The mathematical description of the process of material milling in the zone of intersecting flows in a centrifugal counter-flow mill

This article presents the analytical expression for the determination of the degree of milling of particles in a centrifugal counter-flow mill with a selective effect on the material to be milled. The degree of milling is one of the most important factors characterizing the efficiency of particle collisions in the opposite intersecting flows in the tangential sleeve. The projection w _x of the velocity of interaction of particles with an oblique impact is determined on the basis of the value of the tangential stresses in the zone of opposing intersecting flows. In this case, the density of counter-intersecting flows should be such that the collision of particles occurs in the zone of milling. The structural design of the mill rotors provides separation of the particle fluxes in the tangential sleeve depending on their size. This design of the rotors improves the efficiency of grinding and fineness of the finished product. A design diagram is given in order to describe the process of milling of a material in the zone of opposing intersecting flows. As a result of theoretical studies, the analytical expression was obtained that allows determining the degree of milling of material particles in the zone of tangential collisions depending on the design and technological parameters of a centrifugal counter-flow mill.