Onset of convection for autocatalytic reaction fronts in a vertical slab

A fully three-dimensional linear stability analysis shows that ascending autocatalytic reaction fronts in vertical slabs are unstable to convection for large-wavelength perturbations at all finite values of the dimensionless driving parameter S=δga3/νDC. This parameter involves a fractional density difference δ between the unreacted and reacted fluids, the acceleration of gravity g, the slab width a, the kinematic viscosity ν, and the catalyst molecular diffusivity DC. Buoyancy dominates over the competing curvature dependence of the front velocity in a band 0<q<qc of unstable dimensionless wave numbers, with qc→S/24 as S→0 and qc→(S/4)1/3 as S→. As S→0, the perturbation with wave number qm=qc/2 has the maximum dimensionless growth rate σm=DCS2/48ν. For general S, the cutoff wave number qc is calculated using exact analytical solutions for the perturbed fluid velocity. The calculated results should be observable in experiments.