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Influence Study of Perturbations on Inclined Propagation of Reaction Fronts

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Abstract

In this work, we study the influence of vibrations and quasi-periodic vibrations on the propagation of reaction fronts where the monomer is liquid and the polymer is solid and in the case where the experimental tube is subjected to a variable inclination. The mathematical model includes the heat equation, the concentration equation and the Navier–Stockes equation under the Boussinesq approximation. As the reaction zone is narrow, the model is seen as a singular perturbation problem, we perform an asymptotic analysis as proposed by Zeldovich and Frank-Kamenetskii to reduce the problem to an interface problem. We then perform a linear stability analysis to study the interface problem. The linearized problem is solved numerically using a multiquadric radial basis function (MQ-RBF) method to find the neutral convective stability limit. This will allow us to deduce the influence of each physical parameter of the problem on this stability, in particular the different vibrations and the angle of inclination of the experimental tube.

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Authors and Affiliations

  1. Polydisciplinary Faculty of Sidi Bennour, Chouaib Doukkali University, El Jadida, Morocco

    Youssef Joundy

  2. University Hassan II, FST-Mohammadia, Casablanca, Morocco

    Hamza Rouah & Ahmed Taik

Authors
  1. Youssef Joundy
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  2. Hamza Rouah
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  3. Ahmed Taik
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Correspondence to Hamza Rouah.

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Joundy, Y., Rouah, H. & Taik, A. Influence Study of Perturbations on Inclined Propagation of Reaction Fronts. Math Models Comput Simul 15, 574–589 (2023). https://doi.org/10.1134/S2070048223030195

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