ELSEVIER PII: S0950-4230(96)00032-0 J. Loss Prey. Process Ind. Vol. 9. Nn. 6. pp. 383-392, 1996 Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0950-4230196 $15.00 + 0.00 Thermal explosion of dispersed media: critical conditions for discrete particles in an inert or a reactive matrix Saad A. EI-Sayed Department of Power Mechanical Engineering, Zagazig University, E1-Sharkia, Egypt Received 18 June 1996 Classical theories of explosion for isolated reactant particles are extended to cover the cases of reactant paticles embedded in an inert (chemically) and a reactive matrix. In these cases the heat released or absorbed by particles influences the heat released or absorbed in the matrix. The critical conditions for ignition in the particles and matrix may be expressed in terms of the dimensionless groups of the classical theory ~ and 5 as well as some other important para- meters such as /3, 7 or Bio,,, which relate the physical properties of the particles and matrix. The different boundary conditions such as the Semenov boundary condition (uniform internal temperature systems) and the Frank-Kamenetskii boundary condition (distributed internal tem- perature systems) are investigated. Approximate solutions besides the exact ones are used in this study. Important results are obtained showing the effect of thermal interaction between particles and matrix. Copyright © 1996 Elsevier Science Ltd Keywords: explosion, dispersed media, discrete particles, inert and reactive matrix, critical con- ditions Classical thermal explosion theory in simple form has been used for many years to determine the conditions under which isolated and homogeneous masses of reac- tant are able to undergo an exothermic reaction (thermal runaway), by Semenov j, Frank-Kamenetskii 2 and many others. Gray and Jones 3 have developed this problem with respect to layered media, with one reactant dis- persed throughout a second. Their analysis covered only the case of uniform temperature excess within each reac- tive medium. More recently, Boddington et al. 4 have investigated the conditions for the onset of criticality for many reactive particles embedded in an inert matrix, with different boundary conditions for heat transfer pass- ing through both media. Scott 5 has determined the criti- cal conditions for a reactant or collection of reactive zones with distributed internal temperature excess (Frank-Kamenetskii boundary condition) embedded within a reactive matrix subject to Semenov boundary conditions. The reaction in either medium may be exo- thermic or endothermic. The present study includes two different cases: (i) uniform internal temperature for matrix and par- ticles (Semenov case); (ii) distributed temperature within particles (Frank- Kamenetskii case) and uniform temperature within the matrix (Semenov case). In the first case, the shape of the particles and their distribution within the matrix are not important. In the second case, because a temperature distribution is allowed within the reactive particles, the shape of the particles is important. Three shapes of particles (class A bodies) are considered here: infinite slabs, infinite cylin- ders, and spheres. This model of study may have significant practical applications such as the storage of propellants and many others. The present paper provides theoretical analyses that explore the criteria for safe storage of dispersed reactive systems under various boundary conditions. This study also shows how the classical analyses may be extended to derive the critical criteria for thermal ignition for such dispersed systems. The treatments covered are of both reactant particles embedded in a chemically inert matrix and reactant particles embedded in a reactive matrix. The results are offered in terms of two well-known dimensionless groups: Semenov num- ber (~0) and Frank-Kamenetskii parameter (6). The study is extended to cover the exact form of the Arrhenius reaction rate law and Frank-Kamenetskii approximation to that law. The critical values of O and 6 are determined based on the boundary conditions assumed for the reac- tant particles-matrix (inert or reactive) and matrix- environment interfaces. This means that no particle is isolated (classical problem); each is linked to its neigh- bours via the thermal properties of the matrix. 383