Buoyancy-driven instability of an autocatalytic reaction front in a Hele-Shaw cell

An autocatalytic reaction-diffusion front between two reacting species may propagate as a solitary wave, namely, at constant velocity and with a stationary concentration profile. Recent experiments on such reactions have been reported to be buoyancy unstable, under certain conditions. We calculate the linear dispersion relation of the resulting instability, by applying our recent analysis of the Rayleigh-Taylor instability of two miscible fluids in a Hele-Shaw cell. The computed dispersion relation as well as our three-dimensional lattice Bhatnagar-Gross-Krook (BGK) simulations fit reasonably well experimental growth rates reported previously.