On the theory of interphase interaction in a mixture of reacting metal particles

A mathematical model of interphase interaction in a mixture of powders is constructed on the basis of the principles of mechanics of multiphase, multispecies, and heterogeneous media, as applied to SHS processes. The evolution of structural transformations, chemical reactions, and phase transitions are considered at the level of a mesocell of the mixture. Analytical solutions are presented for conjugate thermodiffusion problems on single particles and in the mesocell, which close the equations of conservation laws. By an example of a single-stage chemical reaction in a mixture of nickel and aluminum powders (Ni + Al = NiAl), the problem of the structure of an SHS heat wave propagating over a finite-thickness semi-infinite rod is solved numerically. It is shown that the wave structure is strictly nonstationary and contains inflections and isothermal sectors at the melting point of the components, which vary periodically in time. To solve the problem of thermal explosion in a mixture of metal powders in a three-dimensional domain of complex geometry, a numerical algorithm with the use of the method of dummy domains was developed.