membranes and Their Associated Processes at the Université Paris-Est Créteil: Progress Report, Perspectives, and National and International Collaborations

Research on membranes and their associated processes was initiated in 1970 at the University of Paris XII/IUT de Créteil, which became in 2010 the University Paris-Est Créteil (UPEC). This research initially focused on the development and applications of pervaporation membranes, then concerned the metrology of ion-exchange membranes, then expanded to dialysis processes using these membranes, and recently opened to composite membranes and their applications in production or purification processes. Both experimental and fundamental aspects have been developed in parallel. This evolution has been reinforced by an opening to the French and European industries, and to the international scene, especially to the Krasnodar Membrane Institute (Kuban State University-Russia) and to the Department of Chemistry, (Qassim University-Saudi Arabia). Here, we first presented the history of this research activity, then developed the main research axes carried out at UPEC over the 2012-2022 period; then, we gave the main results obtained, and finally, showed the cross contribution of the developed collaborations. We avoided a chronological presentation of these activities and grouped them by theme: composite membranes and ion-exchange membranes. For composite membranes, we have detailed three applications: highly selective lithium-ion extraction, bleach production, and water and industrial effluent treatments. For ion-exchange membranes, we focused on their characterization methods, their use in Neutralization Dialysis for brackish water demineralization, and their fouling and antifouling processes. It appears that the research activities on membranes within UPEC are very dynamic and fruitful, and benefit from scientific exchanges with our Russian partners, which contributed to the development of strong membrane activity on water treatment within Qassim University. Finally, four main perspectives of this research activity were given: the design of autonomous and energy self-sufficient processes, refinement of characterization by Electrochemical Scanning Microscopy, functional membrane separators, and green membrane preparation and use.

Electroconvective Flow in Liquid Electrolytes Containing Oligomer Additives

Metal electrodeposition in batteries is fundamentally unstable and affected by different instabilities depending on operating conditions and electrolyte chemistry. Particularly, at high charging rates, a hydrodynamic instability loosely termed electroconvection sets in, which complicates all electrochemical processes by creating a nonuniform ion flux and preferential deposition at the electrode. Here, we isolate and study electroconvection by experimentally investigating how oligomer additives in liquid electrolytes interact with the hydrodynamic instability at a cation selective interface. From electrochemical measurements and direct visualization experiments, we find that electroconvection is delayed and suppressed at all voltages in the presence of oligomers. The underlying mechanism is revealed to involve formation of an oligomer ad-layer at the interface, which in response to perturbation is believed to exert an opposing body force on the surrounding fluid to preserve the ad-layer structure and in so doing suppresses electroconvection. Our results therefore reveal that in battery electrolytes without obvious sources of bulk elasticity, surface forces produced by adsorbed polymers can be used to advantage for suppressing instability.

Current-Voltage Characteristics of Membranes with Different Cation-Exchanger Content in Mineral Salt-Neutral Amino Acid Solutions under Electrodialysis

The features of the electrochemical behavior of experimental heterogeneous ion-exchange membranes with different mass fractions of sulfonated cation-exchange resin (from 45 to 65 wt%) have been studied by voltammetry during electrodialysis. Electromembrane systems with 0.01 M NaCl solution and with a mixed 0.01 M NaCl + 0.05 M phenylalanine (Phe) solution have been investigated. A significant influence of the ion-exchanger content on the parameters of current-voltage curves (CVCs) was established for the first time. Electrodialysis of the sodium chloride solution revealed a decrease in the length of the limiting current plateau and in the resistances of the second and third sections of the CVCs with an increase in the resin content in the membrane. The fact of the specific shape of the CVCs of all studied cation-exchange membrane samples in mixed solutions of the mineral salt and the amino acid was established. A specific feature of current-voltage curves is the presence of two plateaus of the limiting current and two values of the limiting current, respectively. This phenomenon in electromembrane systems with neutral amino acids has not been found before. The value of the first limiting current is determined by cations of the mineral salt, which are the main current carriers in the system. The presence of the second plateau and the corresponding second limiting current is due to the appearance of additional carriers due to the ability of phenylalanine as an organic ampholyte to participate in protolytic reactions. In the cation-exchange electromembrane system with the phenylalanine containing solution, two mechanisms of H⁺/OH^- ion generation through water splitting and acid dissociation are shown. The possibility of the generation of H⁺/OH^- ions at the enriched solution/cation-exchange membrane interface during electrodialysis of amino acid containing solutions is shown for the first time. The results of this study can be used to improve the process of electromembrane demineralization of neutral amino acid solutions by both targeted selection or the creation of new membranes and the selection of effective current operating modes.

Efficient Anion-Exchange Membranes with Anti-Scaling Properties Obtained by Surface Modification of Commercial Membranes Using a Polyquaternium-22

Anion-exchange membranes modified with a polyquaternium-22 (PQ-22) polymer were studied for their use in electrodialysis. The use of PQ-22 for modification makes it possible to "replace" weakly basic amino groups on the membrane surface with quaternary amino groups. It was found that the content of quaternary amino groups in PQ-22 is higher than the content of carboxyl groups, which is the reason for the effectiveness of this polymer even when modifying Ralex AHM-PES membranes that initially contain only quaternary amino groups. In the case of membranes containing weakly basic amino groups, the PQ-22 polymer modification efficiency is even higher. The surface charge of the modified MA-41P membrane increased, while the limiting current density on the current-voltage curves increased by more than 1.5 times and the plateau length decreased by 2.5 times. These and other characteristics indicate that the rate of water splitting decreased and the electroconvective mixing at the membrane surface intensified, which was confirmed by direct visualization of vortex structures. Increasing the surface charge of the commercial MA-41P anion-exchange membrane, reducing the rate of water splitting, and enhancing electroconvection leads to mitigated scaling on its surface during electrodialysis.

Measurement of Electrokinetically induced hydrodynamics at Ion-selective interfaces using 3D Micro particle tracking velocimetry (µPTV)

Electrokinetic flow phenomena are ubiquitous in electrical systems for desalination, chemical conversion, or mixing at a micro-scale. However, the important features of resulting 3D flow fields are only accessible through cost-intensive numerical simulations. Experimental 2D recording of the chaotic three-dimensional velocity fields developing for example at currents exceeding the limiting current density does not capture the complex 3D structures present in such flow fields. Additionally, numerical 3D studies are limited to dimensions three orders of magnitude smaller as found in real applications and only short run times due to the enormous computational effort. To apply the theoretical knowledge in real-world systems and create the possibility for detailed parameter studies, we present the first experimental method for recording and quantifying the time-resolved velocity field in an electrochemical microfluidic cell in 3D with dimensions found in industrial applications. We utilize this method in a co-submitted paper to record the 3D velocity field of electroconvection at a cation-exchange membrane.•

Cell design suitable for simultaneous electrochemical experiments with optical 3D velocity quantification

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Method optimized for velocity reconstruction of membrane-to-membrane distances found in industrial cells

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Highly adaptable cell design, for optical characterization of electrochemical systems

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.

Observation of Remote Electroconvection and Inert-Cation Concentration Valley within Supporting Electrolytes in a Microfluidic-Based Electrochemical Device

The electrochemical system is playing an increasingly important role in the advanced technology development for drinkable water and energy storage. While the binary electrolyte has been widely studied, such as the associated intriguing interfacial instabilities, multi-component electrolyte is by far less known. Here, based on the classic Cu|CuSO₄ |Cu electrochemical system, the effect of supporting electrolyte is systematically investigated by highlighting the inert cations. In an annulus microfluidic device, the suppression of a previously known electro-osmotic instability and the emergence of an array of the remote electroconvection along the azimuthal direction is found. A distinctive inert-cation concentration valley propagates radially outward at a speed limited by the electromigration velocity. Remarkably, the simultaneous visualization of spatiotemporal evolution demonstrates the correlation of the concentration valley and electroconvection at a microscopic level. The underlying physical mechanism of their correlation is discussed, and the scaling analysis agrees with experiments. This work might inspire more future work on the multi-component electrolyte, such as for the suppression of interfacial hydrodynamic instability and mitigation of dendrite growth, with the technological implications for water treatment and energy storage in batteries.

Experimental Study on Ion Transport in Microfluidic Electrodialysis Using Partially Masked Ion Exchange Membranes

Electrodialysis using anion-exchange membranes (AEMs) and cation-exchange membranes (CEMs) has been widely used for water desalination and the management of various ionic species. During commercial electrodialysis, the available area of an ion-exchange membrane is reduced by a non-conductive spacer that is in contact with the AEM/CEM. Although multiple reports have described the advantages or disadvantages of spacers, fewer studies have explored the effects of spacers on the mass transport effect of the reduced membrane area excluding the fluid flow change. In this paper, we present our experimental studies concerning mass transport in microfluidic electrodialysis systems with partially masked ion-exchange membranes. Six different types of masking membranes were prepared by the deposition of non-conductive films on parts of the membranes. The experimental results showed that the overlapped types (in which masking was vertically aligned in the AEM/CEM) exhibited a larger electrical conductance and better current/energy efficiency, compared with the non-overlapped types (in which masking was vertically dislocated in the AEM/CEM). We also observed that a reduction in the unit length of the unmasked ion-exchange membrane enhanced overall mass transport. Our results demonstrate the effects of patterned membranes on electrical resistance and desalination performance; they also identify appropriate arrangements for electromembrane systems.

A Review on Ion-Exchange Membranes Fouling during Electrodialysis Process in Food Industry, Part 2: Influence on Transport Properties and Electrochemical Characteristics, Cleaning and Its Consequences

Ion-exchange membranes (IEMs) are increasingly used in dialysis and electrodialysis processes for the extraction, fractionation and concentration of valuable components, as well as reagent-free control of liquid media pH in the food industry. Fouling of IEMs is specific compared to that observed in the case of reverse or direct osmosis, ultrafiltration, microfiltration, and other membrane processes. This specificity is determined by the high concentration of fixed groups in IEMs, as well as by the phenomena inherent only in electromembrane processes, i.e., induced by an electric field. This review analyzes modern scientific publications on the effect of foulants (mainly typical for the dairy, wine and fruit juice industries) on the structural, transport, mass transfer, and electrochemical characteristics of cation-exchange and anion-exchange membranes. The relationship between the nature of the foulant and the structure, physicochemical, transport properties and behavior of ion-exchange membranes in an electric field is analyzed using experimental data (ion exchange capacity, water content, conductivity, diffusion permeability, limiting current density, water splitting, electroconvection, etc.) and modern mathematical models. The implications of traditional chemical cleaning are taken into account in this analysis and modern non-destructive membrane cleaning methods are discussed. Finally, challenges for the near future were identified.

Conceptual Progress for Explaining and Predicting Self-Organization on Anodized Aluminum Surfaces

Over the past few years, researchers have made numerous breakthroughs in the field of aluminum anodizing and faced the problem of the lack of adequate theoretical models for the interpretation of some new experimental findings. For instance, spontaneously formed anodic alumina nanofibers and petal-like patterns, flower-like structures observed under AC anodizing conditions, and hierarchical pores whose diameters range from several nanometers to sub-millimeters could be explained neither by the classical field-assisted dissolution theory nor by the plastic flow model. In addition, difficulties arose in explaining the basic indicators of porous film growth, such as the nonlinear current–voltage characteristics of electrochemical cells or the evolution of hexagonal pore patterns at the early stages of anodizing experiments. Such a conceptual crisis resulted in new multidisciplinary investigations and the development of novel theoretical models, whose evolution is discussed at length in this review work. The particular focus of this paper is on the recently developed electroconvection-based theories that allowed making truly remarkable advances in understanding the porous anodic alumina formation process in the last 15 years. Some explanation of the synergy between electrode reactions and transport processes leading to self-organization is provided. Finally, future prospects for the synthesis of novel anodic architectures are discussed.

Investigation of ion-exchange membranes by means of chronopotentiometry: A comprehensive review on this highly informative and multipurpose technique

Electrodialysis is mostly used for drinking water production but it has gained applicability in different new fields in recent decades. Membrane characteristics and ion transport properties strongly influence the efficiency of electrodialysis and must be evaluated to avoid an intense energy consumption and ensure long membrane times of usage. To this aim, conducting studies on ion transport across membranes is essential. Several dynamic characterization methods can be employed, among which, chronopotentiometry has shown special relevance because it allows a direct access to the contribution of the potential in different states of the membrane/solution system. The present paper provides a critical review on the use of chronopotentiometry to determine the main membrane transport properties and to evaluate mass transfer phenomena. Properties, such as limiting current density, electrical resistances, plateau length, transport number of counter-ions in the membrane, transition times, and apparent fraction of membrane conductive area have been intensively discussed in the literature and are presented in this review. Some of the phenomena evaluated using this technique are concentration polarization, gravitational convection, electroconvection, water dissociation, and fouling/scaling, all of them also shown herein. Mathematical and experimental studies were considered. New trends in chronopotentiometric studies should include ion-exchange membranes that have been recently developed (presenting anti-fouling, anti-microbial, and monovalent-selective properties) and a deeper discussion on the behaviour of complex solutions that have been often treated by electrodialysis, such as municipal wastewaters. New mathematical models, especially 3D ones, are also expected to be developed in the coming years.

Pulsed electric field-assisted overlimiting current enhancement through a perm-selective membrane

Overlimiting current through a perm-selective membrane has been actively researched not only for the fundamental advancement of electrokinetics but also for energy/environmental applications such as electrodialysis, fuel cells, etc. In particular, various strategies were reported for the enhancement of overlimiting current because these applications demand efficient mass transport through the membrane. In this work, we presented in operando visualization and rigorous numerical study for the overlimiting current density enhancement using a pulsed electric field which is one of the most cost-effective parameters to be externally controlled. We clearly demonstrated that the current density had a peak value as a function of the pulse frequency and would suggest its correlation to a concentration profile and diffusion relaxation time ([small tau, Greek, tilde]diff). As the pulse frequency was chosen which is similar to ([small tau, Greek, tilde]diff)-1, the concentration profiles (i.e. established current paths) were maintained even in off-state due to remnant current paths helping the fast ion transportation. The fundamental evidence presented in this work would provide a strategical design of a perm-selective membrane system for a higher mass transportation efficiency.

Structure and Dynamics of Electric-Field-Driven Convective Flows at the Interface between Liquid Electrolytes and Ion-Selective Membranes

At voltages above a certain critical value, V_c ≈ 20 kT/e, a space charge layer forms near ion-selective interfaces in liquid electrolytes. Interactions between the space charge and an imposed electric field drives a hydrodynamic instability known as electroconvection. Through particle tracking velocimetry we experimentally study the structure and dynamics of the resultant electroconvective flow. Consistent with previous numerical simulations, we report that, following imposition of a sufficiently large voltage, electroconvection develops gradually as pairs of counter-rotating vortices, which nucleate at the interface between an ion-selective substrate and a liquid electrolyte. Depending on the imposed voltage and cell geometry, the vorticies grow to length scales of hundreds of micrometers. Electroconvective flows are also reported to be structured and multiscale, with the size ratio of the largest to the smallest observable vortices inversely proportional to the Debye screening length.

Suppression of dendrite growth by cross-flow in microfluidics

Formation of rough, dendritic deposits is a critical problem in metal electrodeposition processes and could occur in next-generation, rechargeable batteries that use metallic electrodes. Electroconvection, which originates from the coupling of the imposed electric field and a charged fluid near an electrode surface, is believed to be responsible for dendrite growth. However, few studies are performed at the scale of fidelity where root causes and effective strategies for controlling electroconvection and dendrite growth can be investigated in tandem. Using microfluidics, we showed that forced convection across the electrode surface (cross-flow) during electrodeposition reduced metal dendrite growth (97.7 to 99.4%) and delayed the onset of electroconvective instabilities. Our results highlighted the roles of forced convection in reducing dendrite growth and electroconvective instabilities and provided a route toward effective strategies for managing the consequences of instability in electrokinetics-based processes where electromigration dominates ion diffusion near electrodes.

Novel Homogeneous Anion Exchange Membranes for Reproducible and Sensitive Nucleic Acid Detection via Current-Voltage Characteristic Measurement

One-pot synthesis of novel hydrogel-based anion exchange membranes (AEMs), with only a single-phase monomer mixture, was used to eliminate surface heterogeneity and generate reproducible electroconvective microvortices in the over-limiting region of the current-voltage characteristic (CVC) curves. Diallyldimethylammonium chloride (DDA) was used as the main component to provide the cation charge groups, and 2-hydroxyethyl methacrylate (HEMA) and ethylene glycol dimethyl acrylate (EGDMA) were used as the auxiliary structure monomers. The uniform membrane structure allowed reproducible and sensitive DNA detection and quantification, as probe-target surface complexes can gate the ion flux and produce large voltage shifts in the over-limiting region. Suppressed membrane curvature due to controlled swelling is a crucial part to avoid the reduction of depletion region for maintaining the influence of target gene hybridization. Fourier-transform infrared (FTIR) spectroscopy verified the synthesized membrane structure, with a residual vinyl group that allows easy carboxylation via additional photografting reaction. Consequently, a significantly higher DNA probe functionalization efficiency is obtained on the homogeneous AEMs, evidenced by the increasing nitrogen element content and bonding via X-ray photoelectron spectroscopy (XPS). The DDA content was optimized to provide a sufficient coulomb force between AEM and nucleic acid backbone to promote the specific binding efficiency but without high dimensional swelling which might change the surface geometry and restrict the voltage shifting for sensing in the over-limiting region, and the optimal DDA/HEMA ratio was found to be 4/10. The synthesized AEM sensor for recombinant 35S promoter sequence identification exhibited a reproducible calibration standard curve with dynamic range between 30 fM and 1 μM and high selectivity with only 0.01 V shift for 1 μM nontarget oligo.

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).

100th Anniversary of Macromolecular Science Viewpoint: Integrated Membrane Systems

Membranes fabricated from self-assembled materials are one recent example of how polymer science has been leveraged to advance membrane technology. Due to their well-defined nanostructures, the performance of membranes made from these materials is pushing the boundaries of size-selective filtration. Still, there remains a need for higher performance and more selective membranes. The advent of functional membrane platforms that rely on mechanisms beyond steric hindrance (e.g., charge-selective membranes and membrane sorbents) is one approach to realize improved solute-solute selectivity and further advance membrane technology. To date, the lab-scale demonstration of these platforms has often relied on fabrication schemes that require extended processing times. However, in order to translate lab-scale demonstrations to larger-scale implementation, it is critical that the rate of the functionalization scheme is reconciled with membrane manufacturing rates. In this viewpoint, it is postulated that substrates lined by reactive moieties that are amenable to postfabrication modification would enable the production of membranes with controlled nanostructures while providing access to a diverse array of pore wall chemistries. A comparison of reaction and manufacturing rates suggests that mechanisms that exhibit second-order reaction rate constants of at least 1 M^-1 s^-1 are needed for roll-to-roll processing. Furthermore, for mechanisms that exhibit rate constants greater than 300 M^-1 s^-1, it may be possible to integrate multiple functional domains over the membrane surface such that useful properties emerge. These multifunctional systems can expand the capabilities of membranes when the patterned chemistries interact at the heterojunctions between domains (e.g., Janus and charge-patterned mosaic membranes) or if they exhibit cooperative responses to external operating conditions (e.g., membrane pumps).

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.

Structure, Rheology, and Electrokinetics of Soft Colloidal Suspension Electrolytes

When ion transport in a binary liquid electrolyte is driven at potentials above the thermal voltage, an extended space charge region forms at the electrolyte/electrode interface and triggers the hydrodynamic instability termed electroconvection. We experimentally show that this instability can be completely arrested in soft colloidal suspension electrolytes composed of low concentrations of polymer-grafted nanoparticles in a liquid host. The mechanism is revealed by means of X-ray scattering, Brownian dynamics calculations, and linear stability analysis to involve overlap of the soft particles at low particle fractions to create a jammed, nanoporous medium that resists convective flow by a Darcy-Brinkman like drag on the electrolyte solvent.

Multilevel self-organization on anodized aluminium: discovering hierarchical honeycomb structures from nanometre to sub-millimetre scale

Herein, the one-step spontaneous formation of multiscale hierarchical honeycomb-like textures on anodized aluminium is reported for the first time. A self-organized array of unprecedentedly large sub-millimetre hemispherical pores was observed on the upper hierarchy level, while superimposed well-ordered hexagonal cells on the lower hierarchy level maintained their classically known nanoscale self-ordering periodicity (50-60 nm). The larger macroscopic cells (0.45-0.90 mm) show great morphological similarity to the conventional nanosized porous anodic structures, but arise on a purely metallic surface without any analytically detectable amount of deposited alumina. The observed cell size expansion (approximately by a factor of 104) during Al anodizing is colossal in comparison with the size variation ranges reported in the literature so far. It reveals a dramatic nonlinearity effect in a dynamic self-organizing system upon a moderate change of experimental parameters (specifically, this work focuses on the effect of anodizing temperature). Such multilevel self-organization in a single aluminium anodizing process sheds new light on the origin of self-ordered anodic structures and allows rethinking the whole range of opinions regarding their formation mechanism that have been proposed to date.

The Development of Electroconvection at the Surface of a Heterogeneous Cation-Exchange Membrane Modified with Perfluorosulfonic Acid Polymer Film Containing Titanium Oxide

One way to enhance mass transfer and reduce fouling in wastewater electrodialysis is stimulation of electroconvective mixing of the solution adjoining membranes by modifying their surfaces. Several samples were prepared by casting the perfluorosulfonic acid (PFSA) polymer film doped with TiO₂ nanoparticles onto the surface of the heterogeneous cation-exchange membrane MK-40. It is found that changes in surface characteristics conditioned by such modification lead to an increase in the limiting current density due to the stimulation of electroconvection, which develops according to the mechanism of electroosmosis of the first kind. The greatest increase in the current compared to the pristine membrane can be obtained by modification with the film being 20 μm thick and containing 3 wt% of TiO₂. The sample containing 6 wt% of TiO₂ provides higher mass transfer in overlimiting current modes due to the development of nonequilibrium electroconvection. A 1.5-fold increase in the thickness of the modifying film reduces the positive effect of introducing TiO₂ nanoparticles due to (1) partial shielding of the nanoparticles on the surface of the modified membrane; (2) a decrease in the tangential component of the electric force, which affects the development of electroconvection.

Shear electroconvective instability in electrodialysis channel under extreme depletion and its scaling laws

The electroconvective instability (ECI) in an electrodialysis channel under a strong electric field is studied here. The phenomenon of ECI with extreme depletion (ECI-HD) is reported; that is, the overlapping vortices cause the extreme depletion zone to propagate in the horizontal direction. Using scaling theory and direct numerical simulation, we indicate a series of features under the ECI-HD. The decrease in ion transport rate with voltage in ECI-HD is different from the enhancement in the ECI with moderate depletion (ECI-MD), which results in a unique peak in the voltage-current curve. More importantly, we reveal that the ECI is regulated by a scaling factor consisting of the electric field, hydrodynamic coupling coefficient, and Péclet number. For the ECI-HD, the scaling factor has an opposite effect on the vortex size and overlimiting current as that on the ECI-MD. The extreme depletion zone of the ECI-HD also has an uncommon diffusion self-similar dynamics. These unique scaling laws allow one to establish the quantitative bridge between the ion concentration, electric field, and vortex size by the overlimiting current.

Potentiodynamic and Galvanodynamic Regimes of Mass Transfer in Flow-Through Electrodialysis Membrane Systems: Numerical Simulation of Electroconvection and Current-Voltage Curve

Electromembrane devices are usually operated in two electrical regimes: potentiodynamic (PD), when a potential drop in the system is set, and galvanodynamic (GD), when the current density is set. This article theoretically investigates the current-voltage curves (CVCs) of flow-through electrodialysis membrane systems calculated in the PD and GD regimes and compares the parameters of the electroconvective vortex layer for these regimes. The study is based on numerical modelling using a basic model of overlimiting transfer enhanced by electroconvection with a modification of the boundary conditions. The Dankwerts’ boundary condition is used for the ion concentration at the inlet boundary of the membrane channel. The Dankwerts’ condition allows one to increase the accuracy of the numerical implementation of the boundary condition at the channel inlet. On the CVCs calculated for PD and DG regimes, four main current modes can be distinguished: underlimiting, limiting, overlimiting, and chaotic overlimiting. The effect of the electric field regime is manifested in overlimiting current modes, when a significant electroconvection vortex layer develops in the channel.

Effect of Surface Inhomogeneity of Ion-Exchange Membranes on the Mass Transfer Efficiency in Pulsed Electric Field Modes

Despite the growing interest in pulsed electric field modes in membrane separation processes, there are currently not many works devoted to studying the effect of the surface properties and composition of ion-exchange membranes on their efficiency in these modes. In this paper, we have shown the effect of increasing mass transfer using different kinds of ion-exchange membranes (heterogeneous and homogeneous with smooth, undulated, and rough surfaces) during electrodialysis in the pulsed electric field modes at underlimiting and overlimiting currents. It was found that the maximum increment in the average current is achieved when the average potential corresponds to the right-hand edge of the limiting current plateau of the voltammetric curve, i.e., at the maximum resistance of the system in the DC mode. For the first time, the development of electroconvective vortices was visualized in pulsed electric field modes and it was experimentally shown that even at relatively low frequencies, a non-uniform concentration field is preserved at the time of a pause, which stimulates the rapid development of electroconvection when pulses are switched on again. In the case of relatively high pulse frequencies, the electroconvective vortices formed during a pulse lapse do not completely decay during a pause; they only slightly decrease in size.

How Electrical Heterogeneity Parameters of Ion-Exchange Membrane Surface Affect the Mass Transfer and Water Splitting Rate in Electrodialysis

Electrodialysis (ED) has been demonstrated as an effective membrane method for desalination, concentration, and separation. Electroconvection (EC) is a phenomenon which can essentially increase the mass transfer rate and reduce the undesirable water splitting effect. Efforts by a number of researchers are ongoing to create conditions for developing EC, in particular, through the formation of electrical heterogeneity on the membrane surface. We attempt, for the first time, to optimize the parameters of surface electrical heterogeneity for ion-exchange membranes used in a laboratory ED cell. Thirteen different patterns on the surface of two Neosepta anion-exchange membranes, AMX and AMX-Sb, were tested. Low-conductive fluoropolymer spots were formed on the membrane surface using the electrospinning technique. Spots in the form of squares, rectangles, and circles with different sizes and distances between them were applied. We found that the spots' shape did not have a visible effect. The best effect, i.e., the maximum mass transfer rate and the minimum water splitting rate, was found when the spots' size was close to that of the diffusion layer thickness, δ (about 250 μm in the experimental conditions), and the distance between the spots was slightly larger than δ, such that the fraction of the screened surface was about 20%.

Mathematical Modeling of the Effect of Water Splitting on Ion Transfer in the Depleted Diffusion Layer Near an Ion-Exchange Membrane

Water splitting (WS) and electroconvection (EC) are the main phenomena affecting ion transfer through ion-exchange membranes in intensive current regimes of electrodialysis. While EC enhances ion transport, WS, in most cases, is an undesirable effect reducing current efficiency and causing precipitation of sparingly soluble compounds. A mathematical description of the transfer of salt ions and H⁺ (OH⁻) ions generated in WS is presented. The model is based on the Nernst–Planck and Poisson equations; it takes into account deviation from local electroneutrality in the depleted diffusion boundary layer (DBL). The current transported by water ions is given as a parameter. Numerical and semi-analytical solutions are developed. The analytical solution is found by dividing the depleted DBL into three zones: the electroneutral region, the extended space charge region (SCR), and the quasi-equilibrium zone near the membrane surface. There is an excellent agreement between two solutions when calculating the concentration of all four ions, electric field, and potential drop across the depleted DBL. The treatment of experimental partial current–voltage curves shows that under the same current density, the surface space charge density at the anion-exchange membrane is lower than that at the cation-exchange membrane. This explains the negative effect of WS, which partially suppresses EC and reduces salt ion transfer. The restrictions of the analytical solution, namely, the local chemical equilibrium assumption, are discussed.

Characterization of MK-40 Membrane Modified by Layers of Cation Exchange and Anion Exchange Polyelectrolytes

Coating of ion exchange membranes used in electrodialysis with layers of polyelectrolytes is a proven approach that allows for the increasing of the limiting current, the suppressing of sedimentation, the controlling of the intensity of generation of H⁺ and OH⁻ ions, and also the improving of monovalent selectivity. However, in the case when two materials with the opposite sign of the charge of fixed groups come in contact, a bipolar boundary is created that can cause undesirable changes in the membrane properties. In this work, we used a MK-40 heterogeneous membrane on the surface of which a layer of polyethyleneimine was applied by adsorption from a solution as a model of heterogeneous membranes modified with oppositely charged polyelectrolyte. It was found that, on one hand, the properties of modified membrane were beneficial for electrodialysis, its limiting current did not decrease and the membrane even acquired a barrier to non-selective electrolyte transport. At the same time, the generation of H⁺ and OH⁻ ions of low intensity arose, even in underlimiting current modes. It was also shown that despite the presence of a layer of polyethyleneimine, the surface charge of the modified membrane remained negative, which we associate with low protonation of polyethyleneimine at neutral pH.

Interfacial Junctions Control Electrolyte Transport through Charge-Patterned Membranes

Distinct transport mechanisms emerge when nanostructured substrates are patterned with multiple chemistries. For example, charge-patterned mosaic membranes possess surfaces functionalized with discrete domains of both positive and negative charge. These oppositely charged domains provide pathways for both the cation and anion from a dissolved salt to permeate through the membrane without violating the macroscopic constraint of electroneutrality. Here, by systematically varying the geometry and size of the charge pattern, we elucidate the molecular interactions that promote the transport of salts under the action of pressure-driven flow. For patterns that consist of equivalent areal coverages of positively charged and negatively charged domains, the effects of the geometric parameters were encapsulated in a single variable, the interfacial packing density, that quantified the fraction of the membrane surface covered by junctions between oppositely charged domains. Experimentally, the transport of symmetric electrolytes (i.e., KCl and MgSO₄) increased with the value of the interfacial packing density, while the interfacial packing density did not significantly affect the transport of asymmetric electrolytes (i.e., K₂SO₄ and MgCl₂). Simulations of the electrical potential near the membrane surface demonstrate that for symmetric electrolytes the structural charge heterogeneity reduces the barrier to ion partitioning, thereby promoting salt transport through the membranes. For asymmetric electrolytes, the charge heterogeneity skews the local availability of ions from the stoichiometric ratio of the salt, thus hindering salt transport. These findings demonstrate the promise of accessing transport mechanisms, which could find utility in a diverse range of chemical separations and sensing applications, through chemical patterning of membranes.

Behavior of Embedded Cation-Exchange Particles in a DC Electric Field

Electrodialysis and electrodeionization are separation processes whose performance depends on the quality and properties of ion-exchange membranes. One of the features that largely affects these properties is heterogeneity of the membranes both on the macroscopic and microscopic level. Macroscopic heterogeneity is an intrinsic property of heterogeneous ion-exchange membranes. In these membranes, the functional ion-exchange component is dispersed in a non-conductive binder. The functional component is finely ground ion-exchange resin particles. The understanding of the effect of structure on the heterogeneous membrane properties and behavior is thus of utmost importance since it does not only affect the actual performance but also the cost and therefore competitiveness of the aforementioned separation processes. Here we study the electrokinetic behavior of cation-exchange resin particle systems with well-defined geometrical structure. This approach can be understood as a bottom up approach regarding the membrane preparation. We prepare a structured cation-exchange membrane by using its fundamental component, which is the ion exchange resin. We then perform an experimental study with four different experimental systems in which the number of used cation-exchange particles changes from 1 to 4. These systems are studied by means of basic electrochemical characterization measurements, such as measurement of current–voltage curves and direct optical observation of phenomena that occur at the interface between the ion-exchange system and the adjacent electrolyte. Our work aims at better understanding of the relation between the structure and the membrane properties and of how structure affects electrokinetic behavior of these systems.

Electro-Kinetic Instability in a Laminar Boundary Layer Next to an Ion Exchange Membrane

The electro-kinetic instability in a pressure driven shear flow near an ion exchange membrane is considered. The electrochemical system, through which an electrical potential drop is applied, consists in a polarization layer in contact with the membrane and a bulk. The numerical investigation contained two aspects: analysis of the instability modes and description of the Lagrangian transport of fluid and ions. Regarding the first aspect, the modes were analyzed as a function of the potential drop. The analysis revealed how the spatial distribution of forces controls the dynamics of vortex association and dissociation. In particular, the birth of a counter-clockwise vortex between two clockwise vortices, and the initiation of clusters constituting one or two envelopes wrapping a vortex group, were examined. In regards to the second aspect, the trajectories were computed with the fourth order Runge Kutta scheme for the time integration and with the biquadratric upstream scheme for the spatial and time interpolation of the fluid velocity and the ion flux. The results for the periodic mode showed two kinds of trajectories: the trochoidal motion and the longitudinal one coupled with a periodic transverse motion. For the aperiodic modes, other mechanisms appeared, such as ejection from the mixing layer, trapping by a growing vortex or merging vortices. The analysis of the local velocity field, the vortices’ shape, the spatial distribution of the forces and the ion flux components explained these trajectories.