Modeling particle flow in active zone of large-angle concentrator

The study focuses on modeling mineral gravity separation processes, in particular, on a large-angle concentrator designed at the Institute of Mining of the North, Siberian Branch of the Russian Academy of Sciences. The test data on particle motion on an inclined plane under the action of water flow are presented. The aim of this study is mathematical modeling to find probable position of useful fractions as function of certain parameters of the facility. Determination of probable position of a particle uses the Gibbs ensemble method. In steady-flow processes, the concentration of points of the ensemble is a probability distribution of particle location in the test space. The mathematical model was proved on a dedicated pilot installation using markers. The number of the markers in cells makes it possible to assess distribution of particles against water flow velocity and work face angle of slope. Using the mathematical model, the probable distribution of particles along the lower edge of the work face is calculated. The comparison and analysis show good correlation between the theoretical and experimental results. The further optimization of the concentrator design will use the particle motion modeling data.

Keywords: mineral processing, large angle concentrator, mathematical model, Gibbs ensemble, flow, particle, marker.
For citation:

Matveev I. A., Yakovlev B. V., Eremeeva N. G. Modeling particle flow in active zone of large-angle concentrator. MIAB. Mining Inf. Anal. Bull. 2021;(7):146-153. [In Russ]. DOI: 10.25018/0236_1493_2021_7_0_146.


The study was carried out under state contact with the Ministry of Science and Higher Education of the Russian Federation, Registration No.AAAA-A21-121012090008-4.

Issue number: 7
Year: 2021
Page number: 146-153
ISBN: 0236-1493
UDK: 622.7 (681)
DOI: 10.25018/0236_1493_2021_7_0_146
Article receipt date: 03.03.2021
Date of review receipt: 14.04.2021
Date of the editorial board′s decision on the article′s publishing: 10.06.2021
About authors:

I.A. Matveev1, Engineer,
B.V. Yakovlev, Dr. Sci. (Phys. Mathem.), Professor, e-mail:, Physical and Technical Institute, M.K. Ammosov North-Eastern Federal University, 677000, Yakutsk, Republic of Sakha (Yakutia) Russia,
N.G. Eremeeva1, Researcher, e-mail:,
1 Chersky Mining Institute of the North, Siberian Branch, Russian Academy of Sciences, 677980, Yakutsk, Republic of Sakha (Yakutia), Russia.


For contacts:

N.G. Eremeeva, e-mail:


1. Seryy R. S., Taganov V. V., Gevalo K. V. Reducing losses of precious metals on flushing devices by optimizing the operation of fine accumulation gateways. Gornyi Zhurnal. 2018, no. 10, pp. 49—52. [In Russ]. DOI 10.17580/gzh.2018.10.09.

2. Usov G. A., Frolov S. G., Tarasov B. N. Development of technology for extracting alluvial micron gold using dispersion of the clay component of the host rocks. Izvestiya vysshikh uchebnykh zavedeniy. Gornyy zhurnal. 2019, no. 5, pp. 75—82. [In Russ]. DOI: 10.21440/05361028-2019-5-75-82.

3. Ochosov O. Yu., Matveev A. I. Increasing the efficiency of separation of mineral particles under the action of centrifugal forces through the use of directed vibration vibrations. MIAB. Mining Inf. Anal. Bull. 2016, no. 10, pp. 259—265. [In Russ].

4. Oparin V. N., Smolyanitsky B. N., Sekisov A. G., Trubachev A. I., Salikhov V. S., Zykov N. V. Promising mining technologies for gold placers in Transbaikalia. Journal of Mining Science. 2017, vol. 53, no. 3, рр. 489—496.

5. Kökkılıç O., Langlois R., Kristian E. A design of experiments investigation into dry separation using a Knelson Concentrator. Minerals Engineering. 2015, vol. 72. рр. 73–86.

6. Lunyashin P. D. Problems of Russian placers and ways to solve them. Zoloto i tekhnologii. 2018, no. 2, pp. 60—65. [In Russ].

7. Filippov V. E., Eremeeva N. G., Sleptsova E. S., Salomatova S. I. Patent RU 2001101048/03, 10 01.2003. [In Russ].

8. Matveev I. A., Eremeeva N. G., Matveev A. I., Monastyrev A. M. Concentrator for benefication of fine gold. MIAB. Mining Inf. Anal. Bull. 2016, no. 12, pp. 61–68. [In Russ].

9. Das S. K., Godivalla K. M., Panda L., Bhattacharya K. K., Singh R., Mehrotra S. P. Mathematical modeling of separation characteristics of coal-washing spiral. International Journal of Mineral Processing. 2007, vol. 84, рр. 118–132.

10. Germanyuk G. Yu. Matematicheskoe modelirovanie dvizheniya ansamblya chastits s ispol'zovaniem kanonicheskogo metoda integrirovaniya [Mathematical modeling of the movement of an ensemble of particles using the canonical integration method], Candidate’s thesis, Izhevsk, IzhGTU, 2010, 143 p.

11. Krylatova S. R., Matveev A. I., Lebedev I. F., Yakovlev B. V. Determination of probability of position of particle on working surface of spiral pneumoseparator by methods of mathematical modeling. AIP Conference Proceedings. 2017, vol. 1907, article 030032. DOI: 10.1063/1.5012654.

12. Matveev I. A., Eremeeva N. G., Stepanova S. D., Yakovlev B. V. Features of hydraulic size of plane particle. AIP Conference Proceedings. 2018, vol. 2041, article 050012. DOI: 10.1063/1.5079381.

13. Frantskevich V. S., Dorogokupets A. S. Computer simulation of separation processes of crushed materials. Trudy Belorusskogo tehnologicheskogo universiteta. 2011, no. 3, pp. 145–148. [In Russ].

14. Krylatova S. R., Matveev A. I., Lebedev I. F., Yakovlev B. V. Modeling of particle motion in a screw pneumatic separator using statistical methods. Mathematical notes of North-Eastern federal university. 2018, vol. 25, no. 1, pp. 90–97. [In Russ].

15. Matveev A. I., Filippov V. E., Fedorov F. M., Grigor'ev A. N., YAkovlev V. B., Eremeeva N. G., Sleptsova E. S., Gladyshev A. M., Vinokurov V. P. Patent RU 2167005. 20.05.2001. [In Russ].

16. Gibbs Dzh. V. Osnovnye printsipy statisticheskoy mekhaniki [Basic principles of statistical mechanics], Moscow, Leningrad, Gostekhizdat, 1946, 204 p

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