Mathematical Model for Lining the Surface of the Mechanoreactor During Grinding

Abstract

A mathematical model for lining a powder mixture subjected to mechanical treatment during mechanochemical synthesis has been built in the work. The mathematical model comprises the equations which describe a change in the specific surfaces of the initial mixture particles and particles of the agglomerates formed, the dynamics of lining the working surfaces of the mechanical activator and grinding bodies by the particles of the mixture subjected to mechanical treatment, the rate of chemical conversion of the starting components contained in the agglomerates into the reaction product. It is shown that the increase in the mechanical treatment time leads to the increase in the specific surface of powder particles and the volume of substances that take part in the lining process. At the same time, the grinding and lining rates of the plastic component are significantly higher than those of the solid component. Varying the power of the mechanical activator and the duration of its work is found to significantly affect the final parameters of mechanical treatment. The mechanical treatment conditions are found for the lining process with the maximum yield of the final reaction product. In this case, the yield of the product, on the one hand, will be determined by the volume of the powder mixture that has not taken part in the lining, and on the other hand, by the degree of chemical conversion in it. Analytical relations are obtained to evaluate the optimal mechanical treatment time.