Role of inter- and intraparticle diffusion in nonuniform particle size gasless compacted-powder combustion synthesis - I: formulation

The propagation-mode, compacted-powder. gasless combustion synthesis of int ermetallics is modeled through a combined three-scale, particle-level/speci men-level treatment. The specimen-level treatment is based on the local vol ume-averaged conservation equations for species and energy. The particle-le vel treatment considers a uniform temperature, the formation of products th rough a diffusion-controlled heterogeneous reaction, and allows for melting of the product assuming a distinct interface between the phases. The exten t of conversion to the final product depends on the local availability of t he reactants and through a statistical model and assuming that the interpar ticle mass transfer resistance is very large, it is determined a priori fro m the powder particle-size distribution. The influence of the particle-size distribution on the flame structure and the propagation speed is determine d using the reaction rate of an average-size particle and also the ensemble average of the reaction rates experienced by particles of different sizes. In a follow-up article (Part II), the results of these models are compared with each other and with experimental results. (C) 1998 Elsevier Science L td. All rights reserved.