Kinetic Fick’s Law and the Integral-Differential Method of Solving the Neutron Transport Equation

Seliverstov, V. V.

doi:10.1007/s10512-016-0111-1

Cited by 6 publications

(6 citation statements)

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“…First, the influence size of each factor is estimated according to the range, and the effect is proportional to the value of the range. 29 As can be seen from Table 2, the influencing factors of Ni, Co, and Mn are in the same order: hydrogen peroxide has the most obvious effect on the experimental results, followed by the solid−liquid ratio and acid concentration. However, a smaller effect is given by time factor, and a smaller effect is obtained by the temperature among all factors.…”

Section: ■ Experimetal Sectionmentioning

confidence: 84%

“…The orthogonal experiment preliminarily determined the optimum condition and influence sizes of the factors. First, the influence size of each factor is estimated according to the range, and the effect is proportional to the value of the range . As can be seen from Table , the influencing factors of Ni, Co, and Mn are in the same order: hydrogen peroxide has the most obvious effect on the experimental results, followed by the solid–liquid ratio and acid concentration.…”

Section: Resultsmentioning

confidence: 99%

“…The trend of leaching efficiency with acid concentration can be explained by a diffusion model. Fick’s first law is a quantitative analysis which explains the diffusion rate . The formula is In formula , D is called the diffusion coefficient, C is the volume concentration of the diffused substance (component), d C / d x is the concentration gradient.…”

Section: Resultsmentioning

confidence: 99%

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Leaching Mechanisms of Recycling Valuable Metals from Spent Lithium-Ion Batteries by a Malonic Acid-Based Leaching System

Fan

Yang

Huang

et al. 2020

ACS Appl. Energy Mater.

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Considering the shortage and toxicity of raw materials, recycling cathode materials from spent lithium-ion batteries is currently the most promising measure to realize the green sustainability of cathode materials. Presently, most hydrometallurgical recovery methods and some cathode material synthesis methods are based on the use of acidic solutions. This study addresses the dissolution−chelation mechanism and limitations of the LiNi 1/3 Mn 1/3 Co 1/3 O 2 cathode materials in acidic solution, aiming at highlighting the interface reaction mechanism. In this work, malonic acid and hydrogen peroxide were used as the leaching system to conduct efficient green leaching of spent ternary cathode materials. The effects of different reaction parameters on the recovery efficiency of various valuable metal ions were studied by orthogonal and single-factor condition experiments. The results show that under the optimal conditions the leaching efficiency of the lithium ion is 95%, and the leaching efficiencies of Ni, Co, and Mn all reached over 98%. The dissolution mechanism was studied at the macro-and microscales based on the material characterization technology, kinetic studies, and the theoretical calculations of the binding energy of the possible product. Kinetic studies found that the dissolution−chelation process is controlled by chemical reactions or a chemical and diffusion reaction, and calculation results of the activation energy and binding energy show that lithium ions are leached preferentially over other metal ions. In addition, this recovery technology can be effectively used to recycle other spent rechargeable battery materials and may also lay a theoretical foundation for further study on the regeneration and resynthesis of materials.

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Section: ■ Experimetal Sectionmentioning

confidence: 84%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Leaching Mechanisms of Recycling Valuable Metals from Spent Lithium-Ion Batteries by a Malonic Acid-Based Leaching System

Fan

Yang

Huang

et al. 2020

ACS Appl. Energy Mater.

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“…A majority of established models are based on Fick's second law of diffusion, which states that the migration occurring in the thickness of a material can be described by a one‐dimensional second‐order partial differential equation. Seliverstov et al (Seliverstov, 2016) using the second law of diffusion and the Crank model studied the two‐layer model of the single‐layer migration model and established the Begley‐Holhfield model.…”

Section: Introductionmentioning

confidence: 99%

Assessment of migration regularity of phthalates from food packaging materials

Liu

Yang

et al. 2020

Food Science & Nutrition

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Phthalate acid esters (PAEs) are one of the essential plastic additives which may lead to plenty of harmful effects, including reproductive toxicity, teratogenicity, and carcinogenicity. Increasing attention has been paid to the migration of plasticizer. In this article, the disposable plastic lunch boxes were taken as the research object. The result showed that dibutyl phthalate (DBP) and diisobutyl phthalate (DIBP) have been mainly found, whose content was 1.5 mg/kg and 2.4 mg/kg, respectively. The LOD was 2 ng/g, and LOQ was 6.7 ng/g. We further investigated the migration of PAEs into the simulated liquid at different temperature conditions. Then, the linear fitting performing by first‐order kinetic migration model revealed that the lower the polarity of the simulated liquid, the larger the rate constant K 1 and initial release rate V 0 . The higher the temperature, the bigger the K 1 and V 0 .

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“…The H + in the liquid phase needs to diffuse across the liquid film and the solid–liquid phase interface and diffuse onto the solid particles to react. According to Fick's first law, [ 32 ]

J = - D \frac{d_{φ}}{d_{x}}

where J is the diffusion flux, D is the diffusivity, φ is the concentration, x is position, d φ/ d x is the concentration gradient. The d φ/ d x is proportional to the φ in the solution.…”

Section: Resultsmentioning

confidence: 99%

Effect of Hydrogen Peroxide on the Recovery of Valuable Metals from Spent LiNi_0.6Co_0.2Mn_0.2O₂ Batteries

et al. 2022

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Considering the increasing price of raw materials and environmental pollution, the recycling of used lithium battery cathode materials has very important economic and environmental value. In this experiment, a green recycling method is used to recover valuable metals from spent LiNi0.6Co0.2Mn0.2O2 batteries using DL‐malic acid and H2O2 as a leaching system. The effects of reaction temperature, acid concentration, H2O2 volume concentration, reaction time, and solid–liquid ratio on the leaching efficiency are investigated by orthogonal and single variable condition experiments. Under the optimum conditions, the leaching efficiencies of Ni, Co, Mn, and Li are 96.2%, 97.1%, 97.6%, and 98.1%, respectively, while the leaching efficiency of Al is only 3.5%. The effect of H2O2 on the leaching process is further investigated by macroscopic characterization and kinetic analysis. The study indicates that the leaching process is controlled by a chemical reaction in the absence of H2O2, and the leaching process after the addition of H2O2 is controlled by the chemical reaction process and the diﬀusion process.

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Kinetic Fick’s Law and the Integral-Differential Method of Solving the Neutron Transport Equation

Cited by 6 publications

References 1 publication

Leaching Mechanisms of Recycling Valuable Metals from Spent Lithium-Ion Batteries by a Malonic Acid-Based Leaching System

Leaching Mechanisms of Recycling Valuable Metals from Spent Lithium-Ion Batteries by a Malonic Acid-Based Leaching System

Assessment of migration regularity of phthalates from food packaging materials

Effect of Hydrogen Peroxide on the Recovery of Valuable Metals from Spent LiNi_0.6Co_0.2Mn_0.2O₂ Batteries

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Kinetic Fick’s Law and the Integral-Differential Method of Solving the Neutron Transport Equation

Cited by 6 publications

References 1 publication

Leaching Mechanisms of Recycling Valuable Metals from Spent Lithium-Ion Batteries by a Malonic Acid-Based Leaching System

Leaching Mechanisms of Recycling Valuable Metals from Spent Lithium-Ion Batteries by a Malonic Acid-Based Leaching System

Assessment of migration regularity of phthalates from food packaging materials

Effect of Hydrogen Peroxide on the Recovery of Valuable Metals from Spent LiNi0.6Co0.2Mn0.2O2 Batteries

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Effect of Hydrogen Peroxide on the Recovery of Valuable Metals from Spent LiNi_0.6Co_0.2Mn_0.2O₂ Batteries