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Journal articles on the topic 'Shrinking core model'

Author: Grafiati
Published: 4 June 2021
Last updated: 17 June 2025

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1

Wanta, Kevin Cleary, Felisha Hapsari Tanujaya, Ratna Frida Susanti, Himawan Tri Bayu Murti Petrus, Indra Perdana, and Widi Astuti. "Studi Kinetika Proses Atmospheric Pressure Acid Leaching Bijih Laterit Limonit Menggunakan Larutan Asam Nitrat Konsentrasi Rendah." Jurnal Rekayasa Proses 12, no. 2 (2018): 19. http://dx.doi.org/10.22146/jrekpros.35644.

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A B S T R A C TKinetics study of atmospheric pressure acid leaching (APAL) process is indispensable for extractor design in an industrial scale. So far, the kinetic model used for this process is the shrinking core model. In this study, the shrinking core model was evaluated against experimental data for laterite leaching process using a solution of low concentration nitric acid (0.1 M). Variations in temperature and particle size were carried out at 303–358 K and <75–250 microns. Other operating conditions, such as pulp density, stirring speed, and time were kept at 20% w/v, 200 rpm, and 120 minutes, respectively. The model evaluation results showed that the shrinking core model was not suitable for this process because the process controlling stage is not just one stage only.Keywords: kinetics; laterite; leaching; shrinking core.A B S T R A KStudi terkait kinetika proses atmospheric pressure acid leaching (APAL) sangat diperlukan untuk proses perancangan ekstraktor dalam skala industri. Selama ini, model kinetika yang digunakan untuk proses tersebut adalah model shrinking core. Dalam studi ini, model shrinking core dievaluasi terhadap data percobaan proses leaching bijih laterit dengan menggunakan larutan asam nitrat konsentrasi rendah, 0,1 M. Variasi suhu dan ukuran partikel dilakukan pada 303–358 K dan <75–250 mikron. Kondisi operasi lainnya, seperti densitas pulp, kecepatan pengadukan, dan lama proses dijaga tetap pada 20%b/v, 200 rpm, dan 120 menit, secara berurutan. Hasil evaluasi model menunjukkan bahwa model shrinking core tidak cocok untuk proses ini karena tahapan pengendali proses tidak hanya satu tahapan saja.Kata kunci: kinetika; laterit; leaching; shrinking core
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2

Moon, Jeremy, and Veena Sahajwalla. "Derivation of Shrinking Core Model for Finite Cylinder." ISIJ International 41, no. 1 (2001): 1–9. http://dx.doi.org/10.2355/isijinternational.41.1.

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3

Goto, Motonobu, Bhupesh C. Roy, and Tsutomu Hirose. "Shrinking-core leaching model for supercritical-fluid extraction." Journal of Supercritical Fluids 9, no. 2 (1996): 128–33. http://dx.doi.org/10.1016/s0896-8446(96)90009-1.

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4

da Rocha, Dominik, Eckhard Paetzold, and Norbert Kanswohl. "The shrinking core model applied on anaerobic digestion." Chemical Engineering and Processing: Process Intensification 70 (August 2013): 294–300. http://dx.doi.org/10.1016/j.cep.2013.05.003.

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5

Anameric, B., and S. K. Kawatra. "Shrinking-core model for pig iron nugget production." Mining, Metallurgy & Exploration 28, no. 1 (2011): 24–32. http://dx.doi.org/10.1007/bf03402321.

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6

Egorov, Andrey G., and Arthur A. Salamatin. "Bidisperse Shrinking Core Model for Supercritical Fluid Extraction." Chemical Engineering & Technology 38, no. 7 (2015): 1203–11. http://dx.doi.org/10.1002/ceat.201400627.

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7

Homma, Shunji, Shinji Ogata, Jiro Koga, and Shiro Matsumoto. "Gas–solid reaction model for a shrinking spherical particle with unreacted shrinking core." Chemical Engineering Science 60, no. 18 (2005): 4971–80. http://dx.doi.org/10.1016/j.ces.2005.03.057.

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8

Pednekar, Pratik, Debangsu Bhattacharyya, Job S. Kasule, Richard Turton, and Raghunathan Rengaswamy. "Development of a hybrid shrinking-core shrinking-particle model for entrained-flow gasifiers." AIChE Journal 62, no. 3 (2015): 659–69. http://dx.doi.org/10.1002/aic.15055.

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9

Safari, Vida, Gilnaz Arzpeyma, Fereshteh Rashchi, and Navid Mostoufi. "A shrinking particle—shrinking core model for leaching of a zinc ore containing silica." International Journal of Mineral Processing 93, no. 1 (2009): 79–83. http://dx.doi.org/10.1016/j.minpro.2009.06.003.

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10

Kwiatkowska-Marks, Sylwia, Marek Wójcik, and Leonard Kopiński. "An alternative method to determine the diffusion coefficient for the shrinking core model." Polish Journal of Chemical Technology 13, no. 2 (2011): 54–56. http://dx.doi.org/10.2478/v10026-011-0024-7.

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An alternative method to determine the diffusion coefficient for the shrinking core model A new method to determine the effective diffusion coefficient of sorbate in sorbent granule based on the analytical solution of the shrinking core model (SCM) has been proposed. The experimental data presented by Lewandowski and Roe1 concerning the sorption of copper ions by alginate granules have been applied to compare the analytical and numerical methods. The results obtained by both methods are very close.
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11

Jena, Pravat Ranjan, Sirshendu De, and Jayanta Kumar Basu. "A generalized shrinking core model applied to batch adsorption." Chemical Engineering Journal 95, no. 1-3 (2003): 143–54. http://dx.doi.org/10.1016/s1385-8947(03)00097-4.

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12

Sarkar, Debasish, and Amitava Bandyopadhyay. "Shrinking Core Model in characterizing aqueous phase dye adsorption." Chemical Engineering Research and Design 89, no. 1 (2011): 69–77. http://dx.doi.org/10.1016/j.cherd.2010.04.010.

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13

Bolden, Wayne B., Ted White, and Frank R. Groves. "Continuous fixed bed ligand exchange: The shrinking-core model." AIChE Journal 35, no. 5 (1989): 849–52. http://dx.doi.org/10.1002/aic.690350516.

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14

Lee, So-Yeong, Sung-Hun Park, and Ho-Sang Sohn. "Kinetic Study of Selective Chlorination of Iron in Ilmenite Ore." MATEC Web of Conferences 321 (2020): 07009. http://dx.doi.org/10.1051/matecconf/202032107009.

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The selective chlorination of ilmenite with coke and chlorine gas was conducted in the fixed bed reactor and effects of coke content and reaction temperature on reaction rate were investigated. In particular, the chlorination rate of iron in ilmenite was simulated by the unreacted shrinking core model. The reaction rate was simulated by calculating the chlorine gas consumption rate as the unreacted core shrinks. In addition, each of reaction resistances that chemical reaction at the reaction interface, diffusion through the product layer, and boundary film mass transfer resistances were calculated. The simulated reaction rates were in good agreement with the experimental results and the rate controlling step changed as the chlorination reaction progressed. Furthermore, the diffusion resistance through the product layer was dominant at lower reaction temperature, whereas the chemical reaction was dominant as the reaction temperature increased. It is because the diffusion of chlorine gas through the product layer could be hindered at lower reaction temperatures. Key words: Ilmenite, Selective chlorination, Synthetic rutile, Shrinking core model
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15

Pinto, Neville G., and E. Earl Graham. "Application of the shrinking-core model for predicting protein adsorption." Reactive Polymers, Ion Exchangers, Sorbents 5, no. 1 (1987): 49–53. http://dx.doi.org/10.1016/0167-6989(87)90164-4.

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16

JENA, P. "A generalized shrinking core model for multicomponent batch adsorption processes." Chemical Engineering Journal 102, no. 3 (2004): 267–75. http://dx.doi.org/10.1016/j.cej.2003.12.006.

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17

Xu, Fan, Yangchao Huang, Shichen Zhao, and Xi-Qiao Feng. "Chiral topographic instability in shrinking spheres." Nature Computational Science 2, no. 10 (2022): 632–40. http://dx.doi.org/10.1038/s43588-022-00332-y.

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AbstractMany biological structures exhibit intriguing morphological patterns adapted to environmental cues, which contribute to their important biological functions and also inspire material designs. Here, we report a chiral wrinkling topography in shrinking core–shell spheres, as observed in excessively dehydrated passion fruit and experimentally demonstrated in silicon core–shells under air extraction. Upon shrinkage deformation, the surface initially buckles into a buckyball pattern (periodic hexagons and pentagons) and then transforms into a chiral mode. The neighbouring chiral cellular patterns can further interact with each other, resulting in secondary symmetry breaking and the formation of two types of topological network. We develop a core–shell model and derive a universal scaling law to understand the underlying morphoelastic mechanism and to effectively describe and predict such chiral symmetry breaking far beyond the critical instability threshold. Moreover, we show experimentally that the chiral characteristic adapted to local perturbation can be harnessed to effectively and stably grasp small-sized objects of various shapes and made of different stiff and soft materials. Our results not only reveal chiral instability topographies, providing fundamental insights into the surface morphogenesis of the deformed core–shell spheres that are ubiquitous in the real world, but also demonstrate potential applications of adaptive grasping based on delicate chiral localization.
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18

Drozdov, I. V., R. Vaßen, and D. Stöver. "Modelling and evaluation of hydrogen desorption kinetics controlled by surface reaction and bulk diffusion for magnesium hydride." RSC Advances 5, no. 7 (2015): 5363–71. http://dx.doi.org/10.1039/c4ra08089k.

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19

Wanta, Kevin Cleary, Widi Astuti, Indra Perdana, and Himawan Tri Bayu Murti Petrus. "Kinetic Study in Atmospheric Pressure Organic Acid Leaching: Shrinking Core Model versus Lump Model." Minerals 10, no. 7 (2020): 613. http://dx.doi.org/10.3390/min10070613.

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The kinetics study has an essential role in the scale-up process because it illustrates the real phenomena of a process. This study aims to develop a mathematical model that can explain the mechanism of the leaching process of laterite ore using a low concentration of the citric acid solution and evaluate that model using the experimental data. As a raw material, this process used powder-shaped limonite laterite ores with a size of 125–150 µm. The leaching process is carried out using 0.1 M citric acid solution, F:S ratio of 1:20, and a leaching time of 2 h. The temperature parameter was varied at 303, 333, and 358 K. The experimental results showed that the higher the operating temperature, the higher the extracted nickel. The results of this experiment were used to evaluate the shrinking core kinetics model and the lumped model. The simulation results for both models show that the lumped model can provide better simulation results. Quantitatively, the percentage of errors from the shrinking core model is around 3.5 times greater than the percentage of errors from using the lumped model. This result shows that in this leaching process, the process mechanism that occurs involves the reactant diffusion step and the chemical reactions step; those steps run simultaneously.
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20

Zeng, Gui Sheng, Hui Li, Su Hua Chen, Xin Man Tu, and Wen Bin Wang. "Leaching Kinetics and Seperation of Antimony and Arsenic from Arsenic Alkali Residue." Advanced Materials Research 402 (November 2011): 57–60. http://dx.doi.org/10.4028/www.scientific.net/amr.402.57.

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The separation of antimony and arsenic and leaching kinetics of arsenic from arsenic alkali residue were investigated. The influencing factors such as solid/liquid ratio, stir speed, temperature and time on leaching of arsenic were studied. The results show that the leaching rate reaches 87.75% at the condition of solid/liquid ratio of 1:4 , stir speed of 600r/min ,temperature of 90°C and time of 60min. The leaching process was controlled by the surface chemical reaction and the kinetics of leaching arsenic followed the model of shrinking core. The activation energy was found to be 666.57kJ/mol. The kinetics equation was expressed as shrinking core model.
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21

Kim, Hee-Joon, Guo-Qing Lu, Ichiro Naruse, Jianwei Yuan, and Kazutomo Ohtake. "Modeling on Combustion Characteristics of Biocoalbriquettes." Journal of Energy Resources Technology 123, no. 1 (2000): 27–31. http://dx.doi.org/10.1115/1.1347988.

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A biocoalbriquette, a new artificial solid fuel, is manufactured by a mixture of coal and biomass under a high-compression pressure. The combustion characteristics of biocoalbriquettes were investigated in this study experimentally and numerically. The combustion process of biocoalbriquettes appears in two stages: the volatile combustion stage followed by the char combustion stage. It was found that the volatile combustion happens over the whole pellet of biocoalbriquette, whereas the char combustion proceeds in a shrinking-core mode. A volume model and a shrinking-core reaction model were introduced and modified here to simulate the two stages of combustion process. The simulation results are found to be consistent with the experimental results.
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22

Chen, Fei Fei, Guang Hui Wang, Wei Li, and Feng Yang. "Kinetics of Glycolysis of Poly (ethylene Terephthalate) by Shrinking-Core Model." Advanced Materials Research 233-235 (May 2011): 627–31. http://dx.doi.org/10.4028/www.scientific.net/amr.233-235.627.

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Poly (ethylene terephthalate) (PET) wastes were depolymerised using excess ethylene glycol (EG) in the presence of zinc acetate as transesterificaion catalyst. Influences of particle size, reaction temperature, weight ratio of ethylene glycol (EG) to PET and weight ratio of catalyst to PET on the yield of bis(hydroxyethyl terephthalate)(BHET) were investigated. The kinetics of glycolysis of PET in EG could be interpreted by the shrinking-core model of chemical reaction control, the activation energy of the glycolysis was 133 KJ/mol. The glycolysis product was analyzed and identified by FTIR and Element analysis.
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23

Kim, Cherng-Ju. "Application of Shrinking-Core Model for Ionization of Hydrophobic Ionic Beads." Drug Development and Industrial Pharmacy 22, no. 4 (1996): 307–11. http://dx.doi.org/10.3109/03639049609041994.

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24

Giri, C. C., and D. K. Sharma. "Kinetic studies and shrinking core model on solvolytic extraction of coal." Fuel Processing Technology 68, no. 2 (2000): 97–109. http://dx.doi.org/10.1016/s0378-3820(00)00112-0.

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25

Subramanian, Venkat R., Harry J. Ploehn, and Ralph E. White. "Shrinking Core Model for the Discharge of a Metal Hydride Electrode." Journal of The Electrochemical Society 147, no. 8 (2000): 2868. http://dx.doi.org/10.1149/1.1393618.

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26

Fadli, Ahmad, Subkhan Maulana, and Drastinawati. "Shrinking core model of demineralization of chitin isolation from shrimp shell." MATEC Web of Conferences 154 (2018): 01014. http://dx.doi.org/10.1051/matecconf/201815401014.

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Chitin is a naturally abundant polymer and most of it was used as a surfactant and cosmetic raw materials. Chitin be able to derive from natural sources like shrimp shell waste. The aim of this research was to study the kinetic model of chitin demineralization with approach to shrinking core model (SCM) with variation of hydrochloric acid concentration. There models were used: Fluid Film Layer Diffusion, Ash Layer Diffusion and Chemical Reaction. It was began with deproteination at first with NaOH 3,5 % and continued with demineralization using hydrochloric acid at concentration 0,3 N; 0,6 N; 0,9 N and 1,2 N with variation of reaction time at 15, 30 and 15 minute. The calcium content in the product was analyzed after it was dried in the air oven. The results showed calcium concentration decrease along with increasing of hydrochloric acid concentration. It get kinetic model at concentration 0,3 N of hydrochloric acid usage with form: [see formula in PDF] with the highest value of R2 is 0,9555 and the smallest percentage error is 5,92%. Meanwhile with usage of hydrochloric acid at concentration 0,6 N; 0,9 N and 1,2 N were get kinetic model with form: [see formula in PDF] with the highest value of R2 is 0,9794.
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27

Bhandari, Vinay M., Vinay A. Juvekar, and Suresh R. Patwardhan. "Modified Shrinking Core Model for Reversible Sorption on Ion-Exchange Resins." Separation Science and Technology 27, no. 8-9 (1992): 1043–64. http://dx.doi.org/10.1080/01496399208019023.

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28

Pritzker, Mark D. "Shrinking-core model for systems with facile heterogeneous and homogeneous reactions." Chemical Engineering Science 51, no. 14 (1996): 3631–45. http://dx.doi.org/10.1016/0009-2509(95)00403-3.

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29

Jayathilake, Madhawa, Souman Rudra, and Lasse A. Rosendahl. "Hydrothermal liquefaction of wood using a modified multistage shrinking-core model." Fuel 280 (November 2020): 118616. http://dx.doi.org/10.1016/j.fuel.2020.118616.

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30

Maulana, Fariz Risqi, Nur Fadhilah, Ruri Agung Wahyuono, and Doty Dewi Risanti. "Hydrogen Production from Waste Aluminum Foil AA1235 Using the Aluminum-Water Reaction Method with Thickness Variations." Advanced Materials Research 1175 (February 20, 2023): 9–15. http://dx.doi.org/10.4028/p-587vv6.

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Aluminium-water reaction is one of the most promising ways to produce clean and economical hydrogen. In this study, the effect of the waste Aluminium foil AA1235 thickness on Aluminium-water reaction process was investigated. The thickness of aluminum used are 6.5 m, 11.5 m and 19.5 m. Aluminum foil was cut by size 20 mm x 30 mm in each thickness variation. The 0.4 M NaOH and 0.01 M NaAlO2 was added as promoter on the process. The initial composition of the aluminum and the dislocations in the aluminum are also considered. The experimental results was evaluated by the mass reduction and shrinking core models. The initial composition of the aluminum and the dislocations in the aluminum are also considered. The experimental results were evaluated by the mass reduction and shrinking core models. The results obtained that aluminum with thinner thickness can be approximated by the 1-dimensional slab shrinking core model. Aluminum with a thicker thickness can be approached with a mass reduction model. It is also found out that smaller thickness has larger dislocation and better effects of NaAlO2 resulting higher yield of hydrogen production.
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31

KURNIA, JUNDIKA CANDRA, ERIK BIRGERSSON, and ARUN S. MUJUMDAR. "A PHENOMENOLOGICAL MODEL FOR HYDROGELS WITH RIGID SKIN FORMATION." International Journal of Applied Mechanics 04, no. 01 (2012): 1250007. http://dx.doi.org/10.1142/s1758825112001361.

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A phenomenological model for stimuli sensitive hydrogels immersed in water subject to changes in temperature is presented and analyzed. In short, the model takes into account conservation of mass and momentum for polymer network and interstitial fluid with an expression for permeability to capture the rigid skin formation during shrinking. The nature of this expression is secured from the observation of and validation with experimental deformation kinetics. Overall, good agreement is achieved between model predictions and their experimental counterparts; the rigid skin formation and rigid core presence are also captured reasonably well. The model can be extended to account for arbitrary-shaped hydrogels as well as for other types of stimuli-sensitive hydrogels that exhibit rigid-skin formation during shrinking.
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32

Kelzenberg, Stefan, Norbert Eisenreich, Sebastian Knapp, and Volker Weiser. "SHRINKING CORE MODEL TO DESCRIBE METAL PARTICLE OXIDATION FROM THERMAL ANALYSIS DATA." International Journal of Energetic Materials and Chemical Propulsion 15, no. 1 (2016): 35–48. http://dx.doi.org/10.1615/intjenergeticmaterialschemprop.2015011379.

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33

Buckmaster, John, and Thomas L. Jackson. "An examination of the shrinking-core model of sub-micron aluminum combustion." Combustion Theory and Modelling 17, no. 2 (2013): 335–53. http://dx.doi.org/10.1080/13647830.2013.765040.

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34

Eikani, Mohammad H., Nahid Khandan, Elnaz Feyzi, and Iman M. Ebrahimi. "A shrinking core model for Nannochloropsis salina oil extraction using subcritical water." Renewable Energy 131 (February 2019): 660–66. http://dx.doi.org/10.1016/j.renene.2018.07.091.

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35

Ndukwe, O. C. N., and C. E. Uchendu. "Shrinking core model applied to the bioleaching of iron from silica sand." International Journal of Academic Research 4, no. 4 (2012): 182–87. http://dx.doi.org/10.7813/2075-4124.2012/4-4/a.25.

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36

Kumar, Santosh, and Chandan Guria. "Alkaline Hydrolysis of Waste Poly(Ethylene Terephthalate): A Modified Shrinking Core Model." Journal of Macromolecular Science, Part A 42, no. 3 (2005): 237–51. http://dx.doi.org/10.1081/ma-200050346.

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37

Gbor, Philip K., and Charles Q. Jia. "Critical evaluation of coupling particle size distribution with the shrinking core model." Chemical Engineering Science 59, no. 10 (2004): 1979–87. http://dx.doi.org/10.1016/j.ces.2004.01.047.

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38

Sriramoju, Santosh Kumar, A. Suresh, Pratik Swarup Dash, and P. K. Banerjee. "Parameter Estimation of Kinetic Model Equations for Chemical Leaching of Coal." Chemical Product and Process Modeling 9, no. 2 (2014): 133–41. http://dx.doi.org/10.1515/cppm-2014-0009.

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Abstract Coals are invariably associated with mineral matter, which makes it unsuitable for efficient utilisation. For difficult-to-wash coals, advanced coal beneficiation technologies like chemical leaching methods are under development. In this paper, kinetic equations using different methods have been evolved, and related parameters have been estimated, using the experimental results obtained during coal leaching process. As coal is a heterogeneous rock, three different methods namely (i) parametric estimation through rate equation, (ii) non-linear regression and (iii) parametric estimation through shrinking core model have been developed and validated to check the minimum level of permitted error tolerance. Experiments were designed, using full factorial design with three variables, which are sensitive to the process. Values of activation energy and k0 obtained, using the parametric estimation of rate equation and shrinking core model, are almost in the same range. The order of the reaction for silica and alumina is two, using rate equation method. The parametric data obtained from the polynomial regression method were compared with the actual data. The exponential polynomial provides a better fit for the chemical leaching process of coal.
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39

Sarwan, S. Sandhu. "Shrinking Core Model Formulation for the Electrochemical Performance Analysis of a Lithium/Carbon Monofluoride Cell." RA JOURNAL OF APPLIED RESEARCH 09, no. 03 (2023): 135–44. https://doi.org/10.5281/zenodo.7754759.

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A shrinking core model formulation has been developed based on lithium-ion diffusion through the product layer of carbon monofluoride cathode active material being the predominate mechanism controlling the cell discharge behavior. The formulation expresses the cell discharge time; speed of the moving reaction zone towards the center of a spherical active material, carbon monofluoride, particle; cell current, and the fractional amount of charge involved in the cell electrochemical reaction in terms of the fractional conversion of the cell cathode limiting reactant, carbon monofluoride. An experimental data-based correlation between the required, lithium-ion effective diffusivity and cell voltage loss is also provided to explain the cell discharge behavior under the constant current condition.
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40

Xiao, Xiong, Billy W. Hoogendoorn, Yiqian Ma, et al. "Ultrasound-assisted extraction of metals from Lithium-ion batteries using natural organic acids." Green Chemistry 23, no. 21 (2021): 8519–32. http://dx.doi.org/10.1039/d1gc02693c.

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Ultrasound-assisted extraction of metal ions from Lithium batteries with weak organic acids is reported. Leaching reached ≥98% Li and Co recovery due to improved residue layer diffusion and mass transfer, illustrated by the shrinking core model.
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41

Muzayanha, Soraya Ulfa, Cornelius Satria Yudha, Luthfi Mufidatul Hasanah, Linggar Tungga Gupita, Hendri Widiyandari, and Agus Purwanto. "Comparative Study of Various Kinetic Models on Leaching of NCA Cathode Material." Indonesian Journal of Chemistry 20, no. 6 (2020): 1291. http://dx.doi.org/10.22146/ijc.49412.

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The kinetics study of NCA leaching in the HCl system was proposed. Various kinetic models such as shrinking core, logarithmic rate law, and Avrami equation were used to find out the most appropriate kinetic models for this process. The effect of HCl concentrations, leaching temperatures, solid to liquid (S/L) ratio, and leaching duration were observed. The optimum conditions of NCA leaching were at HCl concentration of 4 M, temperature of 80 °C, S/L ratio of 100 g/L, and leaching time of 1 h. The result shows that shrinking core model with diffusion control process of residue layer describes well the leaching mechanism in this research, which is indicated by the good fitting of coefficient values of correlation (R2) and confirmed by the activation energy values of Ni, Co, Al that were less than 40 kJ/mol.
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42

Oancea, Ana Maria S., Cristian Matei, Marius Radulescu, and Eugen Pincovschi. "APPLICABILITY OF SHRINKING CORE MODEL FOR ION EXCHANGE PROCESSES ON SULFONATED GEL RESINS." Environmental Engineering and Management Journal 1, no. 3 (2002): 375–81. http://dx.doi.org/10.30638/eemj.2002.039.

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43

Kovalev, N. V., V. N. Kovalev, V. A. Holodnov, and M. Yu Lebedeva. "Mathematical Model “Shrinking Core” Describing the Process of Gold Leaching from Multifractional Ore." Vestnik Tambovskogo gosudarstvennogo tehnicheskogo universiteta 22, no. 4 (2016): 565–80. http://dx.doi.org/10.17277/vestnik.2016.04.pp.565-580.

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44

Imuetinyan, Agho, Timothy, Okuo, James Majebi, and Emeribe, Favour Oluchi. "Optimization of Tantalite Ore Dissolution Using Hydrofluoric-sulphuric Acid and Shrinking Core Model." Asian Journal of Applied Chemistry Research 15, no. 4 (2024): 172–93. http://dx.doi.org/10.9734/ajacr/2024/v15i4305.

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Aim: This study investigates the dissolution of tantalite mineral from granitic pegmatite in Okpella, Northern Edo State, Nigeria. Study Design: Elemental and mineral composition analysis of tantalite ore sample from Okpella was carried out using X-ray fluorescence and X-ray diffraction. Response Surface Methodology (RSM) and the shrinking core model were used in designing the study while the effects of temperature, stirring speed, particle diameter, and mixed acids concentrations were investigated in the dissolution rates of the mineral. Duration of Study: 50 experimental runs were designed using RSM Central Composite Design (CCD) to optimize variables including HF concentration (1-8 M), H2SO4 concentration (0.5-3 M), temperature (32-82°C), stirring speed (0-500 rpm), and particle size (0.1-0.3 mm), with a constant contact time of 240 minutes. Methodology: Pulverized tantalite samples (0.1-0.3 mm) were reacted with varying concentrations of hydrofluoric and sulphuric acids (1-8 M and 0.5-3.0 M, respectively) for 240 minutes, with stirring speeds between 0-500 rpm and temperatures from 32 to 82°C. The mixture was stirred in a water bath with 50 ml of mixed acids solution and 2 g of ore. After the reaction, the solution was decanted, and the residual ore was washed, dried at 60 °C, and weighed. The difference between the initial and final weights indicated the amount of undissolved tantalite ore. Results: Ore characterization results revealed high concentration of tantalum (34.17%), iron (12.55%), niobium (8.38%), and titanium (6.01%), with other elements present in smaller amounts. Optimal conditions were found to be 8 M HF, 0.5 M H2SO4, 82°C, 500 rpm stirring speed, and 0.1 mm particle size, resulting in 97.28% dissolution of tantalite ore. Regression analysis demonstrated model robustness with an F-value of 16.70 and a P-value of 0.0001, indicating HF concentration and stirring speed as the most impactful factors. The model’s R² value of 0.9201 and adjusted R² of 0.8650 confirm its predictive accuracy. Analysis using the shrinking sphere model showed that film diffusion control is the primary limiting step with t/τ=0.999, while reaction control resulted in slightly lower conversion with t/τ=0.973, highlighting film diffusion as the main constraint but with high conversion efficiency. Conclusion: The findings from this investigation not only reveal the dissolution of tantalite ore through a detailed experimental approach, identifying optimal conditions -8 M HF, 0.5 M H2SO4, 82 oC, 500 rpm stirring speed and 0.1 mm particle size- that achieve a 97.28% dissolution, but they also enhance our understanding of mineral processing. These understanding are crucial for mineral dissolution up scaling technologies in industrial applications, which will potentially leads to a more efficient extraction method that could significantly reduce costs and environmental impacts in the mining sector. This research could drive advancements in sustainable resource recovery and contribute to sourcing of critical minerals.
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45

Amiri, Amirpiran, Gordon D. Ingram, Nicoleta E. Maynard, Iztok Livk, and Andrey V. Bekker. "An Unreacted Shrinking Core Model for Calcination and Similar Solid-to-Gas Reactions." Chemical Engineering Communications 202, no. 9 (2014): 1161–75. http://dx.doi.org/10.1080/00986445.2014.910771.

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46

Vijayasekaran, B., and C. Ahmed Basha. "Shrinking core discharge model for the negative electrode of a lead-acid battery." Journal of Power Sources 158, no. 1 (2006): 710–21. http://dx.doi.org/10.1016/j.jpowsour.2005.10.006.

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47

Pritzker, Mark. "Modified shrinking core model for uptake of water soluble species onto sorbent particles." Advances in Environmental Research 8, no. 3-4 (2004): 439–53. http://dx.doi.org/10.1016/s1093-0191(02)00125-9.

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48

Westerlund, T., S. Karrila, and K. Perander. "A shrinking unreacted core model for estimating the compressive strength of portland cement." Cement and Concrete Research 15, no. 6 (1985): 959–63. http://dx.doi.org/10.1016/0008-8846(85)90085-7.

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49

Takasu, Hiroki, Shigehiko Funayama, Naoto Uchiyama, Hitoshi Hoshino, Yoshirou Tamura, and Yukitaka Kato. "Kinetic analysis of the carbonation of lithium orthosilicate using the shrinking core model." Ceramics International 44, no. 10 (2018): 11835–39. http://dx.doi.org/10.1016/j.ceramint.2018.03.273.

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50

Sloman, Benjamin M., Colin P. Please, and Robert A. Van Gorder. "Homogenization of a Shrinking Core Model for Gas--Solid Reactions in Granular Particles." SIAM Journal on Applied Mathematics 79, no. 1 (2019): 177–206. http://dx.doi.org/10.1137/17m1159634.

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