Initiation of free-radical polymerization waves

Frontal polymerization is a process of converting a monomer into a polymer by means of a self-propagating thermal reaction wave. We study initiation of polymerization waves by a high temperature heat source. A five species reaction model is considered with a focus on the evolution of two of these species and the temperature of the mixture. The temperature is tracked from the inert heating to the transition stage. Through an asymptotic analysis, the first correction to the temperature in transition is found as the solution to an integral equation. Two parameters govern the qualitative behavior of the solution to the integral equation. Depending on the magnitude of these parameters, the solution exhibits either bounded or unbounded behavior indicating the onset or inhibition of propagation of a polymerization wave.