Numerical simulation of propagating fronts of addition polymerization
Frontal propagation of a highly exothermic addition polymerization reaction in a liquid was studied with the goal of developing a mathematical model of the process and determining the thermal and convective stability of the front. A three-step reaction mechanism, including initiation, propagation, and termination steps, as well as a more simple one-step mechanism, was considered. For both reaction mechanisms the loss of stability of descending polymerization fronts was observed as a sequence of period doubling bifurcations leading to chaos, but the three-step reaction mechanism gave better agreement with the experimental measurements. One and two dimensional numerical simulations were performed to observe various planar and nonplanar periodic modes (flat pulsations, single and multiple head spin modes), and the stability for different kinetic schemes was compared. Convective stability of two dimensional ascending polymerization fronts was studied analytically and numerically in the assumption of zeroth order reaction. Critical Rayleigh numbers for appearance of two experimentally observed convective modes were computed, and the stability boundaries for both modes were calculated on the viscosity/front velocity diagram.