Reaction fronts in porous media, influence of Lewis number, linear stability analysis. (English) Zbl 1458.76105

Salhi, L.; Taik, A.

Int. J. Adv. Appl. Math. Mech. 5, No. 1, 15-27 (2017).

Summary: This work is devoted to the investigation of propagating polymerization fronts in porous media. We consider a simplified mathematical model which consists of coupling two convection-diffusion-reaction equations for the temperature and depth of conversion to the Darcy equation for the pressure. A formal asymptotic analysis of the problem is carried out taking into account the Zeldovich-Frank-Kamanetskii approximation. We fulfill the linear stability analysis of the stationary propagating front and show that the Lewis number influences conditions of the convective instability.

MSC:

76S05	Flows in porous media; filtration; seepage
76V05	Reaction effects in flows
76T30	Three or more component flows
76E17	Interfacial stability and instability in hydrodynamic stability
76M45	Asymptotic methods, singular perturbations applied to problems in fluid mechanics
74F10	Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)

Keywords:

frontal polymerization; Zeldovich-Frank-Kamanetskii approximation; asymptotic solution

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