Boltzmann's knock: auto-ignition delay times from Arrhenius theory

Abstract

An exact series solution is given for the first-order equation describing delay times in chemical kinetics, especially auto-ignition of fuels, employing the Arrhenius rate factor. Provision is made for both a constant pressure and a constant volume process by means of an index that describes the temperature dependence of the reaction rate. To allow for the common circumstance that the activation temperature is well above the temperature that would be recognised as the onset of combustion, an onset of combustion is defined analogous to the boundary layer theory of Blasius. Exact offset times are tabulated in non-dimensional form. The limitations of a Taylor-series expansion are discussed.