Transport Of Salt Ions Research Articles

Designing salt stress-resilient crops: Current progress and future challenges.

Excess soil salinity affects large regions of land and is a major hindrance to crop production worldwide. Therefore, understanding the molecular mechanisms of plant salt tolerance has scientific importance and practical significance. In recent decades, studies have characterized hundreds of genes associated with plant responses to salt stress in different plant species. These studies have substantially advanced our molecular and genetic understanding of salt tolerance in plants and have introduced an era of molecular design breeding of salt-tolerant crops. This review summarizes our current knowledge of plant salt tolerance, emphasizing advances in elucidating the molecular mechanisms of osmotic stress tolerance, salt-ion transport and compartmentalization, oxidative stress tolerance, alkaline stress tolerance, and the trade-off between growth and salt tolerance. We also examine recent advances in understanding natural variation in the salt tolerance of crops and discuss possible strategies and challenges for designing salt stress-resilient crops. We focus on the model plant Arabidopsis (Arabidopsis thaliana) and the four most-studied crops: rice (Oryza sativa), wheat (Triticum aestivum), maize (Zea mays), and soybean (Glycine max).

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.

Reducing Chloride Ion Permeation during Seawater Electrolysis Using Double-Polyamide Thin-Film Composite Membranes.

Low-cost polyamide thin-film composite membranes are being explored as alternatives to expensive cation exchange membranes for seawater electrolysis. However, transport of chloride from seawater to the anode chamber must be reduced to minimize the production of chlorine gas. A double-polyamide composite structure was created that reduced the level of chloride transport. Adding five polyamide layers on the back of a conventional polyamide composite membrane reduced the chloride ion transport by 53% and did not increase the applied voltage. Decreased chloride permeation was attributed to enhanced electrostatic and steric repulsion created by the new polyamide layers. Charge was balanced through increased sodium ion transport (52%) from the anolyte to the catholyte rather than through a change in the transport of protons and hydroxides. As a result, the Nernstian loss arising from the pH difference between the anolyte and catholyte remained relatively constant during electrolysis despite membrane modifications. This lack of a change in pH showed that transport of protons and hydroxides during electrolysis was independent of salt ion transport. Therefore, only sodium ion transport could compensate for the reduction of chloride flux to maintain the set current. Overall, these results prove the feasibility of using a double-polyamide structure to control chloride permeation during seawater electrolysis without sacrificing energy consumption.

A High-K+ Affinity Transporter (HKT) from Actinidia valvata Is Involved in Salt Tolerance in Kiwifruit.

Ion transport is crucial for salt tolerance in plants. Under salt stress, the high-affinity K+ transporter (HKT) family is mainly responsible for the long-distance transport of salt ions which help to reduce the deleterious effects of high concentrations of ions accumulated within plants. Kiwifruit is well known for its susceptibility to salt stress. Therefore, a current study was designed to decipher the molecular regulatory role of kiwifruit HKT members in the face of salt stress. The transcriptome data from Actinidia valvata revealed that salt stress significantly induced the expression of AvHKT1. A multiple sequence alignment analysis indicated that the AvHKT1 protein contains three conserved amino acid sites for the HKT family. According to subcellular localization analysis, the protein was primarily present in the cell membrane and nucleus. Additionally, we tested the AvHKT1 overexpression in 'Hongyang' kiwifruit, and the results showed that the transgenic lines exhibited less leaf damage and improved plant growth compared to the control plants. The transgenic lines displayed significantly higher SPAD and Fv/Fm values than the control plants. The MDA contents of transgenic lines were also lower than that of the control plants. Furthermore, the transgenic lines accumulated lower Na+ and K+ contents, proving this protein involvement in the transport of Na+ and K+ and classification as a type II HKT transporter. Further research showed that the peroxidase (POD) activity in the transgenic lines was significantly higher, indicating that the salt-induced overexpression of AvHKT1 also scavenged POD. The promoter of AvHKT1 contained phytohormone and abiotic stress-responsive cis-elements. In a nutshell, AvHKT1 improved kiwifruit tolerance to salinity by facilitating ion transport under salt stress conditions.

Relative Insignificance of Polyamide Layer Selectivity for Seawater Electrolysis Applications.

Low-cost polyamide thin-film composite (TFC) membranes are being explored as alternatives to cation exchange membranes for seawater electrolysis. An optimal membrane should have a low electrical resistance to minimize applied potentials needed for water electrolysis and be able to block chloride ions present in a seawater catholyte from reaching the anode. The largest energy loss associated with a TFC membrane was the Nernstian overpotential of 0.74 V (equivalent to 37 Ω cm2 at 20 mA cm-2), derived from the pH difference between the anolyte and catholyte and not the membrane ohmic overpotential. Based on analysis using electrochemical impedance spectroscopy, the pristine TFC membrane contributed only 5.00 Ω cm2 to the ohmic resistance. Removing the polyester support layer reduced the resistance by 79% to only 1.04 Ω cm2, without altering the salt ion transport between the electrolytes. Enlarging the pore size (∼5 times) in the polyamide active layer minimally impacted counterion transport across the membrane during electrolysis, but it increased the total concentration of chloride transported by 60%. Overall, this study suggests that TFC membranes with thinner but mechanically strong supporting layers and size-selective active layers should reduce energy consumption and the potential for chlorine generation for seawater electrolyzers.

Origin of Limiting and Overlimiting Currents in Bipolar Membranes.

Bipolar membranes (BPMs), a special class of ion exchange membranes with the unique ability to electrochemically induce either water dissociation or recombination, are of growing interest for environmental applications including eliminating chemical dosage for pH adjustment, resource recovery, valorization of brines, and carbon capture. However, ion transport within BPMs, and particularly at its junction, has remained poorly understood. This work aims to theoretically and experimentally investigate ion transport in BPMs under both reverse and forward bias operation modes, taking into account the production or recombination of H+ and OH-, as well as the transport of salt ions (e.g., Na+, Cl-) inside the membrane. We adopt a model based on the Nernst-Planck theory, that requires only three input parameters─membrane thickness, its charge density, and pK of proton adsorption─to predict the concentration profiles of four ions (H+, OH-, Na+, and Cl-) inside the membrane and the resulting current-voltage curve. The model can predict most of the experimental results measured with a commercial BPM, including the observation of limiting and overlimiting currents, which emerge due to particular concentration profiles that develop inside the BPM. This work provides new insights into the physical phenomena in BPMs and helps identify optimal operating conditions for future environmental applications.

Electrochemical response of unconsolidated sediment during liquid pore water phase change and its inspiration for gas hydrate saturation calculation

Electrical exploration is one of the most effective methods to estimate the location and abundance of hydrates. To better understand the relationship between electrical resistivity and gas hydrate saturation, the conduction mechanism of hydrate-bearing sediment needs to be investigated. Ice-bearing sediments with physical properties similar to hydrate-bearing sediment were synthesized using NaCl solution with different initial salinity. Electrical resistivity was detected using electrochemical impedance spectroscopy. Meanwhile, the distribution of relaxation time (DRT) was utilized to separate the electrochemical processes with various time constants and to analysis the conductive mechanism in depth. It is found that ion migration is the main conductive path of ice-bearing sediments. Salt ion transport is the main conducting path when ice saturation is low. Conversely, hydrogen or salt ion transport through ice is the main conducting path when ice saturation is high. The dual effects of ice on ion transport can be reflected in reducing and enhancing pore water resistivity. Based on the DRT results, increased ice saturation in larger pores hiders salt ion migration and promotes hydrogen ion movement, while the ice-sediment interface in smaller pores may form a highly conductive path. Moreover, it is also found that the DRT can be used to calculate water saturation. A cubic polynomial relationship is suggested between the DRT curve area and ice saturation. The application of electrochemical method to data analysis is very beneficial and can provide valuable information for obtaining more reliable hydrate saturation from electrical resistivity data. The results of this study are helpful to improve gas hydrate saturation interpretation models and provide significant guidance for gas hydrate production strategy design.

Electrochemical and hydraulic analysis of thin-film composite and cellulose triacetate membranes for seawater electrolysis applications

Polymeric filtration membranes could be a cost-effective alternative to cation exchange membranes (CEMs) in electrolysis with a contained anolyte and saltwater catholyte because they size selectively hinder salt ion transport between compartments while facilitating proton and hydroxide transport. Optimizing membrane performance requires a better understanding of membrane properties that impact electrical resistances and ion retention. Twelve reverse osmosis (RO) membranes, one nanofiltration (NF) membrane, and one cellulose triacetate forward osmosis (FO) membrane were examined for their electrical resistances under conditions typically used for characterization of CEMs. Resistances measured at low current densities (0.07–0.3 mA cm−2) varied between different membranes by over an order of magnitude in 1 M NaCl at neutral pH, from 6.1 ± 0.1 Ω cm2 to 70 ± 30 Ω cm2. There was no significant correlation between membrane resistance and applied potential during saltwater electrolysis at 20 mA cm−2 (p = 0.44), or between membrane resistance and water permeability (p = 0.35). These results indicate that traditional CEM resistance characterization methods do not predict polymeric filtration membrane electrolysis performance because proton and hydroxide transport, which is important during electrolysis when large pH gradients develop, must be considered separately from salt ion and water molecule transport through size selective RO, NF, and FO membranes during water electrolysis.

Mathematical Modeling of the Influence of the Karman Vortex Street on Mass Transfer in Electromembrane Systems

In electromembrane systems, the transfer of ions near ion-exchange membranes causes concentration polarization, which significantly complicates mass transfer. Spacers are used to reduce the effect of concentration polarization and increase mass transfer. In this article, for the first time, a theoretical study is carried out, using a two-dimensional mathematical model, of the effect of spacers on the mass transfer process in the desalination channel formed by anion-exchange and cation-exchange membranes under conditions when they cause a developed Karman vortex street. The main idea is that, when the separation of vortices occurs on both sides in turn from the spacer located in the core of the flow where the concentration is maximum, the developed non-stationary Karman vortex street ensures the flow of the solution from the core of the flow alternately into the depleted diffusion layers near the ion-exchange membranes. This reduces the concentration polarization and, accordingly, increases the transport of salt ions. The mathematical model is a boundary value problem for the coupled system of Nernst-Planck-Poisson and Navier-Stokes equations for the potentiodynamic regime. The comparison of the current-voltage characteristics calculated for the desalination channel with and without a spacer showed a significant increase in the intensity of mass transfer due to the development of the Karman vortex street behind the spacer.

Development of Mixed-Dimensional Membranes Comprising Halloysite Nanotubes and Kevlar Aramid Nanofiber for Enhanced Small-Molecule Dye/Salt Separation

In this work, the novel mixed-dimensional nanofiltration membranes [halloysite nanotubes (HNTs)/Kevlar aramid nanofiber (KANF)] with the ability to separate small-molecule dye/salt mixtures were prepared by comprising the rigid HNTs and the soft KANF. The considerable sieving in separating low-molecule dyes from dye/salt mixture solution was designed via the provision of additional channels for water molecules and salt ion transport via the special structure of the hollow structure of HNTs. The optimal 30% HNTs/KANF membrane displayed an eightfold water flux (39.2 L m–2 h–1) of the HNTs-free membrane, the low rejection of salts (21.7% for Na2SO4 and 7.7% for NaCl), and high rejection of various dyes (98.7% for Coomassie brilliant blue G-250, 95.3% for Congo red, 99.5% for Eriochrome black T, and 98.0% for Tropaeolin O). Besides, owing to the hydrophilicity of HNTs and the highly ordered and compact structure of KANF, the HNTs/KANF mixed-dimensional membrane showed excellent antipollution performance and long-term stability. This study provides some ideas for improving the permeability and selectivity of nanofiltration membranes by adding nanomaterials with special structures.

INFLUENCE OF SPACE CHARGE BREAKDOWN ON THE PERFORMANCE OF ELECTROMEMBRANE SYSTEMS

It is known that the existing methods of using electromembrane systems (EMS) do not allow the most efficient water treatment and water treatment at overlimiting current modes, which is why there is a need to determine the operating parameters of electrodialysis plants to prevent complex destructive effects, it is essential limiting mass transfer, and reducing the efficiency of EMS. In addition, in practice, a contradiction is found in practice - an increase in the potential jump in the existing EMS does not provide an intensification of the transfer of salt ions under overlimiting current modes. The article is devoted to the study of the influence of one of the destructive phenomena - the breakdown of the space charge on the performance of electromembrane systems in highly diluted salt solutions. The aim of this work is a theoretical assessment of the effect of space charge breakdown on the transport of salt ions in electromembrane systems. A mathematical model based on the Nernst-Planck and Poisson equations has been developed. The process of electrodialysis desalination of a NaCl solution located in a flow chamber between an anion exchange membrane (AEM) and a cation exchange membrane (CEM) is considered. The solution flow is directed from bottom to top. Numerical modeling of the effect of space charge breakdown on EMS performance in highly dilute salt solutions has been carried out. The new mathematical model and software have been developed for numerical simulation of the effect of space charge breakdown on EMS performance in highly dilute salt solutions. In this work, using a 2D mathematical model and the formula for the current-voltage characteristic of the desalination channel, the effect of space charge breakdown on the transfer of salt ions in electromembrane systems at various values of the potential jump was determined for the first time. The ranges of currents are determined, which correspond to a high and slight increase in the performance of electromembrane systems, as well as a range of currents in which there is no increase. The obtained results can be used to determine the optimal value of the potential jump according to the criterion of maximum productivity. The results obtained can be applied to the design of industrial EMC to intensify mass transfer and increase productivity.

Hierarchical N-Doped porous 3D network electrode with enhanced capacitive deionization performance

Capacitive deionization (CDI) has emerged as a promising method of desalination owing to its outstanding regeneration efficiency, low energy consumption, and without secondary contamination. The electrosorption capacity is largely determined by the electrode material. Nevertheless, the bottlenecks of present carbon-based CDI electrode materials are their limited desalination capability and single pore channel, which are unfavorable for salt ion diffusion and access to the internal space. Herein, we synthesized nitrogen-doped porous carbon (NPC) and performed a facile activation to obtain hierarchical porous carbon (KNPC) for CDI desalination. The optimized KNPC showed a remarkable desalination performance of 28.40 mg/g in 500 mg/L NaCl solution, with an exceptional regeneration performance of 94.44% after 15 consecutive cycles. The enhanced CDI performance could be attributed to the following aspects: (1) KNPC was introduced plenty of microporous and mesoporous structures, which provides convenient transport channels and accelerated salt ion transport. (2) The enlarged specific surface area and pore volume provide sufficient adsorption sites for salt ions. (3) The modified KNPC exhibited excellent electrochemical properties and wettability, consisting of higher specific capacitance, decreased internal resistance, and ultra-high hydrophilicity. (4) KOH activation promoted the capacitive contribution of the KNPC electrode, thus improving its CDI performance.

Simulating the effect of subsurface tile drainage on watershed salinity using SWAT

Subsurface tile drains in areas with intensive agriculture can be a major contributor of salinity loadings to streams and rivers, as salts in soil and groundwater are transported into the tile drains. Modeling tools can be used to assess baseline conditions, quantify salt mass export, and assess management scenarios to decrease salt removal. In this study, a newly developed version of the SWAT model for salinity transport, SWAT-Salt, was modified to include salt ion transport in subsurface tile drains and used to explore the effects of region-wide implementation of subsurface drainage on salinity transport and export from an irrigated semi-arid watershed. The model includes the transport of 8 major salt ions (SO4, Ca, Na, Cl, Mg, K, CO3, HCO3), and with the inclusion of tile drain transport simulates the fate and reactive transport of these ions in soil water, groundwater, tile drain water, and stream water. The SWAT-Salt model is applied to a 732 km2 salinity-impaired irrigation region within the Arkansas River Valley in southeastern Colorado. The model is first tested against salt ion data in effluent from a 15 km2 tile drainage district, and then applied to the entire region to assess the impact of region-wide implementation of subsurface tile drainage on in-stream salt ion concentrations, in-stream salt ion loading, and total salt export from the watershed. The model can be a useful tool in simulating salinity transport in tile drained watershed and investigating the effect of salinity management practices at a variety of spatial and temporal scales.

Mathematical modeling of the influence of non-catalytic dissociation / recombination of water molecules in the desalination channel on electric convection

The article formulates a two-dimensional mathematical model of non-stationary transport of 1: 1 electrolyte in a potentiodynamic mode, taking into account electroconvection and non-catalytic dissociation / recombination reaction of water molecules in electromembrane systems, which are considered as the desalting channel of an electrodialysis device. The model is described by a system of coupled Navier-Stokes and Nernst-Planck-Poisson equations taking into account the electric force and physically justified boundary conditions. The article establishes the basic laws of mass transport, taking into account the dissociation / recombination of water molecules. It was shown for the first time that a double electric layer of hydrogen and hydroxyl ions arises in the recombination region. It is shown that between the region of recombination and quasi-equilibrium regions of space charge there are regions of electroneutrality and equilibrium with an almost linear distribution of concentrations. It was found that even under prelimiting, but close enough to the limiting current, modes, non-catalytic dissociation of water molecules in the quasi-equilibrium region of space charge occurs so intensely that the concentration of hydrogen and hydroxyl ions becomes comparable to the concentration of potassium and chlorine ions. At overlimiting current densities, due to the appearance of an extended space charge region and intense dissociation of water molecules in this region, as well as an increase in the electric double layer in the recombination region, the space charge and the dissociation / recombination reaction of water molecules significantly affect each other. In turn, this has a decisive effect on electroconvection and, accordingly, on the transport of salt ions.

One-dimensional mathematical models of salt ion transport in electromembrane systems

This article presents a 1D classification and analysis of mathematical models of binary salt ion transport in electromembrane systems. The various phenomena of concentration polarization occurring in these systems are studied using mathematical models, both individually and in combination with each other. In accordance with this, we have carried out the classification of these phenomena, problems and mathematical models. The article presents a hierarchy of subordination of 1D mathematical models. A brief review, comparison, and analysis of the results of the boundary value problems from the proposed hierarchy are carried out. A numerical study and comparison of some mathematical models from the proposed hierarchy are carried out. The scope of applicability and limitations for each model are defined.

Boron and salt ion transport in electrically assisted reverse osmosis

Herein, we report a novel electrically assisted reverse osmosis (EARO) process which integrates an electrochemical process with the conventional RO process. We systematically investigated the behaviors of boron and salt ion (i.e., Na+ and Cl−) transporting through a commercial seawater RO (SWRO) membrane in the EARO process under a range of applied voltages by employing an external porous carbon cloth as cathode on the SWRO membrane surface. The SWRO membrane in the EARO process exhibited a significantly enhanced boron rejection of 93.8% under the applied voltage of 4 V compared with the conventional RO process (~75.0%). The enhancement in boron removal efficiency in EARO is mainly attributed to the locally elevated pH near the RO membrane surface caused by water electrolysis. At elevated pH, boron transforms from the uncharged boric acid to negatively charged and sized-increased borate ion and is more favorably rejected by the SWRO membrane. On the other hand, the variation of salt ion rejection was marginal with increasing the applied voltages in EARO. This study demonstrates that the EARO has a great potential to achieve low-chemical and low-cost boron removal in one-pass RO seawater desalination. To make this process more practically feasible, the future efforts need to optimize the development of the electrically conductive feed spacer and the membrane module.

Theoretical Analysis of the Stationary Transport of 1:1 Salt Ions in a Cross-Section of a Desalination Channel, Taking into Account the Non-Catalytic Dissociation/Recombination Reaction of Water Molecules.

In electromembrane systems, the theoretical study of salt ion transport usually uses mathematical models of salt ion transport in the depleted diffusion layer of ion-exchange membranes. This study uses a one-dimensional mathematical model of salt ion transport in a cross-section of a desalination channel formed by anion-exchange and cation-exchange membranes, taking into account an effect of a dissociation/recombination reaction of water molecules. The reaction on the one hand leads to an overlimiting mass transfer due to the effect of exaltation of the limiting current. On the other hand, an appearance of new electric charge carriers (hydrogen and hydroxyl ions) can reduce the space charge that occurs in membranes and suppress an electroconvective mechanism of overlimiting transport. Thus, there is a problem of studying these phenomena together, taking into account their mutual influence, and this article is devoted to the solution of this problem. Theoretically, using a method of mathematical modeling and numerical research, main regularities are established; in particular, it is shown that the dissociation/recombination reaction of water molecules does not lead to the destruction of the double electric layer at the membranes, but also creates a new double electric layer in the middle of the desalination channel. Thus, the space charge and the dissociation/recombination reaction significantly affect each other and simultaneously the transport of salt ions.

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

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

Hydrophilic microporous membranes for selective ion separation and flow-battery energy storage.

Membranes with fast and selective ion transport are widely used for water purification and devices for energy conversion and storage including fuel cells, redox flow batteries and electrochemical reactors. However, it remains challenging to design cost-effective, easily processed ion-conductive membranes with well-defined pore architectures. Here, we report a new approach to designing membranes with narrow molecular-sized channels and hydrophilic functionality that enable fast transport of salt ions and high size-exclusion selectivity towards small organic molecules. These membranes, based on polymers of intrinsic microporosity containing Tröger's base or amidoxime groups, demonstrate that exquisite control over subnanometre pore structure, the introduction of hydrophilic functional groups and thickness control all play important roles in achieving fast ion transport combined with high molecular selectivity. These membranes enable aqueous organic flow batteries with high energy efficiency and high capacity retention, suggesting their utility for a variety of energy-related devices and water purification processes.

Modeling and numerical analysis of the effect of dissociation/recombination of water molecules on the transport of salt ions in diffusion layer

Introduction. The paper presents a theoretical study on binary salt ion transport considering the water dissociation/recombination reaction. The work objectives are as follows: to build a mathematical model; to develop an algorithm for the numerical solution to the boundary value problem corresponding to the mathematical model; to work out the similarity theory including the transition to a dimensionless form using characteristic quantities; to determine a physical meaning of trivial similarity criteria; to find nontrivial similarity criteria; to build and analyze the volt-ampere characteristic (VAC).Materials and Methods. The theoretical study and numerical analysis of the transport of binary salt ions consider the dissociation/recombination reaction of water. In this case, the heat transfer equation and the mathematical model of electrodiffusion of four types of ions simultaneously (two salt ions, as well as ????+ and ????????−ions) in the diffusion layer of electromembrane systems with a perfectly selective membrane are used. For the first-order differential equations, a singularly perturbed boundary-value problem is set. In the equation for the electric field, the right side is independent of the intensity. In the numerical solution to the digitized system of equations by the Newton-Kantorovich method, this causes the stability of the method. In this regard, the boundary-value problem is reduced for numerical solution: a transition to a system of the second-order equations is provided, and the missing boundary conditions for the electric field strength are calculated.Research Results. A new mathematical model, a numerical algorithm to solve a boundary value problem, and software are developed. A numerical analysis is carried out, and fundamental laws of the transport of salt ions are determined considering the dissociation/recombination reaction of water molecules, temperature effects, and Joule heating. The VAC is built and analyzed.Discussion and Conclusions. The transport of binary salt ions through a diffusion layer near a cation exchange membrane is considered. A mathematical model of this process is proposed. It takes into account the temperature effects due to dissociation/recombination reactions of water molecules and Joule heating in a solution. The basic laws of the transport of salt ions are established considering the dissociation/recombination reaction of water molecules and temperature effects. The temperature effects of the dissociation/recombination reaction and the Joule heating in the electroneutrality region (ENR) are almost imperceptible (with the exception of the recombination region, RR). The Joule heating in the space-charge region (SCR) is by two orders of magnitude larger than the cooling effect of the water dissociation reaction. Upon recombination, approximately the same heat is released in the RR as during Joule heating in the expanded SCR. However, due to the small size of the RR, the effect of this heat is imperceptible. Therefore, we can assume that there is only one heat source at the interface in the SCR, which, due to its noticeable size, causes a significant increase in temperature in the entire diffusion layer. It follows that the emergence and development of gravitational convection is possible. General conclusions, following from the results obtained, open up the possibility of intensifying the process of transport of salt ions in the electrodialysis machines.