Thermal explosion of dispersed media. Criticality for discrete reactive particles in a reactive matrix

The classical treatments of thermal-explosion theory for isolated reactant masses are extended to cover an aggregate of reactant particles embedded in a chemically inert matrix. In this model the heat released by one particle influences the heat-release rates in the others. The critical conditions for thermal runaway can be cast in terms of the classical dimensionless groups ψ or δ, which contain only known thermochemical parameters appropriate to the given reactant. The numerical values of ψ or δ at criticality are determined by a second parameter ω, β or Ω. These parameters compare the resistances to heat transfer of the reactant and the matrix material, and again contain only known or measurable physical quantities. These three different groups are each appropriate to different boundary conditions. We study the following cases: (i) systems where the resistances to heat transfer are concentrated at the reactant and matrix surfaces (low surface heat-transfer coefficients), (ii) systems where the resistance to heat transfer from the matrix is concentrated at the surface, but where there is an internal resistance to heat transfer in the reactant (low reactant thermal conductivity), and (iii) systems where there are internal resistances in both reactant and matrix. Case (i) gives rise to a uniform temperature throughout the matrix and a (higher) uniform temperature throughout each reactant. Case (ii) leads to uniform matrix temperatures but an internal temperature distribution throughout the particles. Case (iii) allows for temperature distributions throughout both matrix and reactant.