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

Abstract

The spatiotemporal dynamics of vertical autocatalytic fronts traveling horizontally in thin solution layers closed to the air can be influenced by buoyancy-driven convection induced by density gradients across the front. We perform here a combined experimental and theoretical study of the competition between solutal and thermal effects on such convection. Experimentally, we focus on the antagonistic chlorite-tetrathionate reaction for which solutal and thermal contributions to the density jump across the front have opposite signs. We show that in isothermal conditions the heavier products sink below the lighter reactants, providing an asymptotic constant finger shape deformation of the front by convection. When thermal effects are present, the hotter products, on the contrary, climb above the reactants for strongly exothermic conditions. These various observations as well as the influence of the relative weight of the solutal and thermal effects and of the thickness of the solution layer on the dynamics are discussed in terms of a two-dimensional reaction-diffusion-convection model parametrized by a solutal R C and a thermal R T Rayleigh number. © 2009 American Institute of Physics. ͓DOI: 10.1063/1.3122863͔ A vertical interface separating two solutions with different densities is always unstable under gravity, as the denser fluid tends to sink under the other one by forming a gravity current. When the interface is the result of the interplay between a reaction with a positive feedback and diffusion, the constant change in density across this selforganized front has both a thermal component originating from the temperature change due to the exothermicity of the reaction and a solutal component arising from the change in the chemical composition in the course of the reaction. For an antagonistic case, the combination of these two effects associated with opposite signs is investigated in an autocatalytic reaction both experimentally and theoretically. In the absence of thermal contribution, the denser product sinks, propagates at the bottom, and a single convection roll forms. The intrusion is characterized by the mixing length that scales with the height of the solution. When the temperature rise is significant, a local decrease in density is observed. The product propagates ahead on the top and several convection rolls develop as the solution cools behind the front. No stable structure evolves, and the number of cellular deformation cells in the front is determined by the height of the fluid.

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

“…We note that oscillations of the concentration field have also been observed in the case of antagonistic solutal and thermal effects in the case of pure buoyancy-driven flows. 44,56 The explanation involves, however, different mechanisms since only surface forces are present here. We have characterized the system dynamics as a function of the Marangoni numbers, quantifying the effect of concentration and temperature gradients on the surface tension, of the Lewis number, measuring the ratio between thermal and molecular diffusivities, and of the layer thickness.…”

“…When the reaction is exothermic, the combination of solutal and thermal density changes comes into play and has been noted to affect for instance the propagation of polymerization fronts in horizontal layers 42,43 and to result in new dynamical behaviors for the case of chemical fronts of the chlorite-tetrathionate (CT) reaction [44][45][46] and of the IAA reaction. 47 On the other hand, the opposite limit case of pure Marangoni flows affecting the propagation of chemical fronts in the absence of density changes has been relatively less investigated except for the case of surface reactions.…”

“…Our goal is on one hand to analyze to what extent thermal effects modify the dynamic properties of the pure solutal Marangoni effects. 1, 55 On the other hand, we plan to see whether the combination of solutal and thermal effects can provide more complex Marangoni dynamics as it has been shown to do in the buoyancy case 44,56 and eventually to compare Marangoni and buoyancy-driven flows around exothermic fronts.…”

“…39 We have next considered the dynamics of an exothermic front propagating in covered layers in the presence of pure buoyancy convection alone showing important modifications in the system with regard to the isothermal dynamics. 44,56 We have investigated two different situations: the first one where the solutal and thermal effects act cooperatively to decrease the density of the solution during the reaction, and the second one where they act antagonistically. In the latter case, temporal oscillations of the concentration, temperature, and velocity fields can occur in a frame of reference moving at a constant speed with the front.…”

Diffúzív és konvektív instabilitás tanulmányozása autokatalitikus reakciófrontokban

“…Azonos reakciókörülményeket alkalmazva a klorit-tetrationát és a jodát-arzénessav rendszerben -ami klorition és arzénessav felesleget, 25 • C-ot, illetve 3 mm vastag reakcióedényt jelent -, majd a meghatározott hatványkitevő értékeket összehasonlítva az mondható el, hogy ezek kísérleti hibán belül megegyeznek, hiszen a CT reakció esetében 1,31 ± 0,08 [89], míg a IAA rendszernél ez az érték 1,33 ± 0,02-nak adódott. Mivel a jodátionok arzénessavval történő reakciója változik a sztöchiometriai aránytól függően, ezért lecsökkentettem a reaktánsarányt 2,8-ra, és megvizsgáltam itt is a kialakuló mintázatot.…”