Thermal and compositional driven convection generated by reaction fronts in Hele-Shaw cells or porous media

Chemical reaction fronts propagating in liquids induced density gradients due to changes in chemical composition and temperature. These density gradients result in buoyancy driven instabilities for flat fronts propagating in the vertical direction. In this work, we analyze the conditions for instability for fronts propagating in Hele-Shaw cells or porous media. We modeled the front propagation using a reaction-diffusion-advection equation corresponding to cubic autocatalysis. The fluid motion is described using the Brinkman equation. We compare our results to solutions using the Navier-Stokes equation and Darcy's Law in the appropriate hydrodynamic limits. A linear stability analysis of a flat reaction-diffusion front shows good agreement to a thin front approximation based on an eikonal relation. This eikonal relation provides the normal front velocity as a function of its curvature. We show that for thermal driven convection, the flat front can be unstable even if the low-density fluid is above the high-density fluid. We solve the nonlinear equations for fluids confined in narrow two-dimensional domains. We observe transitions between different types of fronts propagating with constant velocity and steady curved shapes due to convection.