Ignition/Extinction Phenomena as Dissipative Phase Transitions
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A particular class of reaction-diffusion systems may be defined by the representative example of a highly porous body (e.g. a catalyst pellet or a fuel agglomerate) residing in a stagnant ambient atmosphere which contains some or all of the gaseous reactant species. An exothermic chemical reaction is supposed to take place on the internal surface of the body, with an area much larger than its external surface area. Therefore, the reaction may be regarded as quasihomogeneous, i.e. as distributed over the entire volume of the system. The state of the system is given by the internal temperature T, the species concentrations Y. and the boundary conditions which detail the ambient atmosphere and the transfer processes for heat, reactants and reaction products. The system is generally characterized by the absence of convection and in that its states result from an interaction of essentially different physical processes which comprise the activated process of internal heat release and the transport of mass and heat. It may be noted that the class of reaction-diffusion systems thus defined comprises, e.g. smokeless solid combustion, viscous deformation of solids (with distributed heat release due to internal friction), or electric conduction with distributed Ohmic losses.
KeywordsSolitary Wave Diffusion Control Ignition Point Critical Manifold Stable Stationary State
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