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

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Abstract
The classical treatments of thermal-explosion theory for isolated reactant masses are extended to cover assemblies or aggregates of reactive particles embedded in a matrix. Both phases are considered capable of undergoing chemical change with corresponding heat production or absorption. The temperature within the outer medium is assumed to be spatially uniform (Semenov boundary conditions) whilst an internal temperature distribution through the embedded particles (Frank-Kamenetskii boundary conditions) is allowed. The results are of considerable practical importance affording (i) routes for ab initio calculation of ignition hazards or the scaling of small-scale test data and (ii) an assessment of the effect of coupling exothermic and endothermic processes. In the latter situation there are two competing influences: first, there is a destabilizing effect caused by cladding the particles with the matrix material; secondly, the self-cooling in the endothermic medium leads to self-repression and reduction of the ignition tendency. The critical conditions for thermal runaway in the particles and matrix may be conveniently expressed in terms of the classical dimensionless groups δ and ψ, respectively. Two additional parameters are also important: the ratio of the activation energies for reaction in the matrix and particle, η, and a modified Biot number, β, which relates the heat-transfer characteristics of the two phases. The unified solutions of Boddington et al.(T. Boddington, P. Gray and S. K. Scott, J. Chem. Soc., Faraday Trans. 2, 1982, 78, 1721 and 1731) allow treatment of particles of slab, cylinder and sphere geometry; extension to other stellate shapes is also possible. The classical results for isolated particles play an important role, acting as turning points between different patterns of behaviour. In particular, we find considerable significance in the results for an isolated mass subject to a classical Biot number Bi equal to the value of the modified term β.

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