A mathematical model for the combustion of preliminary activated heterogeneous systems is proposed which includes equations describing heat conduction, chemical kinetics, and the dynamics of the excess energy accumulated in condensed reagents at the stage of preliminary mechanical treatment. The excess energy decreases as a result of structure normalization and chemical transformation, whose activation energy, in turn, depends on the excess energy in the condensed reagents. The case of stationary combustion is analyzed in detail. The effect of mechanical activation on the velocity of the synthesis wave and its structure is analyzed by numerical modeling. The main conclusions are compared with available experimental data.Preliminary mechanical treatment of powder mixtures and separate reagents in an energy-intensive mill is an effective method for increasing chemical-reaction rates [1][2][3]. The intensive energetic action on the mixture increases the reactivity of the reagents by supplying them with additional energy accumulated in the form of structural imperfections, increases the reaction-surface area, and reduces the scale of heterogeneity of the system. The increase in the reaction surface and the decrease in the scale of heterogeneity due to mechanical treatment is manifested in continuous formation and grinding of microcomposites -layered structures of the starting components [4,5]. The activation of the reagents is manifested in a decrease in the energy barrier for chemical interactions. The increase in the interface, reduction in the scale of heterogeneity, and the activation of the reagents intensify chemical transformations. To distinguish the action of each of these factors and to operate them for the purpose of developing effective technologies is a difficult and important fundamental problem, whose solution holds promise for applications.It has been established that preliminary mechanical activation of a mixture or its separate components increases the number of systems that can react in a
A mathematical model for mechanosynthesis in solid-gas systems is constructed which includes the equations of mechanical-reactor heat balance, grinding, the excess-energy dynamics in the condensed substances, which determines the effect of mechanical activation on the chemical-reaction rate, and the reaction kinetics. A brief analysis of the model is presented. A description is given of two simplified models of independent significance derived from the general model, which can be studied by analytical methods. Synthesis in a preactivated system is studied in detail. Relations determining the characteristics of the synthesis are obtained. The accuracy of the analytical estimates is verified by numerical simulation.
Results from experimental studies of the nonisothermal mechanochemical reaction in the titanium-nitrogen system. Experimental data are compared with simulation results. The effective kinetic parameters of mechanical activation of the reactant and the chemical reaction are determined from analytical relations. It is shown that the developed mathematical model is suitable for the analysis of the macrokinetics of nonisothermal chemical reactions in solid reactant-reactive gas systems.
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