E. M. Koltsova, M. A. Babkin, N. A. Popova, A. V. Zhensa
{"title":"Mathematical Modeling of the Process of Grinding Materials","authors":"E. M. Koltsova, M. A. Babkin, N. A. Popova, A. V. Zhensa","doi":"10.1134/S0040579525600172","DOIUrl":null,"url":null,"abstract":"<p>Based on knowledge of thermodynamic flows and driving forces of the crushing process and the application of the principle of minimum entropy production a dependence for determining the size of particles resistant to crushing was obtained and verified using experimental results on grinding corundum in a planetary mill. To model the kinetics of grinding, an integrodifferential equation for the balance of the number of particles by linear dimensions was obtained, where the probability of particle crushing was determined from the physicochemical essence of the thermodynamic crushing flows. The results of calculating the density of the distribution function of the number of particles and the change in the average size of corundum particles during grinding over time are presented, which agree well with the experimental data. Optimal modes for carrying out the process of grinding corundum in a planetary mill to obtain particles of a given size have been found.</p>","PeriodicalId":798,"journal":{"name":"Theoretical Foundations of Chemical Engineering","volume":"58 4","pages":"1055 - 1063"},"PeriodicalIF":0.7000,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Foundations of Chemical Engineering","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1134/S0040579525600172","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, CHEMICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Based on knowledge of thermodynamic flows and driving forces of the crushing process and the application of the principle of minimum entropy production a dependence for determining the size of particles resistant to crushing was obtained and verified using experimental results on grinding corundum in a planetary mill. To model the kinetics of grinding, an integrodifferential equation for the balance of the number of particles by linear dimensions was obtained, where the probability of particle crushing was determined from the physicochemical essence of the thermodynamic crushing flows. The results of calculating the density of the distribution function of the number of particles and the change in the average size of corundum particles during grinding over time are presented, which agree well with the experimental data. Optimal modes for carrying out the process of grinding corundum in a planetary mill to obtain particles of a given size have been found.
期刊介绍：
Theoretical Foundations of Chemical Engineering is a comprehensive journal covering all aspects of theoretical and applied research in chemical engineering, including transport phenomena; surface phenomena; processes of mixture separation; theory and methods of chemical reactor design; combined processes and multifunctional reactors; hydromechanic, thermal, diffusion, and chemical processes and apparatus, membrane processes and reactors; biotechnology; dispersed systems; nanotechnologies; process intensification; information modeling and analysis; energy- and resource-saving processes; environmentally clean processes and technologies.
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