Summary: The influence of an endothermic process on propagation of a premixed laminar flame in an exothermic branched chain is considered. The assumption of a quasi-steady-state for the radical intermediate species allows the branched-chain kinetics to be represented as a second-order reaction system. We show that, depending on the initial concentrations of the fuel and the endothermic reactant and the enthalpies of reaction for the two processes, two different flame solutions can exist. A flame front exists if the exothermic charge in the system exceeds the endothermicity and the temperature rises monotonically through the flame profile. If the endothermicity exceeds the exothermicity, then it is possible to observe flame-pulse solutions in which the temperature increases from its initial value far ahead of the reaction zone to some maximum value before falling back to its initial value far behind the reaction zone. There is no apparent discontinuity in the observed wave speed as the transition from one solution to another occurs. At higher endothermicity, there is ‘quenching’ leading to the ‘failure’ of the flame to develop into a sustained propagating structure. The critical condition for flame failure has been computed numerically as a function of the other system parameters and shows the characteristics of a saddle-node bifurcation with quenching from some non-zero minimum flame speed.
An extension to the model is introduced to examine the situation in which the endothermic reaction leads to the production of a radical scavenger that catalyses the thermoneutral termination of radical chain carriers. It is shown that this additional channel decreases the critical endothermicity for flame quenching. The model is discussed in the context of a premixed flame subject to quenching by water mist with dissolved ionic salts.