On Step-Function Reaction Kinetics Model in the Absence of Material Diffusion

We propose a precise definition of the step‐function kinetics suitable for approximating diffuse propagating reaction fronts in one‐dimensional gasless‐combustion‐type models when a Lewis number is large. We investigate this kinetics in the context of free‐radical frontal polymerization (FP) in which a monomer‐initiator mixture is converted into a polymer via a propagating self‐sustaining reaction front. The notion of step‐function kinetics has been extensively used in studies of the frontal dynamics both in FP and in combustion problems when the material diffusion is negligible. However, the models have always been effectively reduced to their point‐source approximations without defining exactly what the step‐function kinetics is for diffuse reaction fronts. We demonstrate numerically that dynamics of diffuse fronts in systems modeled with step‐function kinetics and in systems modeled with Arrhenius kinetics are qualitatively the same at time scales at which the bulk reaction ahead of the front can be ig...