Frontal Reaction in a Layered Polymerizing Medium

We analyze the dynamics of a reaction propagating along a two-dimensional medium of nonuniform composition. We consider the context of a self-sustaining reaction front that converts a monomer-initiator mixture into an inhomogeneous polymeric material. We model the system with one-step effective kinetics, assuming large activation energy. Using asymptotic methods, we find the analytical expressions for the front profile as well as monomer and temperature distributions. Further, we demonstrate that the predictions of the asymptotic theory match well with the numerical simulations.