MATHEMATICAL MODEL OF THE MOVEMENT OF PARTICLES IN A CYLINDRICAL VIBRATING MIXER CONTAINERS

Abstract

Mixing is the process of bringing different masses of products into close interaction by increasing the contact area in order to obtain the product of the required consistency, to maintain the latter or to evenly distribute impurities in the main volume of products. The process of mixing components with different physical and mechanical properties is realized mainly by creating shear deformations in the entire mass of the product with the help of blades, rotating screws, or other working bodies. At the same time, in order to ensure a uniform distribution of the components, it is necessary to give the particles of the dispersed mass such trajectories that would ensure the greatest probability of their crossing. But the movement of these particles in the volume of the mixture is opposed by the forces of inertia and the forces of dry internal friction (friction of particles against each other) and forces of dry external friction (friction of material particles against the container, blades or other working organs of the mixer), which, as a rule, are on the order of lower than the forces of dry internal friction. In addition, when mixing, it is necessary to overcome the forces of gravity, which try to lower the particles of the material to the bottom, which leads to their delamination. Numerical modeling has been increasingly used in the description of mixing processes of loose materials in recent decades. Numerical modeling is especially convenient when describing the processes of gravity-overflow mixing, when it occurs most actively in a thin layer of material, in which there is a random transition of component particles to the adjacent layer. The article examines the modeling of the movement of particles during the rotating movement of the cylindrical mixer chamber without the use of blade intensifiers and the effect of vibration on the product.