Dispersion relations for the convective instability of an acidity front in Hele-Shaw cells

Autocatalytic chemical fronts of the chlorite-tetrathionate (CT) reaction become buoyantly unstable when they travel downwards in the gravity field because they imply an unfavorable density stratification of heavier products on top of lighter reactants. When such a density fingering instability occurs in extended Hele-Shaw cells, several fingers appear at onset which can be characterized by dispersion relations giving the growth rate of the perturbations as a function of their wave number. We analyze here theoretically such dispersion curves comparing the results for various models obtained by coupling Darcy's law or Brinkman's equation to either a one-variable reaction-diffusion model for the CT reaction or an eikonal equation. Our theoretical results are compared to recent experimental data.