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

Frontal polymerization (FP) is a process in which a spatially localized rea ction zone propagates into a monomer converting it into a polymer. Two type s of FP processes have been observed experimentally. One is exothermic FP, which occurs due to diffusion of heat released in the polymerization reacti ons and which we have previously studied,Thr: other is an isothermal FP pro cess, also referred to as interfacial gel polymerization, which is due to m ass diffusion of the species coupled with the gel effect. In a previous wor k we proposed and studied analytically a model of interfacial gel polymeriz ation. That work discuss the case of an excessive amount of initiator in th e initial mixture. In addition, it was assumed that the parameters of the p roblem were such that the steady-state assumption (SSA) concerning the tota l concentration of radicals holds not only in the bulk region, which is typ ically the case, but also in the gel region, which may limit the applicabil ity of the results. In this work we seek to resolve the limitations associa ted with these two main assumptions. We relax the SSA in the gel region, an alyze the various situations of initiator consumption fur 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 a head of the front, which an in good agreement with our numerical simulation s.