Modeling of the particle motion in an inclined plane under the influence of a stream of water
The work is devoted to modeling the processes of gravitational enrichment of minerals. It presents the results of a study of the motion of particles in an inclined plane under the influence of a stream of water. When developing mathematical models of the collective motion of particles in devices, it is necessary to know the probability for the position of one particle in the device. The aim of this work is to determine the probability for the particle position on an inclined plane under given conditions, for which the Gibbs ensemble method is used. The possible positions of the particles on the working surface of the device are determined by the law of motion, which is obtained by integrating the equation of motion. In stationary processes, the concentration of points of this set, according to the Gibbs method, is the probability distribution for the location of a particle in the space under consideration. In order to verify this mathematical model, an experimental setup has been developed which is represented by a container in the form of a flat hollow rectangular parallelepiped located at an angle to the horizon with an isotropic water flow. Lead markers, moving under the influence of the stream of water and gravity along the inclined plane, fall in the cells located in the lower part of the tank. The number of pellets in the cells allows us to estimate the distribution of the particles in the lower part of the device depending on the speed of the water flow and the angle of inclination of the working surface. Based on the developed mathematical model, the probable distribution of particles along the lower face of the working surface of the device is calculated. Comparison and analysis of the theoretical and experimental results showed a good correlation of the data.
 Kizevalter B. V., Theoretical Bases of Gravitational Processes of Enrichment [in Russian], Nedra, Moscow (1979).
 Merinov N. F., “Features of pneumatic methods of enrichment [in Russian],” Obogashchenie Rud, No. 4, 23–26 (2011).
 Hasankhoei R. A., Banisi S., and Mozafari P., “Designing a spiral splitter at the Zarand coal washing plant,” Indian J. Sci. Res., 1, No. 2, 151–156 (2014).
 Das S. K., Godivalla K. M., Panda L., Bhattacharya K. K., Singh R., and Mehrotra S. P., “Mathematical modeling of separation characteristics of coal-washing spiral,” Int. J. Miner. Process., 84, 118–132 (2007).
 Germanyuk G. Y., Mathematical Modeling of Particle Set Movement Using Canonical Method of Integration [in Russian], Diss. Kand. Fiz.-Mat. Nauk, Izhevsk (2010).
 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,” in: AIP Conf. Proc., 1907, 030032 (2017). https://doi.org/10.1063/1.5012654
 Matveev I. A., Eremeeva N. G., Stepanova S. D., and Yakovlev B. V., “Features of hydraulic size of plane particle,” in: AIP Conf. Proc., 2041, 050012 (2018). https://doi.org/10.1063/1.5079381
 Frantskevich V. S. and Dorogokupets A. S., Computer Modeling of Separation Processes of Crushed Materials,
 Krylatova S. R., Matveev A. I., Lebedev I. F., and Yakovlev B. V., “Modeling of particle motion in a screw pneumoseparator by statistical methods,” Mat. Zamet. SVFU, 25, No. 1, 90–97 (2018).
 Matveev A. I., Filippov V. E., Fedorov F. M., Grigoriev A. N., Yakovlev V. B., Eremeeva N. G., Sleptsova E. S., Gladyshev A. M., and Vinokurov V. P., Patent No. 2167005, Pneumoseparator, IGDS SB RAS, declared 11.06.99, publ. 20.05.2001; Izobreteniya, Polez. Modeli, No. 14, Part 2, 346 (2001).
 Gibbs J., Basic Principles of Statistical Mechanics [in Russian], Gostekhizdat, Moscow; Leningrad (1946).
 Matveev A. I., Eremeeva N. G., Monastyrev A. M., Nechaev P. B., and Matveev I. A., Steeply Inclined Concentrator for Placer Enrichment, Russian Patent No. 2448776, 27.04.2012.
 Landau L. D. and Lifshits E. M., Theoretical Physics, Vol. 5. Statistical Physics [in Russian], Nauka, Moscow (1976).
This work is licensed under a Creative Commons Attribution 4.0 International License.