Mathematical model of anionic vacancy formation and motion during reduction of metals from complex oxides

The paper proposes a mathematical description of anion vacancies being formed and moving when metals are reduced from complex oxides; the process is described in terms of the diffusion and thermal processes occurring in the reductant and oxide phases, as well as in terms of chemical reactions occurring at the interface. It dwells upon a system consisting of a spherical ore particle contained in the atmosphere of a gaseous reductant. Ore particle is a homogeneous gas-tight complex oxide of the following composition: O, Fe, Si, Mg. The gas phase consists of two components, СО and СО2. The ore-particle surface is impervious to the components of both phases. The reductant is unable to get inside the particle, meaning that all the exchange processes occur at the interface. For the ore-particle phase, the researchers have constructed a thermal-conductivity equation as well as phase-component diffusion equation. For the gaseous phase around the particle, the researchers have constructed the equations of thermal-conductivity and diffusion of reagents, which take into account alterations of the particle size. A heat-transfer equation has been derived for the interface, which links both phase-to-interface heat fluxes to the thermal effects of chemical reactions. Furthermore, ore-phase component mass transfer equations have been derived to link the removal of atomic oxygen from the interface to such oxygen being channeled from the ore-particle depth to the interface. Gas-phase component mass transfer equations have been derived to link the supply or reagents to the interface and the superficial flow of such reagents. The research takes into account how basic physicochemical parameters affect the reducing-vacancy formation rate and motion speed. A mathematical model is compiled.