No abstract

Buoyancy-driven instabilities of a horizontal interface between two miscible solutions in the gravity field are theoretically studied in porous media and Hele-Shaw cells (two glass plates separated by a thin gap). Beyond the classical Rayleigh-Taylor (RT) and double diffusive (DD) instabilities that can affect such two-layer stratifications right at the initial time of contact, diffusive-layer convection (DLC) as well as delayed-double diffusive (DDD) instabilities can set in at a later time when differential diffusion effects act upon the evolving density profile starting from an initial step-function profile between the two miscible solutions. The conditions for these instabilities to occur can therefore be obtained only by considering time evolving base-state profiles. To do so, we perform a linear stability analysis based on a quasi-steady-state approximation (QSSA) as well as nonlinear simulations of a diffusion-convection model to classify and analyse all possible buoyancy-driven instabilities of a stratification of a solution of a given solute A on top of another miscible solution of a species B. Our theoretical model couples Darcy's law to evolution equations for the concentration of species A and B ruling the density of the miscible solutions. The parameters of the problem are a buoyancy ratio R quantifying the ratio of the relative contribution of B and A to the density as well as δ, the ratio of diffusion coefficients of these two species. We classify the region of RT, DD, DDD and DLC instabilities in the (R, δ) plane as a function of the elapsed time and show that, asymptotically, the unstable domain is much larger than the one captured on the basis of linear base-state profiles which can only obtain stability thresholds for the RT and DD instabilities. In addition the QSSA allows one to determine the critical time at which an initially stable stratification of A above B can become unstable with regard to a DDD or DLC mechanism when starting from initial step function profiles. Nonlinear dynamics are also analysed by a numerical integration of the full nonlinear model in order to understand the influence of R and δ on the dynamics.

In the gravity field, density changes triggered by a kinetic scheme as simple as A þ B ! C can induce or affect buoyancy-driven instabilities at a horizontal interface between two solutions containing initially the scalars A and B. On the basis of a general reaction-diffusion-convection model, we analyze to what extent the reaction can destabilize otherwise buoyantly stable density stratifications. We furthermore show that, even if the underlying nonreactive system is buoyantly unstable, the reaction breaks the symmetry of the developing patterns. This is demonstrated both numerically and experimentally on the specific example of a simple acid-base neutralization reaction. DOI: 10.1103/PhysRevLett.104.044501 PACS numbers: 82.40.Ck, 47.20.Bp, 47.70.Fw, 82.33.Ln Convective motion due to hydrodynamic instabilities of an interface between two different fluids are known to impact the spatiotemporal distribution and dynamics of passive scalars in numerous applications. Much less studied is the active role that processes involving such scalars can have upon the flow dynamics if these scalars influence a physical property of the fluid such as its density for instance [1][2][3][4]. However, coupling between reactivetype processes and hydrodynamics is at the heart of applications in fields as diverse as earth mantle dynamics [5], geological formations [6], supernovae dynamics [7] or CO 2 sequestration [8], to name a few. Often, the specific active role of the scalars on the flow remains difficult to interpret due to difficulties of in situ experiments, as well as a lack of quantitative modeling and of simple benchmark experiments on which theories could be tested. In this respect, it is still unclear to what extent reactions involving these scalars can trigger hydrodynamic instabilities in a system that would otherwise remain stable and whether convective structures have the same symmetries in reactive and nonreactive situations.To gain insight into these issues, let us consider the generic case of a solution containing the scalar A put on top of a solution of B in the gravity field. For nonreactive systems, various hydrodynamic instabilities can impact such a stratification of miscible fluids. The RayleighTaylor instability occurs when the heavier fluid overlies the lighter fluid [9]. If the upper fluid is lighter, the system can also be destabilized either if B diffuses faster than A, because of double-diffusive fingering [10,11], or if a diffusive-layer convection (DLC) instability is triggered when A diffuses faster than B [12]. In all cases, these buoyancy-driven instabilities lead, in nonreactive miscible fluids, to convective motions which develop similarly above and below the initial contact line because of the symmetry of the underlying density gradient [9][10][11][12]. The situation can however be very different if a chemical reaction takes place between species A and B upon contact and mixing of the solutions.We demonstrate indeed both theoretically and experimentally that a reaction as simple as A þ B ! C ...

Chemical gardens are mineral aggregates that grow in three dimensions with plant-like forms and share properties with selfassembled structures like nanoscale tubes, brinicles, or chimneys at hydrothermal vents. The analysis of their shapes remains a challenge, as their growth is influenced by osmosis, buoyancy, and reaction-diffusion processes. Here we show that chemical gardens grown by injection of one reactant into the other in confined conditions feature a wealth of new patterns including spirals, flowers, and filaments. The confinement decreases the influence of buoyancy, reduces the spatial degrees of freedom, and allows analysis of the patterns by tools classically used to analyze 2D patterns. Injection moreover allows the study in controlled conditions of the effects of variable concentrations on the selected morphology. We illustrate these innovative aspects by characterizing quantitatively, with a simple geometrical model, a new class of self-similar logarithmic spirals observed in a large zone of the parameter space.C hemical gardens, discovered more than three centuries ago (1), are attracting nowadays increasing interest in disciplines as varied as chemistry, physics, nonlinear dynamics, and materials science. Indeed, they exhibit rich chemical, magnetic, and electrical properties due to the steep pH and electrochemical gradients established across their walls during their growth process (2). Moreover, they share common properties with structures ranging from nanoscale tubes in cement (3), corrosion filaments (4) to larger-scale brinicles (5), or chimneys at hydrothermal vents (6). This explains their success as prototypes to grow complex compartmentalized or layered self-organized materials, as chemical motors, as fuel cells, in microfluidics, as catalysts, and to study the origin of life (7-18). However, despite numerous experimental studies, understanding the properties of the wide variety of possible spatial structures and developing theoretical models of their growth remains a challenge.In 3D systems, only a qualitative basic picture for the formation of these structures is known. Precipitates are typically produced when a solid metal salt seed dissolves in a solution containing anions such as silicate. Initially, a semipermeable membrane forms, across which water is pumped by osmosis from the outer solution into the metal salt solution, further dissolving the salt. Above some internal pressure, the membrane breaks, and a buoyant jet of the generally less dense inner solution then rises and further precipitates in the outer solution, producing a collection of mineral shapes that resembles a garden. The growth of chemical gardens is thus driven in 3D by a complex coupling between osmotic, buoyancy, and reaction-diffusion processes (19,20).Studies have attempted to generate reproducible micro-and nanotubes by reducing the erratic nature of the 3D growth of chemical gardens (10,11,13,15,21). They have for instance been studied in microgravity to suppress buoyancy (22, 23), or by injecting aqueous ...

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.