Curvature effects in the reaction-diffusion system governing frontal polymerization

Frontal polymerization is a fast and energy-efficient curing process of thermoset polymers involving the self-sustained propagation of a sharp front that transforms a liquid monomer or gel into a polymer. The temperature, speed, and geometry of the polymerization front are closely intertwined quantities that can affect the curing process and the mechanical properties of the polymer. This work investigates the effect of the front curvature on the front propagation speed based on a reaction-diffusion model. The proposed analytical relations between front speed and curvature are verified by finite element simulations and validated through experiments. The models show that a concave front has a higher front temperature and speed than its convex counterpart. When the curvature of a convex front reaches a critical value, the reaction can no longer be sustained, and the front is quenched. The relation between the speed of a steadily propagating front and its geometry is derived, showing good agreement with experimental observations. This study also provides analytical estimates of the thickness of the polymerization front and insight into the relationship between the front curvature and the kinetics of the exothermic reaction.