Kinetics of autoignition: a simple intuitive interpretation and its relation to the Livengood-Wu integral

It is well known that the gas-phase autoignition phenomenon often involves branched chain reactions as well as the acceleration of reactions by thermal feedback. Despite the huge combustion kinetic mechanisms of large hydrocarbons found in practical fuels, chain reactions in the early stages of alkane autoignition exhibit simple kinetics since the pseudo-first-order assumption and the linear approximation are valid. In this study, this simple picture of autoignition will be presented starting from the H2-O2 system and then extending to practical fuel-air mixtures. The present interpretation gives the theoretical rationale for the Livengood-Wu integral which is known as an empirical method to predict the timing of knock in spark-ignition engines.