Electrokinetic and Electroconvective Effects in Ternary Electrolyte Near Ion-Selective Microsphere.

The paper presents theoretical and experimental investigations of the behavior of an electrolyte solution with three types of ions near an ion-selective microparticle with electrokinetically and pressure-driven flow. A special experimental cell has been developed for the investigations. An anion-selective spherical particle composed of ion-exchange resin is fixed in the center of the cell. An enriched region with a high salt concentration appears at the anode side of the particle when an electric field is turned on, according to the nonequilibrium electrosmosis behavior. A similar region exists near a flat anion-selective membrane. However, the enriched region near the particle produces a concentration jet that spreads downstream akin to a wake behind an axisymmetrical body. The fluorescent cations of Rhodamine-6G dye are chosen as the third species in the experiments. The ions of Rhodamine-6G have a 10-fold lower diffusion coefficient than the ions of potassium while bearing the same valency. This paper shows that the concentration jet behavior is described accurately enough with the mathematical model of a far axisymmetric wake behind a body in a fluid flow. The third species also forms an enriched jet, but its distribution turns out to be more complex. The concentration of the third species increases in the jet with an increase in pressure gradient. The pressure-driven flow stabilizes the jet, yet electroconvection has been observed near the microparticle for sufficiently strong electric fields. The electrokinetic instability and the electroconvection partially destroy the concentration jet of salt and the third species. The conducted experiments show good qualitative agreement with the numerical simulations. The presented results could be used in future for implementing microdevices based on membrane technology for solving problems of detection and preconcentration, and thus simplifying chemical and medical analyses utilizing the superconcentration phenomenon. Such devices are called membrane sensors, and are actively being studied.

Electrochemical Oxidation of Organic Pollutants in Aqueous Solution Using a Ti4O7 Particle Anode.

Anodes based on substoichiometric titanium oxide (Ti4O7) are among the most effective for the anodic oxidation of organic pollutants in aqueous solutions. Such electrodes can be made in the form of semipermeable porous structures called reactive electrochemical membranes (REMs). Recent work has shown that REMs with large pore sizes (0.5-2 mm) are highly efficient (comparable or superior to boron-doped diamond (BDD) anodes) and can be used to oxidize a wide range of contaminants. In this work, for the first time, a Ti4O7 particle anode (with a granule size of 1-3 mm and forming pores of 0.2-1 mm) was used for the oxidation of benzoic, maleic and oxalic acids and hydroquinone in aqueous solutions with an initial COD of 600 mg/L. The results demonstrated that a high instantaneous current efficiency (ICE) of about 40% and a high removal degree of more than 99% can be achieved. The Ti4O7 anode showed good stability after 108 operating hours at 36 mA/cm2.

Modeling the Conductivity and Diffusion Permeability of a Track-Etched Membrane Taking into Account a Loose Layer.

The microheterogeneous model makes it possible to describe the main transport properties of ion-exchange membranes using a single set of input parameters. This paper describes an adaptation of the microheterogeneous model for describing the electrical conductivity and diffusion permeability of a track-etched membrane (TEM). Usually, the transport parameters of TEMs are evaluated assuming that ion transfer occurs through the solution filling the membrane pores, which are cylindrical and oriented normally to the membrane surface. The version of the microheterogeneous model developed in this paper takes into account the presence of a loose layer, which forms as an intermediate layer between the pore solution and the membrane bulk material during track etching. It is assumed that this layer can be considered as a "gel phase" in the framework of the microheterogeneous model due to the fixed hydroxyl and carboxyl groups, which imparts ion exchange properties to the loose layer. The qualitative and quantitative agreement between the calculated and experimental concentration dependencies of the conductivity and diffusion permeability is discussed. The role of the model input parameters is described in relation to the structural features of the membrane. In particular, the inclination of the pores relative to the surface and their narrowing in the middle part of the membrane can be important for their properties.

High Diffusion Permeability of Anion-Exchange Membranes for Ammonium Chloride: Experiment and Modeling.

It is known that ammonium has a higher permeability through anion exchange and bipolar membranes compared to K+ cation that has the same mobility in water. However, the mechanism of this high permeability is not clear enough. In this study, we develop a mathematical model based on the Nernst−Planck and Poisson's equations for the diffusion of ammonium chloride through an anion-exchange membrane; proton-exchange reactions between ammonium, water and ammonia are taken into account. It is assumed that ammonium, chloride and OH− ions can only pass through membrane hydrophilic pores, while ammonia can also dissolve in membrane matrix fragments not containing water and diffuse through these fragments. It is found that due to the Donnan exclusion of H+ ions as coions, the pH in the membrane internal solution increases when approaching the membrane side facing distilled water. Consequently, there is a change in the principal nitrogen-atom carrier in the membrane: in the part close to the side facing the feed NH4Cl solution (pH < 8.8), it is the NH4+ cation, and in the part close to distilled water, NH3 molecules. The concentration of NH4+ reaches almost zero at a point close to the middle of the membrane cross-section, which approximately halves the effective thickness of the diffusion layer for the transport of this ion. When NH3 takes over the nitrogen transport, it only needs to pass through the other half of the membrane. Leaving the membrane, it captures an H+ ion from water, and the released OH− moves towards the membrane side facing the feed solution to meet the NH4+ ions. The comparison of the simulation with experiment shows a satisfactory agreement.

Mathematical Modeling of Monovalent Permselectivity of a Bilayer Ion-Exchange Membrane as a Function of Current Density.

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.

Mathematical Modeling of the Effect of Pulsed Electric Field Mode and Solution Flow Rate on Protein Fouling during Bipolar Membrane Electroacidificaiton of Caseinate Solution.

A one-dimensional non-stationary model was developed for a better understanding of the protein fouling formation mechanism during electroacidification of caseinate solution using electrodialysis with bipolar membranes (EDBM) in pulsed electric field (PEF) mode. Four different PEF modes were investigated with pulse-pause durations of 10-10 s, 10-20 s, 10-33 s, 10-50 s. For each current mode 3 different flow rates were considered, corresponding to Reynolds numbers, Re, equal to 187, 374 and 560. The processes are considered in the diffusion boundary layer between the surface of the cation-exchange layer of bipolar membrane and bulk solution of the desalination compartment. The Nernst-Planck and material balance equation systems describe the ion transport. The electroneutrality condition and equilibrium chemical reactions are taken into account. The calculation results using the developed model are in qualitative agreement with the experimental data obtained during the previous experimental part of the study. It is confirmed that both the electrical PEF mode and the flow rate have a significant effect on the thickness (and mass) of the protein fouling during EDBM. Moreover, the choice of the electric current mode has the main impact on the fouling formation rate; an increase in the PEF pause duration leads to a decrease in the amount of fouling. It was shown that an increase in the PEF pause duration from 10 s to 50 s, in combination with an increase in Reynolds number (the flow rate) from 187 to 560, makes it possible to reduce synergistically the mass of protein deposits from 6 to 1.3 mg/cm2, which corresponds to a 78% decrease.

Ion and Water Transport in Ion-Exchange Membranes for Power Generation Systems: Guidelines for Modeling.

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.

Ion-Exchange Membranes and Processes (Volume II).

Ion exchange membranes (IEMs) and related processes have generated increased interest among researchers in the last few years, according to the analysis of publication activity in Scopus [...].

A Simple 1D Convection-Diffusion Model of Oxalic Acid Oxidation Using Reactive Electrochemical Membrane.

In recent years, electrochemical methods utilizing reactive electrochemical membranes (REM) have been recognized as the most promising technologies for the removal of organic pollutants from water. In this paper, we propose a 1D convection-diffusion-reaction model concerning the transport and oxidation of oxalic acid (OA) and oxygen evolution in the flow-through electrochemical oxidation system with REM. It allows the determination of unknown parameters of the system by treatment of experimental data and predicts the behavior of the electrolysis setup. There is a good agreement in calculated and experimental data at different transmembrane pressures and initial concentrations of OA. The model provides an understanding of the processes occurring in the system and gives the concentration, current density, potential, and overpotential distributions in REM. The dispersion coefficient was determined as a fitting parameter and it is in good agreement with literary data for similar REMs. It is shown that the oxygen evolution reaction plays an important role in the process even under the kinetic limit, and its contribution decreases with increasing total organic carbon flux through the REM.

Modeling the Formation of Gas Bubbles inside the Pores of Reactive Electrochemical Membranes in the Process of the Anodic Oxidation of Organic Compounds.

The use of reactive electrochemical membranes (REM) in flow-through mode during the anodic oxidation of organic compounds makes it possible to overcome the limitations of plate anodes: in the case of REM, the area of the electrochemically active surface is several orders of magnitude larger, and the delivery of organic compounds to the reaction zone is controlled by convective flow rather than diffusion. The main problem with REM is the formation of fouling and gas bubbles in the pores, which leads to a decrease in the efficiency of the process because the hydraulic resistance increases and the electrochemically active surface is shielded. This work aims to study the processes underlying the reduction in the efficiency of anodic oxidation, and in particular the formation of gas bubbles and the recharge of the REM pore surface at a current density exceeding the limiting kinetic value. We propose a simple one-dimensional non-stationary model of the transport of diluted species during the anodic oxidation of paracetamol using REM to describe the above effects. The processing of the experimental data was carried out. It was found that the absolute value of the zeta potential of the pore surface decreases with time, which leads to a decrease in the permeate flux due to a reduction in the electroosmotic flow. It was shown that in the solution that does not contain organic components, gas bubbles form faster and occupy a larger pore fraction than in the case of the presence of paracetamol; with an increase in the paracetamol concentration, the gas fraction decreases. This behavior is due to a decrease in the generation of oxygen during the recombination reaction of the hydroxyl radicals, which are consumed in the oxidation reaction of the organic compounds. Because the presence of bubbles increases the hydraulic resistance, the residence time of paracetamol-and consequently its degradation degree-increases, but the productivity goes down. The model has predictive power and, after simple calibration, can be used to predict the performance of REM anodic oxidation systems.

Mathematical Modeling of the Effect of Pulsed Electric Field on the Specific Permselectivity of Ion-Exchange Membranes.

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).

A 2D Convection-Diffusion Model of Anodic Oxidation of Organic Compounds Mediated by Hydroxyl Radicals Using Porous Reactive Electrochemical Membrane.

In recent years, electrochemical methods utilizing reactive electrochemical membranes (REM) have been considered as a promising technology for efficient degradation and mineralization of organic compounds in natural, industrial and municipal wastewaters. In this paper, we propose a two-dimensional (2D) convection-diffusion-reaction model concerning the transport and reaction of organic species with hydroxyl radicals generated at a TiOx REM operated in flow-through mode. It allows the determination of unknown parameters of the system by treatment of experimental data and predicts the behavior of the electrolysis setup. There is a good agreement in the calculated and experimental degradation rate of a model pollutant at different permeate fluxes and current densities. The model also provides an understanding of the current density distribution over an electrically heterogeneous surface and its effect on the distribution profile of hydroxyl radicals and diluted species. It was shown that the percentage of the removal of paracetamol increases with decreasing the pore radius and/or increasing the porosity. The effect becomes more pronounced as the current density increases. The model highlights how convection, diffusion and reaction limitations have to be taken into consideration for understanding the effectiveness of the process.

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.

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.

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%.

Transport Characteristics of Fujifilm Ion-Exchange Membranes as Compared to Homogeneous Membranes АМХ and СМХ and to Heterogeneous Membranes MK-40 and MA-41.

Ion-exchange membranes (IEMs) find more and more applications; the success of an application depends on the properties of the membranes selected for its realization. For the first time, the results of a comprehensive characterization of the transport properties of IEMs from three manufactures (Astom, Japan; Shchekinoazot, Russia; and Fujifilm, The Netherlands) are reported. Our own and literature data are presented and analyzed using the microheterogeneous model. Homogeneous Neosepta AMX and CMX (Astom), heterogeneous MA-41 and MK-40 (Shchekinoazot), and AEM Type-I, AEM Type-II, AEM Type-X, as well as CEM Type-I, CEM Type-II, and CEM Type-X produced by the electrospinning method (Fujifim) were studied. The concentration dependencies of the conductivity, diffusion permeability, as well as the real and apparent ion transport numbers in these membranes were measured. The counterion transport number characterizing the membrane permselectivity increases in the following order: CEM Type-I ≅ MA-41 < AEM Type-I < MK-40 < CMX ≅ CEM Type-II ≅ CEM Type-X ≅ AEM Type-II < AMX < AEM Type-X. It is shown that the properties of the AEM Type-I and CEM Type-I membranes are close to those of the heterogeneous MA-41 and MK-40 membranes, while the properties of Fujifilm Type-II and Type-X membranes are close to those of the homogeneous AMX and CMX membranes. This difference is related to the fact that the Type-I membranes have a relatively high parameter f2, the volume fraction of the electroneutral solution filling the intergel spaces. This high value is apparently due to the open-ended pores, formed by the reinforcing fabric filaments of the Type-I membranes, which protrude above the surface of these membranes.

Partial Fluxes of Phosphoric Acid Anions through Anion-Exchange Membranes in the Course of NaH2PO4 Solution Electrodialysis.

Electrodialysis (ED) with ion-exchange membranes is a promising method for the extraction of phosphates from municipal and other wastewater in order to obtain cheap mineral fertilizers. Phosphorus is transported through an anion-exchange membrane (AEM) by anions of phosphoric acid. However, which phosphoric acid anions carry the phosphorus in the membrane and the boundary solution, that is, the mechanism of phosphorus transport, is not yet clear. Some authors report an unexpectedly low current efficiency of this process and high energy consumption. In this paper, we report the partial currents of H2PO4-, HPO42-, and PO43- through Neosepta AMX and Fujifilm AEM Type X membranes, as well as the partial currents of H2PO4- and H+ ions through a depleted diffusion layer of a 0.02 M NaH2PO4 feed solution measured as functions of the applied potential difference across the membrane under study. It was shown that the fraction of the current transported by anions through AEMs depend on the total current density/potential difference. This was due to the fact that the pH of the internal solution in the membrane increases with the growing current due to the increasing concentration polarization (a lower electrolyte concentration at the membrane surface leads to higher pH shift in the membrane). The HPO42- ions contributed to the charge transfer even when a low current passed through the membrane; with an increasing current, the contribution of the HPO42- ions grew, and when the current was about 2.5 ilimLev (ilimLev was the theoretical limiting current density), the PO43- ions started to carry the charge through the membrane. However, in the feed solution, the pH was 4.6 and only H2PO4- ions were present. When H2PO4- ions entered the membrane, a part of them transformed into doubly and triply charged anions; the H+ ions were released in this transformation and returned to the depleted diffusion layer. Thus, the phosphorus total flux, jP (equal to the sum of the fluxes of all phosphorus-bearing species) was limited by the H2PO4- transport from the bulk of feed solution to the membrane surface. The value of jP was close to ilimLev/F (F is the Faraday constant). A slight excess of jP over ilimLev/F was observed, which is due to the electroconvection and exaltation effects. The visualization showed that electroconvection in the studied systems was essentially weaker than in systems with strong electrolytes, such as NaCl.