Interaction between buoyancy and diffusion-driven instabilitiesof propagating autocatalytic reaction fronts. I. Linear stability analysis

摘要

The interaction between buoyancy-driven and diffusion-driven instabilities that can develop along apropagating reaction front is discussed for a system based on an autocatalytic reaction. Twelve different cases are possible depending on whether the front is ascending or descending in the gravity field, whether the reactant is heavier or lighter than the products, and whether the reactant diffusesfaster, slower, or at the same rate as the product. A linear stability analysis (LSA) is undertaken, in which dispersion curves (plots of the growth rate Oagainst wave numberk)are derived for representative cases as well as an asymptotic analysis for small wave numbers. The results from theLSA indicate that, when the initial reactant is denser than the reaction products, upward propagatingfronts remain unstable with the diffusion-driven instability enhancing this instability. Buoyantly stable downward propagating fronts become unstable when the system is also diffusionally unstable.When the initial reactant is lighter than the reaction products, any diffusionally unstable upward propagating front is stabilized by small buoyancy effects. A diffusional instability enhances thebuoyant instability of a downward propagating front with there being a very strong interaction between these effects in this case.