A micromechanistic model of the combustion synthesis process: Part I. Theoretical development

Abstract

A theoretical model of the combustion synthesis process has been developed. In particular, a set of nonlinear and interrelated partial differential equations is given that accounts for all of the relevant physical and chemical processes that occur during the combustion synthesis process. The appropriate conservation equations for thermal energy, mass, and momentum densities are correctly described—for each phase at each point in the sample—at all times during the process. In addition, details of the necessary interphase transfer terms are expressed in a number of constitutive relationships, in which the dependence of an independent variable upon its dependent variable(s) is given explicitly. In doing so, microstructural details are accounted for, derived primarily from percolation concepts as applied to disordered porous media. All assumptions that are incorporated into the theoretical model have been tabulated in detail. This theoretical model establishes an approach to the development of a sound, quantitative, and fundamental understanding of the combustion synthesis process, particularly with respect to the processing-microstructure-properties relationship. It also provides a point of departure for conducting detailed, quantitative computer experiments of the combustion synthesis process.