Gravitational instability of miscible fluids in a Hele-Shaw cell and chemical reaction

Autocatalytic reaction fronts are able to propagate as a solitary wave, that is at a constant velocity and with a stationary concentration profile which result from a balance between diffusion and chemical reaction. Experiments in thin cells have shown a buoyant instability due to the slightly smaller density of the reacted fluid. We provide an extension of our recent analysis of the Rayleigh-Taylor instability of the interface between two miscible fluids by including the chemical process by a reaction-convection-diffusion approach. The computed dispersion relation as well as our lattice BGK simulations compare reasonably well with the growth rates obtained experimentally.