Mathematical model for mechanical treatment of a reactive binary mixture passivated by inert material

Abstract

A macroscopic mathematical model was built to theoretically study the mechanical treatment of a reactive solid mixture passivated by an inert substance milled from the walls of a mill chamber and grinding bodies. The model includes equations for the rate of chemical transformations, change in the mass of substances involved in the mechanical treatment, dynamics of excess energy in components and a reaction product. The process is considered to be isothermal. An equation is derived to obtain the function of the interphase, which is a superposition for the grinding of components and their passivation with an inert substance. The dynamics of the chemical transformation depth, the amount of a milled inert substance, the function of the interphase and reactivity of the mixture versus the mechanical treatment time are numerically calculated. The final fraction of the reaction product in the mechanically treated powder mixture is found as a function of the parameter characterizing the level of slagging of reagents with an inert substance. Based on the constructed calculation diagrams, it is shown that depending on the parameters determining the mechanical treatment, different modes that characterize either activation or passivation of chemical interaction in the reactive powder mixture were found.