Scaling of ion-exchange membranes is one of the major challenges that reduce the performance of electrodialysis (ED) desalination. The mechanism of scale formation depends on the solution under treatment. The presence of phosphates in solutions circulated through the ED compartments promotes scaling. This study shows that scale formation in such systems may be due to the "acid dissociation" mechanism of H+/OH- ion generation. According to this mechanism, OH- ions are formed when multicharged phosphate anions leave an anion-exchange membrane (AEM) and enter the enriched solution. Scaling is possible, when a small amount of scale-forming cation (e. g. Ca2+) is present in the concentrate compartment. We investigated the effect of current density on scaling during ED with a heterogeneous anion-exchange MA-41P membrane, using a 0.045 & Mcy; KH2PO4 + 0.001 M CaCl2 solution circulated through the concentrate compartments. It was found that CaHPO4 precipitates on the MA-41P membrane, when the current density was almost 4 times lower than the empirical limiting current density. No scaling was observed in the diluate compartments. Simulation based on the Nernst-Planck-Poisson equations confirmed the "acid dissociation" mechanism of pH increase and accurately enough predicted the threshold current density at which scale formation begins.

In the electrodialysis process, the concentration polarization phenomenon determines the value of the limiting current density and, consequently, significantly affects energy consumption. Commercial spacers are commonly used to mix the solution and enhance ion delivery to ion-exchange membranes, and its shape has a crucial impact on the electrodialysis optimization. The target features of spacers development are better mixing and lower shadow effect. In a binary NaCl electrolyte solution with different diffusion coefficients of ions (DNa approximate to 1.5 DCl) the limiting current is determined by the cation-exchange membrane, according to Peers' equation, because its counterion has the minimal value of D in the solution. Recently using 2D simulation and corresponding experiment it was found that the limiting current of an electrodialysis channel with NaCl solution may be increased by displacing the spacer filaments towards the anion-exchange membrane. This arrangement increases the flow velocity of the solution near the surface of the cation-exchange membrane, thus, thereby reducing the boundary layer thickness near it. In this work, using 3D simulation, we investigated several types of spacers. For the first time, an unobvious result was found: displacing the filaments toward the cation-exchange membrane in NaCl solution leads to an increase in the total limiting current and the effect is more pronounced then in the case of displacement toward the anion-exchange membrane. It is theoretically shown that in 3D systems, better solution mixing and ion delivery may be achieved in nonintuitive ways and the comprehensive analysis should be done to predict the system behavior.

Phosphate transport through anion-exchange membranes (AEM) during electrodialysis (ED) is complicated by proton-transfer reactions, which are absent in the case of strong electrolytes. This complexity hinders the full practical utilization of ED ' s benefits due to a lack of understanding of the underlying transport mechanisms. In this work, the mechanisms of phosphate transport are studied by chronopotentiometry using a Neosepta AMX membrane in 0.02 M KH 2 PO 4 solution at pH 4.7. Experimental chronopotentiograms measured at different current densities are simulated using a new non-stationary mathematical model. The model makes it possible for the first time to describe ion transport, complicated simultaneously by proton-transfer reactions and electroconvection. Good quantitative agreement between simulated and experimental chronopotentiograms is obtained. The reasons for the appearance of two transition times on the chronopotentiograms are theoretically justified. It is found that after applying a direct current to the membrane system, which is initially in equilibrium, a gradual decrease in the current efficiency of pentavalent phosphorus recovery, ri P , occurs over about 20 min; the value of ri P may decrease by 40 %.

In recent, nutrient recovery from wastewater by selective electrodialysis has been getting more attention, especially for non-renewable elements like phosphorus. However, phosphates usually possess a slow transfer flux in the electrodialysis process. This study aimed to decipher the influence of competing anions and dissolved organic matters (DOM) on phosphate migration with and without electric field. Anions that do and do not participate in protonation-deprotonation reactions showed discrepant effects on competitive phosphate transport. Carbonates enhance the sorption of phosphates in the anion exchange membrane and their diffusion through the membrane. However, this advantage gradually reduced with the increasing voltage during the selective electrodialysis, caused by the development of water splitting and an increase of the carbonate charge in the membrane. DOM substances, especially humic and fulvic acids, delay the phosphate transfer by the formation of fouling and biofouling and substantially intensify water splitting. With the increase of electric field, fouling of humic and fulvic acids were enhanced, while the presence of DOM has little effect on phosphate in Donnan dialysis. These findings help the understanding of phosphorus transfer in the electrodialysis process, and providing insights into the underlying mechanisms of membrane selectivity in competitive ion transport.

At present, the nature of the limiting state of electromembrane systems in solutions of strong electrolytes (e.g., NaCl) is well known. The value of the limiting current in these systems with a rotating membrane disk (RMD) can be calculated quite accurately using the Levich equation. In cases where weak acids and/or their salts are present in the electromembrane system, this equation ceases to be satisfied and the electrodiffusion ion transport is complicated by proton-transfer chemical reactions between these acids, their anions, and water. In this work, the effect of these reactions on the limiting current density in a system with a rotating disk of a cation-exchange membrane and acetic acid has been experimentally studied. The results of voltammetry and their theoretical interpretation using the known mathematical model are presented. Conditions under which the mass transfer rate is limited by the diffusion delivery of acetic acid molecules to the membrane surface, as well as conditions under which the limiting stage is the reaction of their dissociation at the membrane/depleted solution interface, have been revealed.

Electrodialysis (ED) is a cost-effective and environmentally friendly process; it is considered a key step in Zero Liquid Discharge systems. However, the ED process producing a fairly concentrated solution is not well understood. An ED process where 10 L of 0.5 M NaCl was circulated in diluate stream (DS) and 0.1 L of initially 2.0 M NaCl circulated in concentrate stream (CS) was studied. The concentration of concentrate increased up to 3.5 M. The electrodialyzer ' s design eliminated current leakage. Ion -exchange membranes, MK -40, MA -41 (Shchekinoazot) and CJMA-3 (Chemjoy Polymer Materials), were characterized prior to ED. Based on the concentration dependences of membrane conductivity and diffusion permeability, the " true " ( t i *) ion transport numbers in the membranes were found; the water transport number ( t w ) was found from volumetric measurements. It was shown that the current efficiency, eta , found using t i * is quantitatively consistent with eta found in the ED experiments. To calculate the time dependences of solution concentration and volume in CS, a mathematical model was built. For the first time, t i * and t w determined in independent experiments, were used as parameters. The only fitting parameter was the osmotic permeability coefficient. A good agreement with experimental results is obtained.

Insufficient understanding of transport mechanism of polybasic acid species (phosphoric, citric, malic, etc.) through anion-exchange membranes (AEMs) hinders the widespread use of electrodialysis for processing salt solutions of such acids, e.g. the recovery of phosphates from mixed solutions. In this paper, we present experimental current-voltage characteristics (CVC) and partial fluxes of H2PO4 ? and HPO42 ? across an AEM. These data are simulated using a mathematical model based on the Nernst-Planck-Poisson equations coupled with the kinetic equations for chemical reactions. The model describes the nonstationary transport of phosphate acid species through an AEM and adjacent solution diffusion boundary layers. It is shown that the proton-transfer reactions determine the occurrence of two limiting currents. The electric current sweep rate and the values of dissociation rate constants of acid anions largely affect the values of these limiting currents and generally the shape of the CVC. It is found that due to chemical reactions involving polybasic anions, the formation of their concentration profiles in the membrane occurs much slower than in the case of monobasic salts. Numerical simulation shows that a quasi-stationary CVC is possible only when the current sweep rate is such that measurements are carried out for at least 10 h.

In spite of wide variety of commercial ion-exchange membranes, their characteristics, in particular, electrical conductivity and counterion permselectivity, are unsatisfactory for some applications, such as electrolyte solution concentration. This study is aimed at obtaining an anion-exchange membrane (AEM) of high performance in concentrated solutions. An AEM is prepared with a polypyrrole (PPy)-based modification of a heterogeneous AEM with quaternary ammonium functional groups. Concentration dependences of the conductivity, diffusion permeability and Cl− transport number in NaCl solutions are measured and simulated using a new version of the microheterogeneous model. The model describes changes in membrane swelling with increasing concentration and the effect of these changes on the transport characteristics. It is assumed that PPy occupies macro- and mesopores of the host membrane where it replaces non-selective electroneutral solution. Increasing conductivity and selectivity are explained by the presence of positively charged PPy groups. It is found that the conductivity of a freshly prepared membrane reaches 20 mS/cm and the chloride transport number > 0.99 in 4 M NaCl. A choice of input parameters allows quantitative agreement between the experimental and simulation results. However, PPy has shown itself to be an unstable material. This article discusses what parameters a membrane can have to show such exceptional characteristics.

Artificial ion-exchange and other charged membranes, such as biomembranes, are self-organizing nanomaterials built from macromolecules. The interactions of fragments of macromolecules results in phase separation and the formation of ion-conducting channels. The properties conditioned by the structure of charged membranes determine their application in separation processes (water treatment, electrolyte concentration, food industry and others), energy (reverse electrodialysis, fuel cells and others), and chlore-alkali production and others. The purpose of this review is to provide guidelines for modeling the transport of ions and water in charged membranes, as well as to describe the latest advances in this field with a focus on power generation systems. We briefly describe the main structural elements of charged membranes which determine their ion and water transport characteristics. The main governing equations and the most commonly used theories and assumptions are presented and analyzed. The known models are classified and then described based on the information about the equations and the assumptions they are based on. Most attention is paid to the models which have the greatest impact and are most frequently used in the literature. Among them, we focus on recent models developed for proton-exchange membranes used in fuel cells and for membranes applied in reverse electrodialysis.

The deposition of several alternating anion- and cation-exchange surface layers (layer-by-layer method) is a promising technique for the modification of ion-exchange membranes, which makes it possible to essentially increase their selectivity to singly charged ions. This paper presents a one-dimensional model, which is based on the Nernst–Planck–Poisson equations and describes the competitive transfer of singly and doubly charged ions through a multilayer composite ion-exchange membrane. It has been revealed for the first time that, as in the earlier studied case of a bilayer membrane, the dependence of the specific permselectivity coefficient ( P 1/2 ) of a multilayer membrane on the electrical current density passes through a maximum ( P_1 / . -0em 2^max). It has been shown that an increase in the number of nanosized modification bilayers n leads to the growth of P_1 / . -0em 2^max, but the flux of a preferably transferred ion decreases in this case. It has been established that P_1 / . -0em 2^max is attained at underlimiting current densities and relatively low potential drop. The simulated dependences P_1 / . -0em 2^max ( n ) qualitatively agree with the known literature experimental and theoretical results.

For more than a century, the theoretical concepts proposed in the works of Sand have been used by scientists in the field of chronopotentiometry of electrode and membrane systems. The development of these representations makes it possible to more accurately determine the parameters of objects under study and to identify significant factors that seemed insignificant. In this article, using a nonstationary two-dimensional galvanostatic convective-diffusion model of salt ion transport, a theoretical analysis is made of the influence of the dimensions of the electrodialyzer flow-through desalting compartment on the transition time, τ, of chronopotentiograms. It is shown that the local density of electric current is distributed unevenly along the entire length of the desalting channel, and its value at the entrance is more than an order of magnitude higher than the average and is 1–13% (depending on the length of the channel) lower in the rest of the region. The Sand theory, in turn, assumes a uniform distribution of current density. It has been established that the τ values obtained using the two-dimensional model are greater than those calculated using the Sand equation, τs. As the desalting channel length L decreases, the difference between τ and τs increases from 3% (at L = 30 mm) to 14% (at L = 1 mm). The results obtained are in good agreement with the experimental data presented in the previous paper for the homogeneous Neosepta CMX membrane. The found dependence will reduce the error in measuring the properties of flow-through electrodialyzers using the chronopotentiometic transition time.

Electroconvective (EC) vortex structures formed at the surface of an AMX anion-exchange membrane in 0.02 M NaCl and NaHT solutions have been compared. The AMX membrane surface is undulated and consists of alternating staggered hills and valleys. Electroconvective mixing zones have been visualized using the fluorescent agent rhodamine. In the case of NaCl, the vortex EC structures and concentration distributions have been calculated using a “basic” model involving the Nernst–Planck–Poisson–Navier–Stokes equations. According to the calculation, the zone of low concentration approximately coincides in its boundaries with a large vortex localized near the bottom of the valley. Visualization shows that the EC vortices are larger and the electrolyte concentration in them is higher in the case of NaCl compared with NaHT at the same current to limiting current ratio. The reason is more intense generation of Н+ ions at the depleted solution/membrane boundaries, which is due to proton loss by a part of the tartrate anions when they enter the membrane. The generated H+ ions are additional charge carriers; their flux from the depleted membrane surface decreases (in absolute value) the space charge density at the membrane surface, and, hence, the intensity of electroconvection.

Modification of an ion-exchange membrane with a thin layer, the charge of which is opposite to the charge of the substrate membrane, has proven to be an effective approach to obtaining a composite membrane with permselectivity towards monovalent ions. However, the mechanism of permselectivity is not clear enough. We report a 1D model based on the Nernst–Planck–Poisson equation system. Unlike other similar models, we introduce activity coefficients, which change when passing from one layer of the membrane to another. This makes it possible to accurately take into account the fact that the substrate membranes usually selectively sorb multiply charged counterions. We show that the main cause for the change in the permselectivity coefficient, P1/2, with increasing current density, j, is the change in the membrane/solution layer, which controls the fluxes of the competing mono- and divalent ions. At low current densities, counterion fluxes are controlled by transfer through the substrate membrane, which causes selective divalent ion transfer. When the current increases, the kinetic control goes first to the modification layer (which leads to the predominant transfer of monovalent ions) and then, at currents close to the limiting current, to the depleted diffusion layer (which results in a complete loss of the permselectivity). Thus, the dependence P1/2 − j passes through a maximum. An analytical solution is obtained for approximate assessment of the maximum value of P1/2 and the corresponding fluxes of the competing ions. The maximum P1/2 values, plotted as a function of the Na+ ion current density at which this maximum is reached, gives the theoretical trade-off curve between the membrane permselectivity and permeability of the bilayer monovalent selective ion-exchange membrane under consideration.

The application of pulsed electric field (PEF) in electrodialysis has been proven to be efficient for a number of effects: increasing mass transfer rate, mitigation of scaling and fouling, reducing water splitting. Recently, the improvement of the membrane permselectivity for specific counterions was discovered experimentally by the group of Laurent Bazinet (N. Lemay et al. J. Memb. Sci. 604, 117878 (2020)). To better understanding the effect of PEF in electrodialysis, simulations were performed using a non-stationary mathematical model based on the Nernst–Planck and Poisson equations. For the first time, it was not only the condition used when the current density is specified but also the condition when the voltage is set. A membrane and two adjacent diffusion layers are considered. It is shown that when applying the regime used by Lemay et al. (the same current density in conventional continuous current (CC) mode and during the pulses in PEF mode), there is a significant gain in specific permselectivity. It is explained by a reduction in the membrane concentration polarization in PEF mode. In the CC mode of electrodialysis, increasing current density leads to a loss in specific permselectivity: concentration profiles in the diffusion layers and membrane are formed in such a way that ion diffusion reduces the migration flux of the preferentially transferred ion and increases that of the poorly transferred ion. In PEF mode, the concentration profiles are partially restored during the pauses when the current is zero. However, if a different condition is used than the condition applied by Lemay et al., that is, when the same average current density is applied in both the PEF and CC modes, there is no gain in specific permeability. It is shown that within the framework of the applied mathematical model, the specific selectivity depends only on the average current density and does not depend on the mode of its application (CC or PEF mode).

Chronopotentiometry using pulses of a constant current of density j is a powerful method for characterizing ionexchange membranes (IEMs). We report on the influence of coion transport on the shape of chronopotentiogram (ChP) and the consequent new possibility of quantifying coion transport based on ChP analysis. We show that in the case where the bathing solution contains Ca2+ or Mg2+ ions, the ChPs of the homogeneous (CMX) and heterogeneous (MK-40) cation-exchange membranes at overlimiting current densities have a maximum (a peak), which appears a few seconds after the transition time. The time required to reach a stationary state is of the order of d(2)/(D) over bar (2) (where d is the membrane thickness and (D) over bar (2) is the coion diffusion coefficient in the membrane); this time under our experiment conditions is about 300-400 s. We show that the cause of the maximum is the increase in coion transfer caused by the current-induced concentration polarization of the bathing solution. This increase in coion transfer results in increasing the limiting current density j(lim), which at j = const leads to a reduction in the resistance of the depleted diffusion layer over time and the appearance of a maximum on the ChP. 1D mathematical modeling is based on the Nernst-Planck-Poisson equations. The main assumption inspired by the works of Levich and Amatore is that the apparent electrolyte diffusion coefficient in the depleted solution increases with increasing electroconvection. The stationary value of this diffusion coefficient is found from the I-V curve. The only fitting parameter is the critical potential difference, which refers to the onset of intensive electroconvection.

Transition time, tau, is a very crucial characteristic in chronopotentiometry; it is important to have a simple equation to calculate this value. As early as in 1901, Sand has deduced his famous equation for calculating tau in electrode/solution systems with infinitely large diffusion layer. The exact analytical solution for the case of finite diffusion-layer thickness was obtained by Sheldeshov et al. in 1986. However, tau enters this solution as an implicit function of the current density, i. Recently, van Soestbergen and coauthors proposed an approximate formula where the transition time is an explicit function of i. In this paper, we examine the above equations along with our numerical solution by comparing the calculated values of tau with our experimental data for homogeneous (Fuji CEM Type I, Type II, Type X, Neosepta CMX) and heterogeneous (MK-40) membranes. A large gamma of current densities (from i - 1.0i(lim) to 2.5i(lim), where i(lim) is the limiting current density) is applied. The most simple in use is the formula of van Soestbergen et al., which, however, gives at i > 1.0i(lim) the values of tau slightly (about 0.7%) lower than the exact analytical solution of Sheldeshov et al. We show that a better approximation to the exact solution is obtained when the first-order approximation of the analytical solution (obtained by van Soestbergen et al.) is applied in the range of i from 1.0 to 1.9i(lim), while for i > 1.9i(lim), the Sand equation is used. We find nevertheless that the experimental values of tau are higher than the theoretical ones for all the studied membranes. The causes of this deviation, which are mainly electroconvection and surface electric heterogeneity, are discussed. (c) 2020 Elsevier Ltd. All rights reserved.