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Keywords = solution-diffusion-electromigration

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23 pages, 3666 KB  
Article
Electromigration of Chloride Ions in Cementitious Material: Extension of Nernst–Planck Theory
by Xingji Zhu, Yujie Hao, Jie Wang and Changrong Xiao
Buildings 2025, 15(18), 3429; https://doi.org/10.3390/buildings15183429 - 22 Sep 2025
Cited by 1 | Viewed by 763
Abstract
The transport of chloride ions in concrete is often affected by electric fields, and its concentration distribution is generally evaluated using the Nernst–Planck equation. The Nernst–Planck theory can only effectively predict the mass electromigration in ideal porous media. However, under an electric field, [...] Read more.
The transport of chloride ions in concrete is often affected by electric fields, and its concentration distribution is generally evaluated using the Nernst–Planck equation. The Nernst–Planck theory can only effectively predict the mass electromigration in ideal porous media. However, under an electric field, cementitious materials still have a certain binding ability to chloride ions. This causes the transport model to have significant prediction errors, and the specific value of the electromigration coefficient cannot be accurately measured. This article systematically investigated the transfer rate of chloride ions in cementitious material under different current densities. An analytical solution of the Nernst–Planck equation containing an independent electromigration coefficient was presented, and its value was quantitatively measured and discussed. The results indicated that the relationship between the electromigration and the apparent diffusion coefficient of chloride ions needs to be fitted in segments corresponding to various electric voltage intensities; but the electromigration coefficient shows a highly linear relationship with the pure effective diffusion coefficient. This work can provide assistance and valuable data support for the evaluation of mass transport in non-ideal porous media, such as cementitious materials, using the Nernst–Planck theory. Full article
(This article belongs to the Section Building Materials, and Repair & Renovation)
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18 pages, 2121 KB  
Article
Li+ Separation from Multi-Ionic Mixtures by Nanofiltration Membranes: Experiments and Modeling
by Tobias Hubach, Marcel Pillath, Clemens Knaup, Stefan Schlüter and Christoph Held
Modelling 2023, 4(3), 408-425; https://doi.org/10.3390/modelling4030024 - 20 Sep 2023
Cited by 8 | Viewed by 3256
Abstract
Aqueous sources like salt lake brines and seawater are the most abundant source for lithium ions and might contribute to the growing demand for lithium for energy storage. By coupling with the increasingly relevant reverse osmosis systems, nanofiltration can provide a promising process [...] Read more.
Aqueous sources like salt lake brines and seawater are the most abundant source for lithium ions and might contribute to the growing demand for lithium for energy storage. By coupling with the increasingly relevant reverse osmosis systems, nanofiltration can provide a promising process alternative to conventional methods such as water evaporation and salt precipitation from ores or brines for this purpose. One possible model for nanofiltration is the solution-diffusion-electromigration model (SDEM). First, the model was parametrized by determining the permeances from simple electrolyte mixtures containing two salts. Then, the SDEM was used to predict the rejections of complex multi-electrolyte solutions that mimic seawater and reverse osmosis brine, without fitting additional parameters to experimental data of this complex mixture. This allowed predicting ion rejections satisfactorily. Negative rejections due to spontaneously generated electric fields in the membrane could also be qualitatively described. In summary, this SDEM modeling can provide an important contribution to the purification of Li+ from aqueous sources. Full article
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19 pages, 7185 KB  
Article
Model-Based Optimization of Multi-Stage Nanofiltration Using the Solution-Diffusion–Electromigration Model
by Tobias Hubach, Stefan Schlüter and Christoph Held
Processes 2023, 11(8), 2355; https://doi.org/10.3390/pr11082355 - 4 Aug 2023
Cited by 1 | Viewed by 2419
Abstract
Nanofiltration is well suited to separate monovalent ions from multivalent ions, such as the separation of Li+ and Mg2+ from seawater, a potential lithium source for the production of lithium-ion batteries. To the best of our knowledge, there is no existing [...] Read more.
Nanofiltration is well suited to separate monovalent ions from multivalent ions, such as the separation of Li+ and Mg2+ from seawater, a potential lithium source for the production of lithium-ion batteries. To the best of our knowledge, there is no existing work on the optimization of a multi-stage membrane plant that differentiates between different ions and that is based on a validated transport model. This study presents a method for modeling predefined membrane interconnections using discretization along the membrane length and across the membrane thickness. The solution-diffusion–electromigration model was used as the transport model in a fundamental membrane flowsheet, and the model was employed to optimize a given flowsheet with a flexible objective function. The methodology was evaluated for three distinct separation tasks, and optimized operating points were found. These show that permeances and feed concentrations might cause negative rejections and positive rejections (especially for bivalent ions) depending on the ions’ properties and fluxes, thereby allowing for a favorable separation between the ions of different valence at optimized conditions. In an application-based case study for the separation of Li+ and Mg2+ from seawater, the method showed that under optimal conditions, the mol-based ratio of Mg2+/Li+ can be reduced from 2383 to 2.8 in three membrane stages. Full article
(This article belongs to the Section Separation Processes)
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23 pages, 1428 KB  
Review
The Role of pH, Electrodes, Surfactants, and Electrolytes in Electrokinetic Remediation of Contaminated Soil
by Brian Gidudu and Evans M. N. Chirwa
Molecules 2022, 27(21), 7381; https://doi.org/10.3390/molecules27217381 - 30 Oct 2022
Cited by 42 | Viewed by 5977
Abstract
Electrokinetic remediation has, in recent years, shown great potential in remediating polluted environments. The technology can efficiently remove heavy metals, chlorophenols, polychlorinated biphenyls, phenols, trichloroethane, benzene, toluene, ethylbenzene, and xylene (BTEX) compounds and entire petroleum hydrocarbons. Electrokinetic remediation makes use of electrolysis, electroosmosis, [...] Read more.
Electrokinetic remediation has, in recent years, shown great potential in remediating polluted environments. The technology can efficiently remove heavy metals, chlorophenols, polychlorinated biphenyls, phenols, trichloroethane, benzene, toluene, ethylbenzene, and xylene (BTEX) compounds and entire petroleum hydrocarbons. Electrokinetic remediation makes use of electrolysis, electroosmosis, electrophoresis, diffusion, and electromigration as the five fundamental processes in achieving decontamination of polluted environments. These five processes depend on pH swings, voltage, electrodes, and electrolytes used in the electrochemical system. To apply this technology at the field scale, it is necessary to pursue the design of effective processes with low environmental impact to meet global sustainability standards. It is, therefore, imperative to understand the roles of the fundamental processes and their interactions in achieving effective and sustainable electrokinetic remediation in order to identify cleaner alternative solutions. This paper presents an overview of different processes involved in electrokinetic remediation with a focus on the effect of pH, electrodes, surfactants, and electrolytes that are applied in the remediation of contaminated soil and how these can be combined with cleaner technologies or alternative additives to achieve sustainable electrokinetic remediation. The electrokinetic phenomenon is described, followed by an evaluation of the impact of pH, surfactants, voltage, electrodes, and electrolytes in achieving effective and sustainable remediation. Full article
(This article belongs to the Topic Green and Sustainable Chemistry)
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16 pages, 6906 KB  
Article
Effect of Bonding Strength on Electromigration Failure in Cu–Cu Bumps
by Kai-Cheng Shie, Po-Ning Hsu, Yu-Jin Li, K. N. Tu and Chih Chen
Materials 2021, 14(21), 6394; https://doi.org/10.3390/ma14216394 - 25 Oct 2021
Cited by 18 | Viewed by 5075
Abstract
In microelectronic packaging technology for three-dimensional integrated circuits (3D ICs), Cu-to-Cu direct bonding appears to be the solution to solve the problems of Joule heating and electromigration (EM) in solder microbumps under 10 μm in diameter. However, EM will occur in Cu–Cu [...] Read more.
In microelectronic packaging technology for three-dimensional integrated circuits (3D ICs), Cu-to-Cu direct bonding appears to be the solution to solve the problems of Joule heating and electromigration (EM) in solder microbumps under 10 μm in diameter. However, EM will occur in Cu–Cu bumps when the current density is over 106 A/cm2. The surface, grain boundary, and the interface between the Cu and TiW adhesion layer are the three major diffusion paths in EM tests, and which one may lead to early failure is of interest. This study showed that bonding strength affects the outcome. First, if the bonding strength is not strong enough to sustain the thermal mismatch of materials during EM tests, the bonding interface will fracture and lead to an open circuit of early failure. Second, if the bonding strength can sustain the bonding structure, voids will form at the passivation contact area between the Cu–Cu bump and redistribution layer (RDL) due to current crowding. When the void grows along the passivation interface and separates the Cu–Cu bump and RDL, an open circuit can occur, especially when the current density and temperature are severe. Third, under excellent bonding, when the voids at the contact area between the Cu–Cu bump and RDL do not merge together, the EM lifetime can be more than 5000 h. Full article
(This article belongs to the Topic Metallurgical and Materials Engineering)
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12 pages, 1816 KB  
Article
Nanofiltration of Multi-Ion Solutions: Quantitative Control of Concentration Polarization and Interpretation by Solution-Diffusion-Electro-Migration Model
by Marc Fernández de Labastida and Andriy Yaroshchuk
Membranes 2021, 11(4), 272; https://doi.org/10.3390/membranes11040272 - 8 Apr 2021
Cited by 14 | Viewed by 3289
Abstract
For effective use of advanced engineering models of nanofiltration quality of experimental input is crucial, especially in electrolyte mixtures where simultaneous rejections of various ions may be very different. In particular, this concerns the quantitative control of concentration polarization (CP). This work used [...] Read more.
For effective use of advanced engineering models of nanofiltration quality of experimental input is crucial, especially in electrolyte mixtures where simultaneous rejections of various ions may be very different. In particular, this concerns the quantitative control of concentration polarization (CP). This work used a rotating disklike membrane test cell with equally accessible membrane surface, so the CP extent was the same over the membrane surface. This condition, which is not satisfied in the conventional membrane test cell, made possible correcting for CP easily even in multi-ion systems. Ion rejections were studied experimentally for several dominant salts (NaCl, MgCl2, Na2SO4 and MgSO4) and trace ions (Na+, NH4+, Cl and NO3) using NF270 membrane. The solution–diffusion–electro–migration model was used to obtain ion permeances from the experimental measurements. The model could well fit the experimental data except in the case of NH4+. The correlations between the ion permeances and type of dominant salt are discussed in the context of the established mechanisms of NF such as Donnan and dielectric exclusion. The obtained information contributes to the systematic transport characterization of NF membranes and may be ultimately useful for computational fluid dynamics simulations of the performance of the membranes in various applications. Full article
(This article belongs to the Special Issue New Phenomenological Findings in Nanofiltration)
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