Model Of Ion Transport Research Articles

Multiscale modeling of ion transport in porous electrodes

AbstractIon transport through nanoporous materials is of fundamental importance for the design and development of filtration membranes, electrocatalysts, and electrochemical devices. Recent experiments have shown that ion transport across porous materials is substantially different from that in individual pores. Here, we report a new theoretical framework for ion transport in porous materials by combining molecular dynamics (MD) simulations at nanopore levels with the effective medium approximation to include pore network properties. The ion transport is enhanced with the combination of strong confinement and dominating surface properties at the nanoscale. We find that the overlap of electric double layers and ion–water interaction have significant effects on the ionic distribution, flux, and conductance of electrolytes. We further evaluate the gap between individual nanopores and complex pore networks, focusing on pore size distribution and pore connectivity. This article highlights unique mechanisms of ion transport in porous materials important for practical applications.

Numerical modeling of ion transport and adsorption in porous media: A pore-scale study for capacitive deionization desalination

A pore-scale model is presented to simulate the dynamic ion transport and adsorption processes in porous electrodes used for capacitive deionization (CDI). The Stokes equation governing water flow is solved using the lattice Boltzmann method and Nernst-Planck equation describing ion transport is solved using the finite volume method. The ion adsorption process is considered at the surface of carbon electrodes. After validation against analytical solutions and published results, the model is used to study the coupled water flow, ion transport and adsorption in both two-dimensional and three-dimensional porous CDI electrodes at the pore scale. The effect of electrode microstructure, electrical potential and flow velocity on the adsorption processes is quantitatively investigated, and the relative importance of various parameters is determined. The presented model can be a powerful numerical tool to quantitatively analyze ion transport and adsorption in porous electrodes, and may provide useful information for the design and optimization of CDI electrodes and operating conditions for desired desalination efficiency, water throughput and cost.

Modelling of sawtooth-induced fast ion transport in positive and negative triangularity in TCV

Internal kinks are a common magneto hydro-dynamic (MHD) instability observed in tokamak operation when the q profile in the plasma core is close to unity. This MHD instability impacts both the transport of the bulk plasma (current, particle and energy transport) and minority species, such as fast ions. In tokamak à configuration variable (TCV) (R 0/a = 0.88 m/0.25 m) the fast ion population is generated in the plasma by neutral beam tangential injection of energies up to 28 keV. TCV features 16 active shaping coils permitting a great flexibility in plasma shape, including negative triangularity (δ) configurations that show surprisingly high confinement. This study focuses on the transport of fast ions induced by sawteeth, by comparing two triangularity cases and simulation results with experimental data. Comparison of two equilibria with opposite δ shows that the fast ion drifts are larger for δ < 0. Furthermore, the sawtooth-induced transport in this case is larger than δ > 0 in similar conditions. Comparison with experimental data confirms the dominance of the modification of thermal kinetic profiles following the sawtooth crash in explaining drops in the neutron rates and fast ion D-α signals. Additional fast ion diffusion, however, improves the interpretation of the experimental data. For δ < 0, the amplitude of the perturbation better representing the experimental data is larger. Finally, an exploratory study for 50 keV particles (soon available in TCV) shows that the situation does not worsen for such particles.

The Dielectric Surface Conductivity Effect on the Dielectric Barrier Discharge Actuator Characteristics

The effect of the surface conductivity on the electrical and mechanical characteristics of the surface dielectric barrier discharge actuator has been numerically investigated in this study. Two typical ac-surface dielectric barrier discharge actuators, wire-to-plate and plate-to-plate, have been considered to control airflow alongside a flat dielectric plate. A sinusoidal high voltage of varied frequencies and amplitudes is supplied to the active electrode, and the passive electrode, which is grounded, is encapsulated inside a dielectric plate. Two-species ion transport model, involving generic positive and negative ions, coupled to the electrostatics model is assumed. The electrostatic field is affected by both the space and the surface charges. The surface charge is accumulated due to ion deposition, but its distribution varies due to the surface ohmic conduction. The Navier–Stokes equations for the flow simulation, which include the time-averaged electrohydrodynamic force determined from the discharge model, are solved to analyze the flow field and the boundary layer morphology. The numerical algorithm has been implemented in the COMSOL commercial package. The significance of the dielectric surface conductivity on the discharge behavior and the flow field has been shown. The dielectric surface conductivity behaves nonmonotonically and affects the flow field by altering the electrohydrodynamics force strength, direction, and distribution.

A Poisson–Nernst–Planck Model of Ion Transport and Interface Segregation in Metal–Insulator–Semiconductor Structures and Solar Cells

A numerical model that describes the transport of mobile ionic species in metal–insulator–semiconductor (MIS) and photovoltaic (PV) devices subject to temperature and voltage stress is presented. The finite element method (FEM) is used to solve the Nernst–Planck equation while imposing Poisson's equation self‐consistently as a restriction for the electrostatic potential. This allows the contribution of the ionic species to the potential to be taken into account. Using a variational formulation eases the implementation of diverse boundary conditions, including the incorporation of segregation kinetics at the device interfaces. Segregation across the dielectric–semiconductor interface is relevant to modeling the electronic device degradation in systems where contamination reaches the semiconductor. The model in closed systems with no‐flux boundary conditions is validated first. In the limiting case of low contamination levels with respect to the gate bias, the FEM solution matches analytically derived approximations. Then, the implementation is broadened to include an open boundary at the dielectric–semiconductor interface to account for leakage of ions. The predicted time dependence of the flatband voltage in Na‐contaminated MIS test structures agrees well with measurements. The model successfully captures the role of long‐range ion transport at concentrations of relevance to electronic and PV device instability and neuromorphic computing.

Salt and Water Transport in Reverse Osmosis Membranes: Beyond the Solution-Diffusion Model

Understanding the salt-water separation mechanisms of reverse osmosis (RO) membranes is critical for the further development and optimization of RO technology. The solution-diffusion (SD) model is widely used to describe water and salt transport in RO, but it does not describe the intricate transport mechanisms of water molecules and ions through the membrane. In this study, we develop an ion transport model for RO, referred to as the solution-friction model, by rigorously considering the mechanisms of partitioning and the interactions among water, salt ions, and the membrane. Ion transport through the membrane is described by the extended Nernst-Planck equation, with the consideration of frictions between the species (i.e., ion, water, and membrane matrix). Water flow through the membrane is governed by the hydraulic pressure gradient and the friction between the water and membrane matrix as well as the friction between water and ions. The model is validated using experimental measurements of salt rejection and permeate water flux in a lab-scale, cross-flow RO setup. We then investigate the effects of feed salt concentration and hydraulic pressure on salt permeability, demonstrating strong dependence of salt permeability on feed salt concentration and applied pressure, starkly disparate from the SD model. Lastly, we develop a framework to analyze the pressure drop distribution across the membrane, demonstrating that cross-membrane transport dominates the overall pressure drop in RO, in marked contrast to the SD model that assumes no pressure drop across the membrane.

Designing a Graphene Coating-Based Supercapacitor with Lithium Ion Electrolyte: An Experimental and Computational Study via Multiscale Modeling.

Graphene electrodes are investigated for electrochemical double layer capacitors (EDLCs) with lithium ion electrolyte, the focus being the effect of the pore size distribution (PSD) of electrode with respect to the solvated and desolvated electrolyte ions. Two graphene electrode coatings are examined: a low specific surface area (SSA) xGNP-750 coating and a high SSA coating based on a-MWGO (activated microwave expanded graphene oxide). The study comprises an experimental and a computer modeling part. The experimental part includes fabrication, material characterization and electrochemical testing of an EDLC with xGNP-750 coating electrodes and electrolyte 1M LiPF6 in EC:DMC. The computational part includes simulations of the galvanostatic charge-discharge of each EDLC type, based on a continuum ion transport model taking into account the PSD of electrodes, as well as molecular modeling to determine the parameters of the solvated and desolvated electrolyte ions and their adsorption energies with each type of electrode pore surface material. Predictions, in agreement with the experimental data, yield a specific electrode capacitance of 110 F g−1 for xGNP-750 coating electrodes in electrolyte 1M LiPF6 in EC:DMC, which is three times higher than that of the high SSA a-MWGO coating electrodes in the same lithium ion electrolyte.

Fast ion transport by sawtooth instability in the presence of ICRF–NBI synergy in JET plasmas

JET experiments have shown that the three-ion scenarios using waves in the ion cyclotron range of frequencies (ICRF) is an efficient way to build fast ion population through beam ion acceleration by radio frequency (RF) waves. Such a heating scheme is applied to plasmas with at least two thermal ion species. Analysis of mixed discharges with complex heating schemes requires a workflow that allows to model thermal and fast ion transport consistently. This paper is dedicated to modelling of a mixed plasma discharge with significant fraction of fast ions and contributes to development of fast ion transport models. For interpretive analysis with the TRANSP code a JET hydrogen–deuterium plasma discharge with neutral beam injection (NBI) and ICRF heating has been chosen. The task is complicated by NBI–ICRF synergy and plasma magnetohydrodynamic activity, like sawtooth crashes. D beam ions accelerated by RF waves form a high energy tail in fast ion distribution. Significant difference between the neutron rate computed by TRANSP and measured one is observed if the same diffusivity for electrons and ions is assumed. Sensitivity studies show that uncertainties in input plasma parameters and thermal ion transport models are crucial for modelling mixed plasma discharges and increased D transport is required to reach the plasma composition consistent with diagnostic measurements at the plasma edge. Fast ion redistribution by a sawtooth instability is characterised by non-resonant transport due to reconnection of magnetic field lines and resonant transport caused by resonance interaction between the instability and fast ions. With ORBIT simulations it has been shown that resonant interaction strongly affects fast ions of high energies, like beam ions accelerated by RF waves and fusion products. For the considered case, fast ion profiles simulated by ORBIT remain peaked after the sawtooth crashes.

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.

Solution Phase Limited Diffusion Modeling in a Li-ion Cell Subject to Concentration-Dependent Pore Wall Flux

Mathematical modeling of ionic transport in a Li-ion cell is critical for understanding and predicting key performance parameters such as cell voltage. Past work on solution phase limitation modeling of a Li-ion cell has assumed constant and uniform pore wall flux, which is valid only under certain conditions. It may be more appropriate to assume, similar to chemical reactions in general, that the pore wall flux is proportional to the local ion concentration. This paper presents a theoretical model for solution phase limited ionic diffusion in a separator-electrode stack under the assumption of the pore wall flux being linearly proportional to the local concentration. The resulting non-linear governing equation is linearized and solved using Laplace transformation technique. Concentration field in the two-layer stack is calculated as a function of space and time in a parameter space of practical interest. A comparison of results with past work based on constant, uniform reaction rate indicates that the assumed nature of concentration-dependence of the pore wall flux plays a significant role in determining the concentration distribution. This work advances the theoretical understanding of ionic diffusion in a Li-ion cell, and may contribute towards understanding and optimizing the performance of Li-ion cells.

The Archaeal Na+/Ca2+ Exchanger (NCX_Mj) as a Model of Ion Transport for the Superfamily of Ca2+/CA Antiporters.

The superfamily of Calcium/Cation (Ca2+/CA) antiporters extrude Ca2+ from the cytosol or subcellular compartments in exchange with Na+, K+, H+, Li+, or Mg2+ and thereby provide a key mechanism for Ca2+ signaling and ion homeostasis in biological systems ranging from bacteria to humans. The structure-dynamic determinants of ion selectivity and transport rates remain unclear, although this is of primary physiological significance. Despite wide variances in the ion selectivity and transport rates, the Ca2+/CA proteins share structural motifs, although it remains unclear how the ion recognition/binding is coupled to the ion translocation events. Here, the archaeal Na+/Ca2+ exchanger (NCX_Mj) is considered as a structure-based model that can help to resolve the ion transport mechanisms by using X-ray, HDX-MS, ATR-FTIR, and computational approaches in conjunction with functional analyses of mutants. Accumulating data reveal that the local backbone dynamics at ion-coordinating residues is characteristically constrained in apo NCX_Mj, which may predefine the affinity and stability of ion-bound species in the ground and transition states. The 3Na+ or 1Ca2+ binding to respective sites of NCX_Mj rigidify the backbone dynamics at specific segments, where the ion-dependent compression of the ion-permeating four-helix bundle (TM2, TM3, TM7, and TM8) induces the sliding of the two-helix cluster (TM1/TM6) on the protein surface to switch the OF (outward-facing) and IF (inward-facing) conformations. Taking into account the common structural elements shared by Ca2+/CAs, NCX_Mj may serve as a model for studying the structure-dynamic and functional determinants of ion-coupled alternating access, transport catalysis, and ion selectivity in Ca2+/CA proteins.

A continuum PNP model of double species ion transport between graphene

In this paper, we employ Poisson–Nernst–Planck equations in conjunction with the Navier–Stokes equations and the mean-field theory to investigate the charge transport of double species monovalent ions in double-layered graphene sheets, driven by an external electric field. Unlike most classical models, we develop a simple mechanical model by incorporating the microscopic effects of the physical systems so that the ionic interactions between ions and the host material, and the steric repulsions among ions are considered. Taking Li+-PF6−1 monovalent ions as an example, we find that the transport pattern for the present double species ionic systems and that for the pure lithium ions are dramatically different. Due to the mutual attractive ionic forces between ions and their counter-ions, such double species systems turn out to be more stable than that of the single species systems. In addition, the storage patterns of the former systems are richer, which depend heavily on initial ionic states, however less on the strength of applied electric fields and external temperatures when the graphene separation is not too large. The fluid flows, the electric conductivities and the stability of such double species systems are subsequently scrutinized. The current study could form a theoretical basis to help designing high-performance lithium batteries and explaining ion transport in biological channels.

Impedance Spectroscopy of Electrochromic Hydrous Tungsten Oxide Films

Tungsten oxide is a widely used electrochromic material with important applications in variable-transmittance smart windows as well as in other optoelectronic devices. Here we report on electrochemical impedance spectroscopy applied to hydrous electrochromic tungsten oxide films in a wide range of applied potentials. The films were able to reversibly bleach and color upon electrochemical cycling. Interestingly, the bleaching potential was found to be significantly higher than in conventional non-hydrous tungsten oxide films. Impedance spectra at low potentials showed good agreement with anomalous diffusion models for ion transport in the films. At high potentials, where little ion intercalation takes place, it seems that parasitic side reactions influence the spectra. The potential dependence of the chemical capacitance, as well as the ion diffusion coefficient, were analyzed. The chemical capacitance is discussed in terms of the electron density of states in the films and evidence was found for a band tail extending below the conduction band edge.

Chloride ion transport performance of lining concrete under coupling the action of flowing groundwater and loading

In this study, the chloride ion transport behavior of lining concrete under the coupling action of flowing groundwater and loading is investigated. The results indicate that the damage layer thickness and chloride ion concentration of the lining concrete increases with the increase of erosion age. The flowing groundwater accelerates the dissolution of the lining concrete, alkaline substances such as CH and NaOH in the lining concrete dissolve out. Under the action of the loading, the micro-cracks in the tension zone of the lining concrete continue to expand and the pores are connected to each other. Therefore, for same erosion age and distance from the lining concrete surface, the chloride ion concentration in the tensile zone is the highest under the coupling action of flowing groundwater and loading; that is followed by the action of flowing groundwater alone, and then, by the action of static groundwater. The chloride ion concentration in the pressure zone is the lowest, and the addition of fly ash and silica fume is found to help in decreasing the total chloride ion concentration and increasing the bound chloride ion concentration. In this study, a chloride ion transport model is established considering the accelerated dissolution of flowing groundwater, damage caused by loading in terms of micro-cracks and pore structure, and the effect of bound chloride ion on the total chloride ion transport, further, the rationality of the model is verified.

Desalination of Complex Multi-Ionic Solutions by Reverse Osmosis at Different pH Values, Temperatures, and Compositions.

For a thorough mechanistic understanding of reverse osmosis (RO), data on ion retention obtained by desalination of multi-ionic solutions are needed. In this paper, we show how to obtain such data under controlled laboratory conditions at any nonextreme pH. For that, we propose a simple method where we use N2 and CO2 gas control to set the composition of a gas phase in equilibrium with the feedwater solution. By increasing the CO2 partial pressure, the pH of the solution will decrease and vice versa. We applied this method of CO2 gas control to extend and validate an existing data set on ion retention of multi-ionic brackish water with 10 different ionic species, whereas conditions in the prior data set were slightly uncontrolled; in our new analysis, we performed experiments at precisely controlled pH and temperature. We run experiments at pH 6.73 and pH 7.11 and in a temperature range of T = 15–31 °C. Our results show that when pH is decreased, or temperature increased, the ion retention of most ions decreases. We also tested the influence of the Na+ to Ca2+ concentration ratio in this multi-ionic solution on ion retention at pH 6.73 and T ∼ 31 °C. We noticed that this ratio has a larger effect on ion retention for cations than for anions. We compare our data with the earlier reported data and describe similarities and differences. The improved data set will be an important tool for future development of accurate and validated RO ion transport models. Such RO models that describe desalination performance in detail are important for successful commercial application of the RO technology. We also discuss a relevant preparation method for water slightly oversaturated with barely soluble CaCO3 by solution preparation at high CO2 pressure, after which the solution is brought to the required pH by the N2 and CO2 gas control method.

Effect of multi‐factors on heterocharges for oil‐impregnated paper in converter transformer using modified charge transport model

The heterocharge accumulated in the oil-paper insulation system of the converter transformer will enhance the local electric field and cause insulation deterioration. Numerical simulation is an effective method to analyze heterocharge. Currently, the numerical simulation of heterocharge is mainly based on the bipolar charge transport (BCT) model and the impurity ion transport (IIT) model. However, the effects of temperature, conductivity, and thickness of oil-impregnated paper on charge transport have not been considered in these models. In view of this, a modified charge transport (MCT) model by introducing the Maxwell–Wagner model and heat conduction equation is proposed in this paper based on the BCT model and IIT model. Then, the influence of multi-factors (temperature gradient, moisture content, and oil-impregnated paper thickness) on heterocharge accumulation is investigated by using the MCT model. The simulation results obtained by the MCT model are more consistent with the experimental results than the BCT model, which proves the accuracy and superiority of the MCT model. Moreover, the increase in temperature gradient, moisture content, and oil-impregnated paper thickness will enlarge the ion dissociation rate, conductivity, and trap density, and thus promote the generation of heterocharge. In that respect, the MCT model is expected to optimize the insulation design and provide a reference for space charge dynamic simulation.

Evaluation of a novel mechanistic approach to predict transport of water and ions through shale

Prediction of transport parameters is an important issue in shale formations. A unique and novel to address this subject is the Revil model (Revil et al. 2011) which has been updated here for multivalent salts. The updated model for water and ion transport through shale has been evaluated against a range of experimental data sets. The updated Revil model only needs a few number of shale properties such as cation exchange capacity (CEC), porosity, and grain density which can be readily measured in laboratory. Also in the present work three parameters (f_Q,β_((+))^S,ν) have been considered as calibration parameters in the dynamic mode.In addition to updating Revil model for multivalent salts, we derived equations to calculate water and ion uptake in shale sample, a simplified equation to estimate IS and a proof for the conjecture that IS correlates with ME.The results show that in static mode, the model predicted the trend of data, however, the effect of semipermeable nature of shale on water uptake and alteration of ionic concentration in pore space was found negligible because of high salt concentrations (i.e. Cf>0.5M). In dynamic mode, by adjusting calibration parameters for each of test data, a complete matching could be obtained. In case of adjusting all experiments with only three common calibration parameters the prediction was not satisfactory, however, the results of intact-anion method was more accurate than Donnan method. When multiple sets of ME data in a broader range of concentration including low concentrations were plotted along with high-concentration data, correlativity was significant (R2>0.9). The present study for the first time in petroleum engineering research, suggested and implemented the updated Revil model as an applied tool for investigating static and dynamic behavior of semipermeable shales.

The transcriptome of anal papillae of Aedes aegypti reveals their importance in xenobiotic detoxification and adds significant knowledge on ion, water and ammonia transport mechanisms

The anal papillae of mosquito larvae are osmoregulatory organs in direct contact with the external aquatic environment that actively sequester ions and take up water in dilute freshwater. In the disease vector Aedes aegypti mechanisms of ion, water and ammonia transport have only been partially resolved. Furthermore, A. aegypti larvae are known to reside in high ammonia sewage and high salt brackish waters, and understanding of anal papillae function in these conditions is in its infancy. The objective of this study was to identify the complement of ion and water transport genes expressed by the anal papillae of freshwater larvae by sequencing their transcriptome, and comparing their expression in anal papillae of larvae abruptly transferred to brackish water for 24 h. Results identified a number of ion and water transport proteins, ammonia detoxifying enzymes, a full suite of xenobiotic detoxifying enzymes and transporters, and G-protein coupled receptors of specific hormones. We identified a marked increase in transcript and protein abundance of aquaporin AaAQP2 in the anal papillae with abrupt transfer to brackish water. We present an updated and more comprehensive model for ion and water transport with additional putative transporters for Na+ and Cl- uptake in the anal papillae. These are organs which are actively engaged in Na+, Cl- and water uptake and regulation when the aquatic larvae encounter fluctuating salinities over the course of their development. Furthermore the transcriptome of the anal papillae includes a full set of xenobiotic detoxification genes suggesting that these are important detoxification organs which is particularly important when larvae reside in polluted water.

(Invited) Understanding Multi-Component Transport and Reaction Phenomena in Bipolar Membranes Used for Electrosynthesis

Bipolar membranes (BPMs), which have long seen usage in electrodialysis reactors for the generation of acid and base, have recently demonstrated potential to become critical components in electrochemical synthesis devices. Because they can operate under large pH gradients, BPMs enable favorable environments for electrocatalysis at the individual electrodes. Critical to the implementation of BPMs in these devices is understanding the kinetics of water dissociation that occurs within the BPM junction as well as the co- and counter-ion crossover through the BPM, which both present significant obstacles to developing efficient and stable BPM-devices for electrosynthesis applications. Prior work has modeled ion transport in bipolar membranes in neutral salt solutions for electrodialysis. However, no model exists for the BPM under the harsh applied pH gradients that would be present in electrosynthesis, and there is significant need to explore the effects of the internal hydration on the lifetime and performance of BPMs in such environments. Additionally, a mechanistic understanding of water dissociation catalysis will be required to develop interfacial catalysts that enable the high current density operation required for scalable electrosynthesis of fuels.In this talk, we discuss modeling methodologies and physics inherent in BPMs and present our recent model of ion transport and water dissociation catalysis in BPMs across the pH scale. Specifically, we simulate multi-ion transport for a BPM with various electrolyte combinations on each side of the membrane, demonstrating the significance of co- and counter-ion crossover in BPMs operating under harsh pH gradients. We then investigate effects caused by hydration gradients that occur due to internal ion-exchange and examine potential methods for improving performance and mitigating crossover. Finally, we examine the impact of the interfacial water dissociation catalyst and perform sensitivity analysis on the key properties (catalyst point of zero charge and pKa) that dictate catalyst performance. These results provide information that is critical to developing a comprehensive understanding of multi-component phenomena in BPMs and to informing the design and implementation of BPMs in next-generation devices for the numerous electrosynthesis chemistries that benefit from operation under an applied pH gradient.

Correlation equation for evaluating energy consumption and process performance of brackish water desalination by electrodialysis

Electrodialysis (ED) is an electro-driven desalination technology that relies on the selective transport of ions through ion exchange membranes. Though several approaches have been developed to model and evaluate the performance of ED, mechanistic ion-transport models, which rigorously solve the fundamental Nernst-Planck equation, remain some of the most reliable and utilized. However, complexity of the involved transport phenomena prevents analytical solutions of such models, and numerical solutions can be prohibitively intensive. Here, we use an equivalent circuit analogue to derive a simple correlation equation that predicts the energetic performance of ED for brackish water desalination. Specifically, our correlation equation predicts the specific energy consumption of ED for a given productivity, set of desalination parameters (i.e., feed salinity, salt removal, water recovery), and system properties. The correlation equation demonstrates robustness in predicting the specific energy consumption across a wide range of operational parameters, showing excellent agreement with a Nernst-Planck ion-transport model and literature-reported experimental data. Furthermore, we use the developed correlation equation to show the dependence of the specific energy consumption on the productivity, highlighting the tradeoff between the thermodynamic energy efficiency and desalination rate of the ED process. Overall, our developed correlation equation provides a convenient alternative to computationally intensive mechanistic models for performance analysis of the ED process.