Influence of some critical parameters on the stability of reaction fronts in liquid medium

Abstract

In this paper, we are interested to study the influence of some critical parameters on thermal frontal polymerisation in two cases: the first one where the monomer and the polymer are both in liquid phase, and the second one when the monomer is liquid and the polymer is solid. The governing equations consist of coupling the Navier-Stockes equation to two convection-diffusion-reaction equations for the temperature and depth of conversion under the Boussinesq approximation. A formal asymptotic analysis is performed based on the Zeldovich and Frank-Kamenetskii approach to obtain an approximate interface problem in either case. The linear stability analysis is investigated to study the resulting interface models for both cases. The obtained dispersion relations of both cases are solved numerically and then the stability conditions of reaction fronts are carried out according to the different critical parameters of the problem considered. The instability conditions obtained are in good agreement with some previous studies.