Navier–Stokes and Darcy–Brinkmann Models for Synthesis of Micron Particles of Magnesium–Zinc Ferrite

The processes of heat and mass transfer in a direct-flow reactor during the synthesis of micron particles of magnesium–zinc ferrite (MCF) are numerically investigated. A new formulation of the problem of synthesis of MCF by the method of carbon combustion is proposed, taking into account the variability of the permeability and porosity of the mixture of the reactant and product particles. The results of calculations using the Navier–Stokes equations with distributed resistance to gas movement in the pores (NS model) and the Darcy–Brinkman equations (DB model) with the same initial parameters are compared. The differences in the calculations of the indicated models for low and high permeability of a mixture of micron-sized reagent particles are discussed. The modes for which both models give similar results and the modes of significant differences in combustion and synthesis rates, caused by the convective mechanism of heat and momentum transfer in the case of variable porosity, are noted. It is shown that more intense heat transfer in the NS model accelerates the growth of the specific volume of the solid phase due to thermal expansion. The calculation results indicate the importance of non-stationary processes of gas momentum transfer in the pores of a flow reactor and confirm the advantages of the NS model in studying the synthesis of micron particles of complex oxides by the carbon combustion method. The studies were conducted for fast-flowing processes and were limited by the synthesis time interval, which was limited by the initial concentrations of the reagents.