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.