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

Authors: Hamza Rouah; Loubna Salhi; Ahmed Taik

Addresses: Department of Mathematics, Faculty of Science and Technology, Hassan II University, Casablanca, Morocco ' Laboratory: Modeling, Simulation and Data Analysis, Mohammed VI Polytechnic University (UM6P), Benguerir, Morocco ' Faculty of Science and Technology, Department of Mathematics, Hassan II University, Casablanca, Morocco; Laboratory: Modeling, Simulation and Data Analysis, Mohammed VI Polytechnic University (UM6P), Benguerir, Morocco

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.

Keywords: frontal polymerisation; reaction fronts; Boussinesq approximation; Lewis number; stability analysis; reaction-diffusion equations; cellular instability; oscillatory instability; Navier-Stokes equations; natural convection.

DOI: 10.1504/IJMIC.2020.115394

International Journal of Modelling, Identification and Control, 2020 Vol.36 No.1, pp.42 - 56

Received: 11 Mar 2020
Accepted: 29 Jul 2020
Published online: 01 Jun 2021 *

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