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This publication is totally included in Chapter 4 of this PhD thesis, but it is not indicated as a reference in the main text.

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a b s t r a c tThe third explosion limit of hydrogen oxidation in closed vessels has always been thought to be the result of the competition between homogeneous gas-phase reactions and diffusion of hydroperoxyl radicals to the walls, where they are destroyed. It has recently been observed that this species actually follows a chemical-kinetic steady state in this regime, with the consequence that its diffusive rate toward the catalytic walls becomes irrelevant. Here we show that the critical explosion conditions are determined instead by the fate of hydrogen peroxide, which emerges as the controlling reactant for the resulting gas-phase chemistry. A simple, accurate analytic expression for the third explosion limit follows from identification of the critical conditions for existence of weakly reactive, diffusion-reaction solutions, thereby providing the answer to a long-standing problem that in early work was characterized as being hopelessly difficult.

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An analysis of the structure of flame balls encountered under microgravity conditions, which are stable due to radiant energy losses from H 2 O, is carried out for fuel-lean hydrogen-air mixtures. It is seen that, because of radiation losses, in stable flame balls the maximum flame temperature remains close to the crossover temperature, at which the rate of the branching step H + O 2 ? OH + O equals that of the recombination step H + O 2 +M ? HO 2 + M. Under those conditions, all chemical intermediates have very small concentrations and follow the steady-state approximation, while the main species react according to the overall step 2H 2 + O 2 ? 2H 2 O; so that a one-step chemical-kinetic description, recently derived by asymptotic analysis for near-limit fuel-lean deflagrations, can be used with excellent accuracy to describe the whole branch of stable flame balls. Besides molecular diffusion in a binary-diffusion approximation, Soret diffusion is included, since this exerts a nonnegligible effect to extend the flammability range. When the large value of the activation energy of the overall reaction is taken into account, the leading-order analysis in the reaction-sheet approximation is seen to determine the flame ball radius as that required for radiant heat losses to remove enough of the heat released by chemical reaction at the flame to keep the flame temperature at a value close to crossover. The results are relevant to burning velocities at lean equivalent ratios and may influence fire-safety issues associated with hydrogen utilization.