PERTURBATION METHODS FOR MATHEMATICAL MODELS OF EXPLOSION PHENOMENA

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Abstract
The ordinary differential equation which describes adiabatic, spatially homogeneous explosions in a chemically reactive mixture of perfect gases is studied by means of perturbation methods. Techniques are developed which permit calculation of solutions uniformly valid in time for the limit of large activation energy. Results which describe the complete solution from initiation to completion are compared with those found from classical ‘ignition’ theory. Explicit time scales are developed for the ‘ignition’, explosion and asymptotic decay phases of the complete reaction. It is shown that the classically defined ‘ignition’ time actually occurs subsequent to most of the reaction process.

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