{"title":"The Particle–Bubble Behavior in Flotation in Low-Viscous Liquid","authors":"S. A. Kondrat’ev, N. P. Moshkin","doi":"10.1134/s1062739124010150","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The authors discuss dynamics of gas bubble and mineral particle in low-viscous fluid. The particle–bubble interaction model represents a system of associated differential algebraic equations. Dynamics of the disturbed system is described using the Lagrangian method. The model takes into account oscillations of bubble surface and attached solid cylindrical particle in the infinitive volume of perfect incompressible liquid. The capillary force retaining the particle on the bubble is governed by the meniscus shape which conditions the wetting angle. The Legendre series expansion is used to represent small axially symmetrical oscillations of the particle–bubble system. The potential and kinetic energies of the system are expressed in terms of the coefficient of this series. The resultant eddy-free velocity field allows including the viscosity effect with regard to the local rates of energy dissipation.</p>","PeriodicalId":16358,"journal":{"name":"Journal of Mining Science","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mining Science","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1134/s1062739124010150","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MINING & MINERAL PROCESSING","Score":null,"Total":0}
引用次数: 0
Abstract
The authors discuss dynamics of gas bubble and mineral particle in low-viscous fluid. The particle–bubble interaction model represents a system of associated differential algebraic equations. Dynamics of the disturbed system is described using the Lagrangian method. The model takes into account oscillations of bubble surface and attached solid cylindrical particle in the infinitive volume of perfect incompressible liquid. The capillary force retaining the particle on the bubble is governed by the meniscus shape which conditions the wetting angle. The Legendre series expansion is used to represent small axially symmetrical oscillations of the particle–bubble system. The potential and kinetic energies of the system are expressed in terms of the coefficient of this series. The resultant eddy-free velocity field allows including the viscosity effect with regard to the local rates of energy dissipation.
期刊介绍：
The Journal reflects the current trends of development in fundamental and applied mining sciences. It publishes original articles on geomechanics and geoinformation science, investigation of relationships between global geodynamic processes and man-induced disasters, physical and mathematical modeling of rheological and wave processes in multiphase structural geological media, rock failure, analysis and synthesis of mechanisms, automatic machines, and robots, science of mining machines, creation of resource-saving and ecologically safe technologies of mineral mining, mine aerology and mine thermal physics, coal seam degassing, mechanisms for origination of spontaneous fires and methods for their extinction, mineral dressing, and bowel exploitation.
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