Mathematical modeling of interfacial gel polymerization for weak and strong gel effects

Frontal polymerization (FP) is a process in which a spatially localized reaction zone propagates into a monomer converting it into a polymer. Two types of FP processes have been observed experimentally. One is exothermic FP, which occurs due to diffusion of heat released in the polymerization reactions and which we have previously studied. The other is an isothermal FP process, also referred to as interfacial gel polymerization, which is due to mass diffusion of the species coupled with the gel effect. In a previous work we proposed and studied analytically a model of interfacial gel polymerization. That work discussed the case of an excessive amount of initiator in the initial mixture. In addition, it was assumed that the parameters of the problem were such that the steady-state assumption (SSA) concerning the total concentration of radicals holds not only in the bulk region, which is typically the case, but also in the gel region, which may limit the applicability of the results. In this work we seek to resolve the limitations associated with these two main assumptions. We relax the SSA in the gel region, analyze the various situations of initiator consumption for a weak gel effect, and study the case of a strong gel effect. We obtain analytical results, including the time-dependent propagation velocity of the reaction zone and the distance traveled by the front before it breaks down due to reactions ahead of the front, which are in good agreement with our numerical simulations.