Model of BaTiO3Synthesis in Three-Zone Reactor Accounting for Thermal and Concentration Expansion Effect

Abstract

This paper reports about a generalization of two-temperature model on study of thermal and mass dispersion and expansion in carbon combustion synthesis of oxides (CCSO) in porous media. The governing system of equations includes the Navier ‒ Stokes equations for the gas phase and the thermoelasticity equations using the Duhamel ‒ Neumann relations. The equations of conservation of mass and heat balance of the gas phase contain tensors of mass and thermal dispersion, conductive and convective transfer. The results of studying the effect of thermal and concentration expansion on variable porosity in the process of synthesis of micron barium titanate powders during carbon combustion are presented. A dimensionless form of the constitutive equations with similarity parameters is given. Dimensionless equations are applied to the nu-merical simulation of the effect of thermal and mass dispersion at variable porosity on the synthesis of micron barium titanate particles in a three-zone reactor. The results of calculations, including the effect of dispersion, pore tortuosity coefficient, particle diameter, local values of Peclet numbers are presented. The proposed model makes it possible to analyze and evaluate the effect of thermal and concentration expansion on the velocity of the combustion and synthesis front, as well as on the uniformity of the distribution of the reactants and the synthesis product in the reactor.