Title: Orientation effect on the stability conditions of fronts in a liquid and porous medium

Authors: Hamza Rouah; Ahmed Taik

Addresses: Department of Mathematics, Faculty of Science and Technology, Hassan II University, Casablanca, Morocco ' Department of Mathematics, Faculty of Science and Technology, Hassan II University, Casablanca, Morocco

Abstract: In this article, we have studied the influence of orientation on the conditions of stability of the reaction fronts in two cases: the first case where the liquid monomer is converted into solid polymer in a liquid medium and the second case where the monomer and the polymer are liquid in a porous medium. The Zeldovich and Frank-Kamenetskii method is used to perform the asymptotic analysis taking the inverse of Zeldovich number as a critical parameter. The linear stability analysis is fulfilled to investigate the resulting interface models for both cases. The dispersion relation obtained for both cases is solved numerically and then the conditions for cellular and oscillatory instability are determined. We showed that the angle of inclination affects the conditions of thermal and convective instability in a liquid and porous medium.

Keywords: frontal polymerisation; reaction-diffusion equations; reaction fronts; stability analysis; asymptotic analysis; cellular instability; oscillatory instability.

DOI: 10.1504/IJMIC.2022.128309

International Journal of Modelling, Identification and Control, 2022 Vol.41 No.4, pp.277 - 288

Received: 15 Aug 2021
Accepted: 10 Jan 2022

Published online: 17 Jan 2023 *

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