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=delta ga(3)/vD(C). This parameter involves a fractional density difference delta between the unreacted and reacted fluids, the acceleration of gravity g, the slab width a, the kinematic viscosity v, and the catalyst molecular diffusivity D-c. Buoyancy dominates over the competing curvature dependence of the front velocity in a band 0<q <q(c) of unstable dimensionless wave numbers, with q(c)-->S/24 as S-->0 and q(c)-->(S/4](1/3) as S-->infinity. As S-->0, the perturbation with wave number q(m)=q(c)/2 has the maximum dimensionless growth rate sigma(m)=DcS2/48v. For general S, the cutoff wave number q(c) is calculated using exact analytical solutions for the perturbed fluid velocity. The calculated results should be observable in experiments.