A MICROMECHANISTIC MODEL OF THE COMBUSTION SYNTHESIS PROCESS .1. THEORETICAL DEVELOPMENT

A theoretical model of the combustion synthesis process has been devel oped. In particular, a set of nonlinear and interrelated partial diffe rential equations is given that accounts for all of the relevant physi cal and chemical processes that occur during the combustion synthesis process. The appropriate conservation equations for thermal energy, ma ss, and momentum densities are correctly described-for each phase at e ach 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 in dependent variable upon its dependent variable(s) is given explicitly. In doing so, microstructural details are accounted for, derived prima rily 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 approa ch to the development of a sound, quantitative, and fundamental unders tanding of the combustion synthesis process, particularly with respect to the processing-microstructure-properties relationship. It also pro vides a point of departure for conducting detailed, quantitative compu ter experiments of the combustion synthesis process.