A homogeneous explosive system will detonate only when a suitable spatially-varying disturbance is impressed upon it. Such a disturbance may be imposed across a boundary (e.g., thermal loading or mechanical impact) or as an initial state (e.g., a nonuniformity in temperature or concentration). Spatial nonuniformities may also emerge naturally as a part of the evolutionary process, as in the transition of a laminar flame into a turbulent flame brush. For thermally sensitive reaction rates and relatively simple kinetics, and for a variety of imposed disturbances, the initiation process has been the subject of a number of theoretical studies, asymptotic as well as numerical. Perhaps the simplest model problem considered is the one suggested and first studied by Zeldovich et al: a system in which an initial temperature gradient is imposed. This paper surveys the existing studies of this problem and supplements them with new results. The intent is to present a detailed and coherent description of the various initiation scenarios that are possible, depending upon the size of the gradient, the extent of the confinement, and the physico-chemical parameters of the system.
It is shown that depending upon the parameters, a conventional, ZND detonation may emerge essentially in one of two ways. For relatively shallow initial gradients, the path to detonation begins with an induction period that culminates in a localized, constant-volume thermal explosion at the hot wall. A supersonic, shockless, weak detonation (the so-called Zeldovich Spontaneous Wave) emerges from the site of the explosion and proceeds towards the cold wall, decelerating as it does so. When the wave speed falls to the CJ value, a weak shock is born at the rear of the reaction zone. It strengthens, and moves to the front of the reaction zone with extreme rapidity, thereby generating the ZND structure.
For relatively moderate initial gradients, the induction process, now confined to a thin boundary layer near the hot wall, culminates in a localized constant-pressure explosion. Expansion within the explosive boundary layer creates a compressive pulse outside it, which steepens into a weak shock. The system now consists of the lead shock followed by an induction zone in which the pressure rises, which in turn is followed by a fast, diffusionless deflagration where the pressure falls and a bulk of the chemical activity occurs. If the initial gradient is too steep, the fast flame and the lead shock remain uncoupled, the separation between them increases, and the detonation fails to materialize. Otherwise, the pressure peak behind the lead shock grows stronger. It either strengthens the lead shock itself, thereby merging the fast flame and the lead shock and leading to a conventional detonation, or else, there occurs a constant-volume explosion some distance behind the lead shock. This explosion leads to a detonation by the procedure described above for shallow gradients, which overtakes the lead shock.
The manner in which the above scenarios are affected by flow divergence is examined as well.