Weakly nonlinear stability analysis of frontal polymerization

A description of frontal polymerization is given via a free boundary model with nonlinear kinetic and kinematic conditions at the free boundary. We perform a weakly nonlinear analysis for the development of pulsating instabilities on the cylinder, building on the linear stability analysis of [1]. We take as a bifurcation parameter an experimentally measurable combination of material and kinetic parameters. The asymptotic analysis leads to the derivation of an ordinary differential equation of Landau-Stuart type for the slowly varying amplitude of a linearly unstable mode. We classify nonlinear dynamics of the polymerization front by doing a parameter sensitivity study of the amplitude equation.