Influence of Periodic and Quasi-periodic Gravitational Modulation on Convective Instability of Reaction Fronts in Porous Media K. Allali and M. Belhaq 1 Introduction Various kinds of instabilities that can influence the propagation of reaction fronts can be encountered in several physical problems, including the thermo-diffusional instability, the hydrodynamical instability as well as the convective instability. For instance, the thermo-diffusional instability appears as a result of competition between the heat production in the reaction zone and heat transfer to the cold reactants. To investigate this type of instability, the density of the medium can be taken as constant to remove the influence of hydrodynamics and to simplify the model. The stability conditions in this case were studied in [1–5]. In hydrodynamic instability of reaction fronts, the density of the medium is variable and usually considered as a given function of the temperature. In this case, the instability is caused by heat expansion of the gas or liquid in a neighborhood of the reaction zone [6–10]. Due to the fact that instabilities of reaction fronts are undesirable phenomena, several works have been devoted to studying the effect of a periodic vibration on the convective instability of these reaction fronts. For instance, it was shown that high-frequency vibrations can influence stability of various convective flows, namely periodic modulations can have a stabilizing effect for low frequencies and a destabilizing effect for high ones [11]. It is worth noticing that the case of reaction fronts with liquid reactant and solid product was considered in [12], while the case where the reactant and the product are liquids was analyzed in [13, 14]. It was concluded in these cases that a periodic K. Allali Department of Mathematics, University Hassan II-Mohammedia, P.O. Box 146, FST-Mohammadia, Morocco M. Belhaq () Department of Mechanics, University Hassan II-Casablanca, P.O. Box 5366, Maˆ arif, Casablanca, Morocco e-mail: mbelhaq@yahoo.fr R.G. Rubio et al. (eds.), Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics, Understanding Complex Systems, DOI 10.1007/978-3-642-34070-3 14, © Springer-Verlag Berlin Heidelberg 2013 71