Relevant bibliographies by topics / Leaching kinetics

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Leaching kinetics'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Leaching kinetics"

1

Sequeira, César A. C. "Application of Mixed Potential Theory to Leaching of Mineral Phases." Reactions 3, no. 2 (2022): 312–28. http://dx.doi.org/10.3390/reactions3020023.

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Leaching is a central unit operation in the hydrometallurgical processing of minerals, which often occurs by means of electrochemical reactions. Application of mixed potential theory to explain the kinetics of oxidative and reductive leaching processes is a useful concept in explaining observed results. Native metals, selected oxides, and most base metal sulfides are electron-conducting phases. For these minerals, leaching may take place by normal corrosion, passivation or galvanic couple mechanisms, which provide individual electrode kinetics enabling the calculation of mixed potentials and o
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Mudruk, N. V., A. A. Antonov, A. I. Nikolaev, and O. V. Rybalkina. "Research on the acid decomposition kinetics of non-conventional titanium raw materials of the Arctic Zone of the Russian Federation." Arctic: Ecology and Economy 13, no. 1 (2023): 58–71. http://dx.doi.org/10.25283/2223-4594-2023-1-58-71.

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Acid leaching kinetics of loparite, perovskite, and titanite concentrates by hydrochloric and nitric acids has been studied. Kinetic parameters of acid leaching have been calculated and fitted to several kinetic models. Deeply kinetic study gives us the knowledge of acid leaching of titanium-containing minerals, and parameters obtained allow us to choose the optimal conditions of the mineral processing.
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Zheng, Fuqiang, Yufeng Guo, Feng Chen, et al. "Fluoride Leaching of Titanium from Ti-Bearing Electric Furnace Slag in [NH4+]-[F−] Solution." Metals 11, no. 8 (2021): 1176. http://dx.doi.org/10.3390/met11081176.

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The effects of F− concentration, leaching temperature, and time on the Ti leaching from Ti-bearing electric furnace slag (TEFS) by [NH4+]-[F−] solution leaching process was investigated to reveal the leaching mechanism and kinetics of titanium. The results indicated that the Ti leaching rate obviously increased with the increase of leaching temperature and F− concentration. The kinetic equation of Ti leaching was obtained, and the activation energy was 52.30 kJ/mol. The fitting results of kinetic equations and calculated values of activation energy both indicated that the leaching rate of TEFS
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Li, Jin, Jing Hua Pang, Cong Deng, Peng Zhao, and Shu Zhen Hou. "Kinetics on the Leaching of Polysaccharide from Arctium lappal Root." Advanced Materials Research 531 (June 2012): 334–37. http://dx.doi.org/10.4028/www.scientific.net/amr.531.334.

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To explore the kinetics parameters in the leaching of polysaccharide from Arctium lappal root. According to Fick’s second law of diffusion, the kinetic equation for polysaccharide leaching process was established with ball model. According to Fick’s second law of diffusion, leaching process was analysed. The results can provide the valuable theory basis for the technical design and further research of polysaccharide leaching process.
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Li, Jin, Peng Zhao, Mei Wang, Lu Wang, and Cong Deng. "Kinetics on the Leaching of Total Flavonoids from Arctium lappal Root." Advanced Materials Research 1021 (August 2014): 56–59. http://dx.doi.org/10.4028/www.scientific.net/amr.1021.56.

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To explore the kinetics parameters in the leaching of total flavonoids from Arctium lappal root. According to Fick’s second law of diffusion, the kinetic equation for total flavonoids leaching process was established with ball model. According to Fick’s second law of diffusion, leaching process was analysed. The results can provide the valuable theory basis for the technical design and further research of polysaccharide leaching process.
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Li, Jin, Chong Deng, Peng Zhao, Na Wang, and Lu Wang. "Kinetics on the Leaching of Polyphenol from Arctium lappal Root." Advanced Materials Research 586 (November 2012): 235–38. http://dx.doi.org/10.4028/www.scientific.net/amr.586.235.

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The kinetics parameters in the leaching of polyphenol from Arctium lappal root was studyed in this paper. According to second Fick’s law of diffusion, the kinetic equation for polyphenol leaching process was established with ball model. The results can provide the valuable theory basis for the technical design and further research of polyphenol from Arctium lappal root leaching process.
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Kontsevoy, A., and S. Kontsevoi. "LEACHING KINETICS OF PLATE-SHAPED PARTICLES." SCIENTIFIC-DISCUSSION, no. 93 (October 13, 2024): 5–7. https://doi.org/10.5281/zenodo.13926612.

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The type of the leaching kinetics equation depends on the area of the process - diffusion or kinetic, the nature of the solid material and solution, and the size and shape of the particles. The authors considered the course of leaching in the kinetic region for a solid polydisperse material in the form of a square plate, while neglecting the surface of the side faces of the plate. The distribution function of the number of particles N by their size r is taken in the form N=a∙r<sup>b</sup> , where a and b are constants. This distribution was used for the mathematical justification of the value
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Rogozhnikov, D. A., and B. V. Kolmachikhin. "Polymetallic Ore Concentration Middlings Nitric Acid Leaching Kinetics." Solid State Phenomena 265 (September 2017): 1065–70. http://dx.doi.org/10.4028/www.scientific.net/ssp.265.1065.

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The purpose of this work is the kinetic evaluation of reactions occurring during nitric acid leaching of pollymetallic sulfide middlings, for the most complete translation of copper, zinc and sulfur in solution and concentration of precious metals in residue. Methodology is pollymetallic sulfide middlings nitric acid leaching kinetics were studied using mathematical methods such as the experimental data numerical differentiation. Relevance/value is the main sulfide minerals kinetic characteristics were obtained for the studied materials, including the rate of the process, order of reaction, th
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Xu, Jingyuan, Shuchen Qin, Chaozhen Zheng, et al. "Study on Column Leaching Behavior of Low-Grade High Calcium and Magnesium Copper Ore." Minerals 14, no. 8 (2024): 822. http://dx.doi.org/10.3390/min14080822.

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This paper studies the process mineralogy, mechanism, and kinetics of column leaching behavior of low-grade high-calcium–magnesium copper ore. The effect of sulfuric acid concentration, leach solution spraying intensity, and material particle size on column leaching kinetics is discussed. The kinetic analysis of column leaching of copper indicates that sulfuric acid concentration has a significant impact. As sulfuric acid concentration increases, the limiting step of reaction shifts from chemical reaction control to a combination of chemical reaction and diffusion mixing control. Spraying inte
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Liu, Kui, and Xi Liu. "Kinetics of Atmospheric Acid Leaching of a Limonitic Laterite." Applied Mechanics and Materials 319 (May 2013): 14–18. http://dx.doi.org/10.4028/www.scientific.net/amm.319.14.

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A limonitic nickel laterite was leached by sulfuric acid at atmospheric pressure. Kinetics of leaching within the temperature range of 75-100°C was studied. The leaching kinetics followed the shrinking core model. The diffusion through the liquid film could be negligible under the agitation speed of 600rpm or above. Surface chemical reaction was the rate-controlling step. The semi-empirical kinetic equation was determined and the activation energy was 52.843kJ/mol.
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Dissertations / Theses on the topic "Leaching kinetics"

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Trejo-Gallardo, Jaime. "Modeling chalcopyrite leaching kinetics." Thesis, University of British Columbia, 2007. http://hdl.handle.net/2429/240.

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Chalcopyrite (CuFeS2) is the most abundant of the copper sulfides and also one of the most refractory for leaching. Several processing routes have been proposed to overcome drawbacks associated with environmental problems related to copper extraction from this mineral. Atmospheric leaching in acidic ferric sulfate is regarded as being particularly attractive over other hydrometallurgical systems. However, the challenge has been to overcome the problem of slow extraction rates due to passivity encountered at high solution potentials in this system. This highlights the need to investigate better
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Sililo, Bernard Liswani. "Modelling uranium leaching kinetics." Diss., University of Pretoria, 2016. http://hdl.handle.net/2263/61336.

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The uranium price decline has negatively impacted on the uranium mining industry. This decline in price requires that uranium metallurgical processes be made to operate more efficiently. Some key parameters that influence the dissolution and kinetics of leaching uraninite (one of the main minerals from which uranium can be extracted) are pH, oxidationreduction potential and iron concentration. A good understanding of the effect these parameters have on the leach kinetics would lead to an efficient operation of metallurgical processes. The objective of this work was therefore to investiga
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Zaayman, Yolande. "Leaching kinetics of synthetic heazlewoodite / Y. Zaayman." Thesis, North-West University, 2004. http://hdl.handle.net/10394/646.

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The sources of base metals are mainly in the form of oxides or sulphides, of which the sulphides are predominantly present in South Africa. These metals are intergrown platinum group and base metals in the form of alloys and sulphides. In order to produce high grade saleable metals, it is necessary to effectively separate the base metals from the precious metals. By means of a hydrometallurgical process, that is leaching, metals can selectively be extracted from ores. The mechanism of leaching can be described by oxidation-reduction and acid-base reactions. During this study, the leaching of a
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Taghi, Nazari Ghazaleh. "Enhancing the kinetics of pyrite catalyzed leaching of chalcopyrite." Thesis, University of British Columbia, 2012. http://hdl.handle.net/2429/41937.

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An investigation has been conducted into the kinetics of chalcopyrite leaching in acidic ferric/ferrous sulfate media at atmospheric pressure and low temperature in the presence of pyrite. It has been found that pyrite samples from different sources affect the rate of chalcopyrite leaching differently. Some pyrite samples accelerate the rate significantly while others have little or no influence. The effectiveness of pyrite has a strong correlation with the level of silver occurring in the pyrite. In this study, the use of silver-enhanced pyrite in the Galvanox™ process to improve the extract
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Dyson, Devy Alexander William. "Modeling the kinetics of the zinc pressure leaching process - oxidative sphalerite leaching in sulphuric acid media." Thesis, University of British Columbia, 2017. http://hdl.handle.net/2429/63409.

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In the field of hydrometallurgy, the industrial uptake of leaching models has been overlooked partially due to the lack of universal models. A model developed for one plant cannot easily be transferred for the application of a different plant without redesigning the leaching kinetics in the code. The Multiple Convolution Integral (MCI)-based model developed in this thesis has the ability to be universally applied by user-controlled inputs. Chemical reactions can be selected while the modeling software calculates the mass and energy balances. Residence times, operating conditions, and the rate-
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Velásquez, Yévenes Lilian de Lourdes. "The kinetics of the dissolution of chalcopyrite in chloride media /." Murdoch University Digital Theses Program, 2009. http://wwwlib.murdoch.edu.au/adt/browse/view/adt-MU20090430.154851.

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Angeles, Carlos. "Kinetics of leaching of covellite in ferric-sulfate-sulfuric acid media." Thesis, University of British Columbia, 2015. http://hdl.handle.net/2429/54587.

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Hydrometallurgy methods to extract copper are becoming more frequently applied in modern industry. However, the leaching kinetics for certain minerals like covellite is poorly understood. This thesis investigates the kinetics of covellite leaching in a ferric-sulfate-sulfuric acid media, with an emphasis first placed on the understanding of the effect of the most common variables such as temperature and redox potential. A natural mineral sample of covellite and an ore sample from the Oyu Tolgoi project in Mongolia were obtained for the leaching studies. The leaching temperature was varied fr
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Barriga, Vilca Abrahan. "Studies on the curing and leaching kinetics of mixed copper ores." Thesis, University of British Columbia, 2013. http://hdl.handle.net/2429/44500.

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Heap leaching is a metal extraction process from low grade ores where crushed ore is stacked on an impermeable pad and irrigated from the top with a solution of chemical reagents. An enriched solution containing the targeted metal is collected at the bottom. This technique involves complex chemical/electrochemical reactions and transport processes. Among the main features of this method of extraction include low capital and operative cost, modularity, and relatively high inventory of solutions. The need to optimize a heap operation has led to research studies in order to understand and interp
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Filippou, Dimitrios. "Reaction kinetics and reactor modelling of zinc-ferrite hot-acid leaching." Thesis, McGill University, 1994. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=41588.

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The main objectives of this Thesis were the determination of the reaction kinetics of the dissolution of zinc-ferrite particles ((Zn$ sb{1-x}$, Fe$ sbsp{x}{2+}$)$ rm Fe sbsp{2}{3+}O sb4$, x $ le$ 0.4) in hot aqueous solutions of sulphuric acid, and the development of a mathematical model for the prediction of the performance of a series of continuous stirred-tank reactors where zinc ferrite is leached.<br>Well-characterised, porous zinc-ferrite particles of industrial origin were subjected to controlled leaching experiments at temperatures close to 373 K in sulphuric acid solutions of concentr
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Yalcin, Sezgin. "Modeling Chromium Leaching From Chromite Ore Processing Waste." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/4/1053412/index.pdf.

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Chromium has been widely used in many industrial applications. As a result of chromite ore processing, large amounts of chromite ore processing waste (COPW) material that can be classified as hazardous have been produced and released into the environment. Therefore, knowledge of migration behavior and leaching rates of chromium through waste materials and soils are of primary concern for environmentally sound management of land-disposal hazardous wastes. Hask&ouml<br>k (1998) experimentally studied leaching rates of total Cr and Cr(VI) using laboratory columns packed with chromium COPW materia
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Books on the topic "Leaching kinetics"

1

Connell, Elaine Nancy A. Reaction kinetics for the leaching of Mno2 by nitrous acid. Laurentian University, School of Engineering, 1985.

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2

Georgiou, Dimitri. Kinetics of nickel dissolution during sulphuric acid pressure leaching for a limonitic laterite. National Library of Canada, 1995.

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Crundwell, F. K. The effect of flocculant additions to the leaching solution on the kinetics of the oxidative dissolution of sphalerite. Council for Mineral Technology, 1987.

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Leaching Kinetics of Valuable Metals. MDPI, 2021. http://dx.doi.org/10.3390/books978-3-0365-0549-7.

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Ubaldini, Stefano. Leaching Kinetics of Valuable Metals. Mdpi AG, 2021.

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Cheung, Miranda. Modelling of the nickel and cobalt kinetics during pressure acid leaching of laterites using Aspen Plus 11.1TM and OLI. 2004.

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Book chapters on the topic "Leaching kinetics"

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He, Kejie, Yating Deng, Yuxin Chen, Shuang Zheng, and Quanzhou Chen. "Leaching Kinetics of Reductive Leaching Manganese from Pyrolusite with Phenol." In Environmental Governance, Ecological Remediation and Sustainable Development. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-52901-6_20.

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Peng, Hong, Steven Peters, and James Vaughan. "Leaching Kinetics of Thermally-Activated, High Silica Bauxite." In Light Metals 2019. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-05864-7_2.

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Zhou, Shengfan, Bianfang Chen, Mingyu Wang, and Xuewen Wang. "Kinetics of Extracting Vanadium from Stonecoal by Alkali Leaching." In Rare Metal Technology 2016. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-48135-7_16.

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Zhou, Shengfan, Bianfang Chen, Mingyu Wang, and Xuewen Wang. "Kinetics of Extracting Vanadium From Stonecoal by Alkali Leaching." In Rare Metal Technology 2016. John Wiley & Sons, Inc., 2016. http://dx.doi.org/10.1002/9781119274834.ch16.

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Youcai, Zhao, and Zhang Chenglong. "Kinetics of Alkaline Leaching of Solid Wastes Bearing Zinc and Lead." In Pollution Control and Resource Reuse for Alkaline Hydrometallurgy of Amphoteric Metal Hazardous Wastes. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55158-6_3.

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Reverberi, A. P., L. Toro, and F. Vegliò. "Modelling of Reaction-diffusion Processes in Ore Leaching with Nonlinear Kinetics." In Nonlinear Dynamics and Control in Process Engineering — Recent Advances. Springer Milan, 2002. http://dx.doi.org/10.1007/978-88-470-2208-9_16.

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Obuz, Hüseyin Eren, Haydar Günes, Aslıhan Kara, Dilan Ugurluer, Yurdaer Babuccuoglu, and Murat Alkan. "Leaching Kinetics of Rare-Earth Elements from Complex Ores by Acidic Solutions." In The Minerals, Metals & Materials Series. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95022-8_201.

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Qiao, Yong, Jiang Diao, Xuan Liu, Xiaosa Li, Tao Zhang, and Bing Xie. "Kinetics of Dephosphorization from Steelmaking Slag by Leaching with C6H8O7NaOH-HCl Solution." In REWAS 2016. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-48768-7_22.

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Cheng, Jie, Hong-Yi Li, Cheng-Chao Wei, Xin-Mian Chen, Jiang Diao, and Bing Xie. "Leaching Kinetics of Vanadium from Calcification Roasted Vanadium Slag in (NH4)2CO3." In Rare Metal Technology 2024. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-50236-1_12.

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Qiao, Yong, Jiang Diao, Xuan Liu, Xiaosa Li, Tao Zhang, and Bing Xie. "Kinetics of Dephosphorization from Steelmaking Slag By Leaching With C6H8O7-Naoh-Hcl Solution." In Rewas 2016: Towards Materials Resource Sustainability. John Wiley & Sons, Inc., 2016. http://dx.doi.org/10.1002/9781119275039.ch22.

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Conference papers on the topic "Leaching kinetics"

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Dutta, Sreya, Kevin Coscia, and Satish Mohapatra. "Understanding Corrosion and Its Inhibition in Chloride Based Molten Salt Heat-Transfer Fluids Used in Concentrated Solar Power Plants." In CORROSION 2013. NACE International, 2013. https://doi.org/10.5006/c2013-02669.

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Abstract Concentrated Solar Power (CSP) provides an efficient way of converting solar energy to electricity and heat. Using expensive high alloy materials for piping in the solar field requires an immense capital cost, so it is beneficial to use less-expensive materials while still being able to circulate the fluid at high temperatures with minimal corrosion. Compared to the other melts, molten chloride salts provide operating temperatures higher than 600 °C which causes extensive corrosion of stainless steel. SEM, EDS and XRD studies showed that rare earth oxide (La2O3) was incorporated to th
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Xie, Hong-Yan, Hui Lu, and Ji-Kun Wang. "KINETICS OF MANGANESE LEACHING DURING PRESSURE ACID LEACHING OF LOW GRADE MANGANESE ORES." In 2015 International Conference on Energy and Mechanical Engineering. WORLD SCIENTIFIC, 2016. http://dx.doi.org/10.1142/9789814749503_0044.

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Zulkifili, Faizatul Syazwani, Norhaslinda Nasuha, Siti Wahidah Puasa, and Hawaiah Imam Maarof. "Leaching Kinetics of Iron from Electric Arc Furnace Slag (EAFS)." In International Technical Postgraduate Conference 2022. AIJR Publisher, 2022. http://dx.doi.org/10.21467/proceedings.141.2.

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The steelmaking process produces a substantial amount of electric arc furnace slag (EAFS). Therefore, this present study conducted acid leaching, with and without the use of oxidants such as hydrogen peroxide (H2O2) and potassium permanganate (KMnO4), to increase the amount of iron (Fe) recovered from the EAFS. The effect that reagent concentration of 0.5-8.0 M, leaching temperatures of 50-90 °C, and oxidant concentrations of 0.1-2.0 M had on leaching activities were investigated. A temperature of 50 °C, a 5 M sulphuric acid (H2SO4) concentration, a 1 M hydrogen peroxide concentration, a leach
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Malyshev, A. S., S. V. Kirillov, E. V. Kirillov, et al. "Influence of mechanoactivation on kinetics of REE leaching from phosphogypsum." In PHYSICS, TECHNOLOGIES AND INNOVATION (PTI-2019): Proceedings of the VI International Young Researchers’ Conference. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5134189.

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Cobos, J., J. A. Serrano, J. P. Glatz, B. Sätmark-Christiansen, and J. de Pablo. "The Kinetic of Dissolution of Irradiated UO2 Fuel Under Oxidising Conditions in Flow Experiments." In ASME 2001 8th International Conference on Radioactive Waste Management and Environmental Remediation. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/icem2001-1128.

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Abstract These leaching experiments report the effects of four important parameters (redox potential, pH, carbonate concentration and temperature) on the dissolution kinetics of the spent fuel matrix phase. The kinetic of dissolution of irradiated UO2 fuel has been studied in deionized water and synthetic granite groundwater under oxidising conditions at room temperature.
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Sandalov, I. P., A. V. Kritskii, and E. A. Kuzas. "KINETICS OF IRON COLLECTOR LEACHING IN HYDROCHLORIC AND HYDROFLUORIC ACID SOLUTIONS." In XVI INTERNATIONAL CONFERENCE "METALLURGY OF NON-FERROUS, RARE AND NOBLE METALS" named after corresponding member of the RAS Gennady Leonidovich PASHKOVA. Krasnoyarsk Science and Technology City Hall, 2023. http://dx.doi.org/10.47813/sfu.mnfrpm.2023.400-411.

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The paper presents the results of studying the kinetics of leaching of an iron collector containing ferrosilicon phases prone to encapsulation of platinum group metals in solutions of hydrochloric and hydrofluoric acids.
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"Kinetics of Vanadium Bearing Slag Leaching with a Mixture of Organic Acids." In Nov. 16-17, 2020 Johannesburg (SA). Eminent Association of Pioneers, 2020. http://dx.doi.org/10.17758/eares10.eap1120278.

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Napol'skikh, J. A., A. A. Shoppert, and I. V. Loginova. "Leaching kinetics of scandium from various red mud types by nitric acid." In PROCEEDINGS OF THE 16TH INTERNATIONAL CONFERENCE ON INDUSTRIAL MANUFACTURING AND METALLURGY (ICIMM 2021). AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0074915.

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Burlakovs, Juris. "MODIFIED CLAY AS SOIL AMENDMENT FOR REMEDIATION: STUDIES OF LEACHING AND SORPTION KINETICS." In 14th SGEM GeoConference on SCIENCE AND TECHNOLOGIES IN GEOLOGY, EXPLORATION AND MINING. Stef92 Technology, 2014. http://dx.doi.org/10.5593/sgem2014/b13/s4.117.

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Verdugo, Luis, Barbara Etschmann, Maryam Abdus-Salam, Andrew Hoadley, Jorge Menacho, and Joel Brugger. "Mechanochemical leaching of chalcopyrite in low moisture conditions." In Proceedings of XVI International Mineral Processing and Recycling Conference, Belgrade, 28-30.05.2025. University of Belgrade, Technical Faculty, Bor, 2024. https://doi.org/10.5937/imprc25395v.

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Copper concentrates represent 80% of the world's copper production. The main processing routes for copper extraction are pyrometallurgical via smelting or hydrometallurgical using moderate to high temperatures and/or high-pressure conditions, which affects the processing costs. An alternative presented in this work is the mechanochemical processing of concentrates, where the combined use of grinding and oxidizing reagents accelerates the leaching kinetics. Several mechanochemical tests were run in a laboratory mill using chalcopyrite in conjunction with various oxidants in low moisture conditi
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Reports on the topic "Leaching kinetics"

1

Abrajano, T. A. Jr, and J. K. Bates. Transport and reaction kinetics at the glass:solution interface region: Results of repository-oriented leaching experiments. Office of Scientific and Technical Information (OSTI), 1986. http://dx.doi.org/10.2172/59992.

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Waganet, R. J., John Duxbury, Uri Mingelgrin, John Hutson, and Zev Gerstl. Consequences of Nonequilibrium Pesticide Fate Processes on Probability of Leaching from Agricultural Lands. United States Department of Agriculture, 1994. http://dx.doi.org/10.32747/1994.7568769.bard.

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Pesticide leaching in heterogeneous field soils is relatively unstudied and is the focus of this project. A wide variety of heterogeneous soils exist, characterized by processes that result from the presence of structural cracks, worm holes, and other preferred pathways within which the majority of transport can occur (called physical non-equilibrium processes), along with the presence of sorption processes that are both equilibrium and kinetic (chemical non-equilibrium processes). Previous studies of pesticide leaching have focused primarily on relatively homogeneous soils, which are less wid
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