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

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.)
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