Theory of explosion limits of hydrogen/oxygen mixtures

Analytical expressions for the classical Z-shaped pressure-vs-temperature explosion limit curve of hydrogen/oxygen mixtures are expeditiously derived based on the leading-order, algebraically linear reactions between the (H, HO₂, H₂O₂) radicals and the (H₂, O₂) background reactants. The analysis yields a detailed ignition mechanism (DIM) and then a skeletal ignition mechanism (SIM) describing the Z-curve, both of which result in close agreement with those computationally obtained with the original reaction mechanism. The solution leads to the ready identification of the first-second and second-third quadratic limits, the associated lower and upper turning points, and the single first, second, and third limits, with the concomitant demonstration that the conventional second limit, $\left[M\right]=2k_1/k_9$, represented by the classical crossover-temperature, is inadequate to describe the transition between the first and third limits. A curvature-reversal, inflection point embedded within the second limit is identified, leading to the precise indication of the controlling transition chemistry between the low- and high-pressure regimes.