On the classification of buoyancy-driven chemo-hydrodynamic instabilities of chemical fronts

Abstract

Exothermic autocatalytic fronts traveling in the gravity field can be deformed by buoyancy-driven convection due to solutal and thermal contributions to changes in the density of the product versus the reactant solutions. We classify the possible instability mechanisms, such as Rayleigh-Bénard, Rayleigh-Taylor, and double-diffusive mechanisms known to operate in such conditions in a parameter space spanned by the corresponding solutal and thermal Rayleigh numbers. We also discuss a counterintuitive instability leading to buoyancy-driven deformation of statically stable fronts across which a solute-light and hot solution lies on top of a solute-heavy and colder one. The mechanism of this chemically driven instability lies in the coupling of a localized reaction zone and of differential diffusion of heat and mass. Dispersion curves of the various cases are analyzed. A discussion of the possible candidates of autocatalytic reactions and experimental conditions necessary to observe the various instability scenarios is presented. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2405129͔It is common knowledge that light fluids rise while heavy fluids sink in the gravity field. Buoyant convection due to a hydrodynamic Rayleigh-Taylor instability can therefore be triggered if a heavy solution lies on top of a lighter one. Rayleigh-Bénard convection appears when a fluid is heated from below. Convection can also result from double-diffusive instabilities of a statically stable density stratification if solutal and thermal effects are in competition. However, it is expected that a stratification of a solute-light and hot fluid over a solute-heavy and cold one should always be stable. Here we show that chemical reactions can change this intuitive picture and trigger convection even in cases where concentration and heat both contribute to a stable density stratification. We find that the balance between intrinsic thermal and solutal density gradients initiated by a spatially localized reaction zone and double-diffusive mechanisms are at the origin of a new convective instability of stable density stratifications the mechanism of which is explained by a displaced particle argument. We also classify the stability properties and dispersion curves to be observed for various classes of exothermic chemical fronts depending whether they ascend or descend in the gravity field and whether their solutal and thermal contributions to the density jump across the front are cooperative or antagonistic.

Buoyancy-driven convection around chemical fronts traveling in covered horizontal solution layers

“…6 The fact that heat diffuses more rapidly than mass and also the possible competition between antagonistic solutal and thermal buoyancy effects is expected to lead to interesting new dynamics as is the case for fronts traveling in vertical geometries. 20,21 In parallel, this work complements our previous studies 9,10 of the influence of pure Marangoni stresses on the deformation and acceleration of fronts traveling in horizontal layers open to the air but in the absence of gravity. In practice, in such geometries, Marangoni and buoyancy effects will most often both be present.…”

“…19 In such a vertical orientation, hydrodynamic flows are due to Rayleigh-Taylor, Rayleigh-Bénard, doublediffusive, or even chemically driven instabilities. 20,21 Flows are triggered typically when the heavier solution lies on top of the lighter one or if double-diffusive effects due to the differential diffusivity of mass and heat are involved. Otherwise, the front remains planar and travels at a reactiondiffusion ͑RD͒ speed v as in a gel.…”

Marangoni-driven convection around exothermic autocatalytic chemical fronts in free-surface solution layers

“…[19][20][21][22][23][24] Various scenarios of buoyancy-driven instabilities have been shown to arise from the combination of solutal and thermal contributions to the density difference across the front. 9,[25][26][27][28][29] In horizontal geometries, the situation can become even more complicated if the solution is open to air. Indeed, besides possible density gradients, there is an additional source of fluid motions, the Marangoni effects triggered by surface tension gradients at the air-liquid interface.…”

Influence of thermal effects on buoyancy-driven convection around autocatalytic chemical fronts propagating horizontally

“…[4][5][6][7][8][9][10][11][12] In that case, the combination of solutal and thermal contributions to the density jump has been shown to lead to various instability scenarios depending on whether ⌬ S and ⌬ T have the same negative sign ͑coop-erative case͒ or different signs ͑⌬ S Ͼ 0, ⌬ T Ͻ 0, antagonistic case͒. 6,13,14 In thin horizontal solution layers, it is known that convection can also deform the dynamic of autocatalytic fronts or waves. 4,[15][16][17][18][19][20][21] In the case of a simple reaction front propagating horizontally, it has been shown both experimentally 17,18,22 and numerically 16,23 that instead of a gravity current leading to a homogeneous solution, the coupling between reaction, diffusion, and convection triggered by the density difference leads in isothermal conditions to CHAOS 19, 023110 ͑2009͒ one solitary vortex structure deforming the front and speeding it up.…”