Methodical approach to studies of magnetic interaction of fine particles in an aqueous suspension using computer simulation

DOI: https://doi.org/10.30686/1609-9192-2023-5S-142-149

Читать на русскоя языкеS.P. Ostapenko, A.S. Opalev
Mining Institute of the Kola Science Centre of the Russian Academy of Science; Apatity, Russian Federation
Russian Mining Industry №5S / 2023 р. 142-149

Abstract: The need to increase the efficiency of mining operations determines the relevance of studying the properties of fine mineral particles for their extraction and reduction of environmental pollution. The development of approaches to studying magnetic interaction of fine particles is of scientific and practical importance and is associated with the complexity of calculating the superposition of their fields when solving the problem of controlling the magnetic properties of a suspension. A computer model of the dynamics of magnetic particle interaction was developed with account for their aggregation under the impact of the magnetic dipole-dipole interaction and the destruction of aggregates during thermal (Brownian) motion in order to predict the magnetic properties of the suspension using the example of magnetite deposits of the Zaimandrovsky iron ore region. The calculation shows that the electrostatic and dispersion interactions do not have a significant effect on the interaction dynamics of micron and submicron particles of magnetite with account of the experimentally measured zeta potential and the Hamaker's constant. A procedure has been developed for calibrating a computer model of the interaction dynamics of magnetic particles using the temperature dependence of the coefficient of translational diffusion of magnetite particles and the concentration dependence of the magnetic susceptibility of a suspension. An array of calculated values of the diffusion coefficient of the model particles and the initial magnetic susceptibility of their system is formed in a wide range of computer model parameters. A procedure has been developed for linking the calculated and experimental data by varying the normalization parameters of the particle size, viscosity of the medium, and thermal energy in order to minimize the maximum discrepancy between the values. The necessity is established of taking into account the change in magnetic properties with a decrease in the size of magnetite particles during the calibration of the magnetic susceptibility of a model system. The developed methodological approach ensures good convergence of the calculated and experimental data and makes it possible to visualize the aggregation of the model particles as the result of dipole-dipole interactions. The developed computer model of the interaction dynamics of magnetic particles can be used to study the effect of an external magnetic field on the aggregation ability of fine magnetite particles in order to control their extraction in separation processes.

Keywords: iron ores, magnetite, fine particles, suspension, aggregation, computer dynamic model, simulation model, diffusion coefficient, magnetic susceptibility, Hamaker constant, zeta potential

Acknowledgments: The work was carried out within the framework of the State Assignment No. FMEZ-2022-0003 "Development of physical, physicochemical and digital bases for the development and industrial adaptation of effective technologies for processing of various types of mineral raw materials".

For citation: Ostapenko S.P., Opalev A.S. Methodical approach to studies of magnetic interaction of fine particles in an aqueous suspension using computer simulation. Russian Mining Industry. 2023;(5S):142–149. https://doi.org/10.30686/1609-9192-2023-5S-142-149


Article info

Received: 23.10.2023

Revised: 22.11.2023

Accepted: 29.11.2023


Information about the authors

Sergey P. Ostapenko – Cand. Sci. (Eng.), Leading Researcher, Mining Institute Kola Science Centre of the Russian Academy of Science, Apatity, Russian Federation; e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Aleksandr S. Opalev – Cand. Sci. (Eng), Deputy Director of Science, Mining Institute Kola Science Centre of the Russian Academy of Sciences, Apatity, Russian Federation; e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.


References

1. Aleksandrova T.N., Chanturiya A.V., Kuznetsov V.V. Mineralogical and technological features and patterns of selective disintegration of ferruginous quartzites of the Mikhailovskoye deposit. Journal of Mining Institute. 2022;256:517–526. https://doi.org/10.31897/PMI.2022.58

2. Zhang J., Chen Z., Shan D., Wu Y., Zhao Y., Li C. et al. Adverse effects of exposure to fine particles and ultrafine particles in the environment on different organs of organisms. Journal of Environmental Sciences. 2024;135:449–473. https://doi.org/10.1016/j.jes.2022.08.013

3. Ericsson M., Löf A., Löf O. Iron ore market report 2019–2020. Russian Mining Industry. 2021;(1):74–82. (In Russ.) https://doi.org/10.30686/1609-9192-2021-1-74-82

4. Kalisz S., Kibort K., Mioduska J., Lieder M., Małachowska A. Waste management in the mining industry of metals ores, coal, oil and natural gas – A review. Journal of Environmental Management. 2022;304:114239. https://doi.org/10.1016/j.jenvman.2021.114239

5. Anthonys G. Mathematical model to investigate the behaviour of the systems of ferromagnetic particles under the magnetic fields. Applied Mathematics and Computation. 2018;320:654–676. https://doi.org/10.1016/j.amc.2017.09.050

6. Lukichev S.V. Digital past, present, and future of mining industry. Russian Mining Industry. 2021;(4):73–79. (In Russ.) https://doi.org/10.30686/1609-9192-2021-4-73-79

7. Ghorbani Y., Zhang S.E., Nwaila G.T., Bourdeau J.E., Safari M., Hadi Hoseinie S. et al. Dry laboratories – Mapping the required instrumentation and infrastructure for online monitoring, analysis, and characterization in the mineral industry. Minerals Engineering. 2023;191:107971. https://doi.org/10.1016/j.mineng.2022.107971

8. Tranchida J., Plimpton S.J., Thibaudeau P., Thompson A.P. Massively parallel symplectic algorithm for coupled magnetic spin dynamics and molecular dynamics. Journal of Computational Physics. 2018;372:406–425. https://doi.org/10.1016/j.jcp.2018.06.042

9. Limbach H.J., Arnold A., Mann B.A., Holm C. ESPResSo – an extensible simulation package for research on soft matter systems. Computer Physics Communications. 2006;174(9):704–727. https://doi.org/10.1016/j.cpc.2005.10.005

10. Liu X., Wang Q., Wang Y., Dong Q. Review of calibration strategies for discrete element model in quasi-static elastic deformation. Scientific Reports. 2023;13:13264. https://doi.org/10.1038/s41598-023-39446-2

11. Bu P., Li Y., Zhang X., Wen L., Qiu W. A calibration method of discrete element contact model parameters for bulk materials based on experimental design method. Powder Technology. 2023;425:118596. https://doi.org/10.1016/j.powtec.2023.118596

12. Guo Y., Tang N., Guo J., Lu L., Li N., Hu T. et al. The aggregation of natural inorganic colloids in aqueous environment: A review. Chemosphere. 2023;310:136805. https://doi.org/10.1016/j.chemosphere.2022.136805

13. Filippov A.V., Starov V. Interaction of nanoparticles in electrolyte solutions. Journal of Physical Chemistry B. 2023;127(29):6562−6572. https://doi.org/10.1021/acs.jpcb.3c01220

14. Ostapenko S.P., Mesyats S.P. Methodological approach to characterizing pollution of natural water bodies using satellite data with account of aggregation of finely dispersed mineral processing waste. Russian Mining Industry. 2021;(6):110–116. (In Russ.) https://doi.org/10.30686/1609-9192-2021-6-110-116

15. Dunlop D.J. The rock magnetism of fine particles. Physics of the Earth and Planetary Interiors. 1981;26(1-2):1–26. https://doi.org/10.1016/0031-9201(81)90093-5

16. Wang Z., Holm C., Muller H.W. Molecular dynamics study on the equilibrium magnetization properties and structure of ferrofluids. Physical Review E. 2002;66(2):021405. https://doi.org/10.1103/PhysRevE.66.021405

17. Opalev A.S., Marchevskaya V.V. Influence of magnetite grain size on magnetic susceptibility of iron ore concentrates. Journal of Mining Science. 2023;59(1):142–147. https://doi.org/10.1134/S1062739123010155

18. Kharitonskii P., Bobrov N., Gareev K., Kosterov A., Nikitin A., Ralin A. et al. Magnetic granulometry, frequency-dependent susceptibility and magnetic states of particles of magnetite ore from the Kovdor deposit. Journal of Magnetism and Magnetic Materials. 2022;553:169279. https://doi.org/10.1016/j.jmmm.2022.169279

19. Martín-Molina A., Quesada-Pérez M. A review of coarse-grained simulations of nanogel and microgel particles. Journal of Molecular Liquids. 2019;280:374–381. https://doi.org/10.1016/j.molliq.2019.02.030