In partially miscible two-layer systems within a gravity field, buoyancy-driven convective motions can appear when one phase dissolves with a finite solubility into the other one. We investigate the influence of chemical reactions on such convective dissolution by a linear stability analysis of a reaction-diffusion-convection model. We show theoretically that a chemical reaction can either enhance or decrease the onset time of the convection, depending on the type of density profile building up in time in the reactive solution. We classify the stabilizing and destabilizing scenarios in a parameter space spanned by the solutal Rayleigh numbers. As an example, we experimentally demonstrate the possibility to enhance the convective dissolution of gaseous CO_{2} in aqueous solutions by a classical acid-base reaction.

Dissolution-driven convection occurs in the host phase of a partially miscible system when a buoyantly unstable density stratification develops upon dissolution. Reactions can impact such convection by changing the composition and thus the density of the host phase. Here we study the influence of A+B→ C reactions on such convective dissolution when A is the dissolving species and B a reactant initially present in the host phase. We perform a linear stability analysis of related reaction-diffusion density profiles to compare the growth rate of the instability in the reactive case to its non reactive counterpart when all species diffuse at the same rate. We classify the stabilizing or destabilizing influence of reactions on the buoyancy-driven convection in a parameter space spanned by the solutal Rayleigh numbers R A,B,C of chemical species A, B, C and by the ratio β of initial concentrations of the reactants. For R A > 0, the non reactive dissolution of A in the host phase is buoyantly unstable. In that case, we show that reaction is enhancing convection provided C is sufficiently denser than B. Increasing the ratio β of initial reactant concentrations increases the effect of chemistry but does not significantly impact the stabilizing/destabilizing classification. When the non reactive case is buoyantly stable (R A < 0), reactions can create in time an unstable density stratification and trigger convection if R C > R B . Our theoretical approach allows classifying previous results in a unifying picture and developing strategies for chemical control of convective dissolution.

Density differences across an autocatalytic chemical front traveling horizontally in covered thin layers of solution trigger hydrodynamic flows which can alter the concentration profile. We theoretically investigate the spatiotemporal evolution and asymptotic dynamics resulting from such an interplay between isothermal chemical reactions, diffusion, and buoyancy-driven convection. The studied model couples the reaction-diffusion-convection evolution equation for the concentration of an autocatalytic species to the incompressible Stokes equations ruling the evolution of the flow velocity in a two-dimensional geometry. The dimensionless parameter of the problem is a solutal Rayleigh number constructed upon the characteristic reaction-diffusion length scale. We show numerically that the asymptotic dynamics is one steady vortex surrounding, deforming, and accelerating the chemical front. This chemohydrodynamic structure propagating at a constant speed is quite different from the one obtained in the case of a pure hydrodynamic flow resulting from the contact between two solutions of different density or from the pure reaction-diffusion planar traveling front. The dynamics is symmetric with regard to the middle of the layer thickness for positive and negative Rayleigh numbers corresponding to products, respectively, lighter or heavier than the reactants. A parametric study shows that the intensity of the flow, the propagation speed, and the deformation of the front are increasing functions of the Rayleigh number and of the layer thickness. In particular, the asymptotic mixing length and reaction-diffusion-convection speed both scale as ͱ Ra for RaϾ 5. The velocity and concentration fields in the asymptotic dynamics are also found to exhibit self-similar properties with Ra. A comparison of the dynamics in the case of a monostable versus bistable kinetics is provided. Good agreement is obtained with experimental data on the speed of iodate-arsenous acid fronts propagating in horizontal capillaries. We furthermore compare the buoyancy-driven dynamics studied here to Marangoni-driven deformation of traveling chemical fronts in solution open to the air in the absence of gravity previously studied in the same geometry ͓L. Rongy and A. De Wit, J. Chem. Phys. 124, 164705 ͑2006͔͒.

Chemical reactions can accelerate, slow down or even be at the very origin of the development of dissolution-driven convection in partially miscible stratifications when they impact the density profile in the host fluid phase. We numerically analyze the dynamics of this reactive convective dissolution in the fully developed non-linear regime for a phase A dissolving into a host layer containing a dissolved reactant B. We show for a general A + B → C reaction in solution, that the dynamics vary with the Rayleigh numbers of the chemical species, i.e. with the nature of the chemicals in the host phase. Depending on whether the reaction slows down, accelerates or is at the origin of the development of convection, the spatial distributions of species A, B or C, the dissolution flux and the reaction rate are different. We show that chemical reactions can enhance the steady-state flux as they consume A and can induce more intense convection than in the non-reactive case. This result is important in the context of CO geological sequestration where quantifying the storage rate of CO dissolving into the host oil or aqueous phase is crucial to assess the efficiency and the safety of the project.

The dynamics of A+B-->C fronts in horizontal solution layers can be influenced by buoyancy-driven convection as soon as the densities of A, B, and C are not all identical. Such convective motions can lead to front propagation even in the case of equal diffusion coefficients and initial concentration of reactants for which reaction-diffusion (RD) scalings predict a nonmoving front. We show theoretically that the dynamics in the presence of convection can in that case be predicted solely on the basis of the knowledge of the one-dimensional RD density profile across the front.

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.

We present a new mechanism through which chemical oscillations and waves can be induced in batch conditions with a simple A þ B → C reaction in the absence of any nonlinear chemical feedback or external trigger. Two reactants A and B, initially separated in space, react upon diffusive contact and the product actively fuels in situ convective Marangoni flows by locally increasing the surface tension at the mixing interface. These flows combine in turn with the reaction-diffusion dynamics, inducing damped spatiotemporal oscillations of the chemical concentrations and the velocity field. By means of numerical simulations, we single out the detailed mechanism and minimal conditions for the onset of this periodic behavior. We show how the antagonistic coupling with buoyancy convection, due to concurrent chemically induced density changes, can control the oscillation properties, sustaining or suppressing this phenomenon depending on the relative strength of buoyancy-and surface-tension-driven forces. The oscillatory instability is characterized in the relevant parametric space spanned by the reactor height, the Marangoni (Ma i ) and the Rayleigh (Ra i ) numbers of the ith chemical species, the latter ruling the surface tension and buoyancy contributions to convection, respectively.

The convective dissolution of carbon dioxide (CO 2 ) in salted water is theoretically studied to determine how parameters such as CO 2 pressure, salt concentration and temperature impact the short-time characteristics of the buoyancy-driven instability.On the basis of a parameter-free dimensionless model, we perform a linear stability analysis of the time-dependent concentration profiles of CO 2 diffusing into the aqueous solution. We explicit the procedure to transform the predicted dimensionless growth rate and wavelength of the convective pattern into dimensional ones for typical laboratory-scale experiments in conditions close to room temperature and atmospheric pressure. This allows to investigate the implicit influence of the experimental parameters on the characteristic length and time scales of the instability. We predict that increasing CO 2 pressure, or decreasing salt concentration or temperature destabilizes the system, leading to a faster dissolution of CO 2 into salted water.PACS numbers: 47.20.Bp, 47.56.+r a) Electronic mail: vloodts@ulb.ac.be 1 When carbon dioxide (CO 2 ) dissolves in an aqueous solution, a buoyancy-driven fingering instability can develop because of the formation of a denser layer of CO 2 -rich solution on top of the less dense water. By a theoretical analysis, we predict how the short-time characteristics of this instability depend on experimental control parameters. To do so, we use a linear stability analysis based on a parameter-free model along with empirical correlations to compute the characteristic time and length scales of the fingering instability. We find that the growth rate of the convective instability increases with increasing CO 2 pressure or decreasing salt concentration or temperature. These results allow to interpret experimental data 1,2 on the impact of salt concentration and gaseous CO 2 pressure on the convective dissolution of CO 2 . Another main result of our analysis is that temperature has only a slight effect for CO 2 pressures close to atmospheric pressure. This study therefore suggests that carefully controlling the temperature of the setup is not needed for reproducibility of experimental studies of convective dissolution of CO 2 in laboratory conditions.