Thermal and compositional driven convection in autocatalytic reaction fronts

Flat reaction fronts propagating vertically separate fluids with differing densities, which can give rise to hydrodynamic instabilities. This change in density may result from an exothermic reaction or from changes in the chemical composition between reacted and unreacted fluids. If the less dense fluid is underneath the front, buoyancy acts as a destabilizing mechanism for convection. However, if the less dense fluid is situated below a denser fluid, instabilities can still arise due to different molecular and thermal diffusivities. In this paper, we show that instability can occur with very small thermal density gradients, even if the combined density gradients contribute to a statically stable configuration. We carry out a linear stability analysis of fixed-wavelength perturbations for both ascending and descending fronts. In both scenarios, we identify ranges of perturbation wavenumbers with positive growth rates, indicating instability. We examine how instability depends on the Lewis number, particularly as it approaches both large and small values. We numerically solve the nonlinear set of equations showing the increase of front speed as they propagate in narrow two-dimensional domains.