Quantitative Analysis of Chemoconvection Patterns in the Methylene-Blue−Glucose System

Chemically-driven convective dissolution

When a solute A dissolves in a host phase with a given solubility, the resulting density stratification is stable towards convection if the density profile increases monotonically along the gravity field. We theoretically and numerically study the convective destabilization by reaction of this dissolution when A reacts with a solute B present in the host phase to produce C via an A + B→C type of reaction. In this reactive case, composition changes can give rise to non-monotonic density profiles with a local maximum. A convective instability can then be triggered locally in the zone where the denser product overlies the less dense bulk solution. First, we perform a linear stability analysis to identify the critical conditions for this reaction-driven convective instability. Second, we perform nonlinear simulations and compare the critical values of the control parameters for the onset of convection in these simulations with those predicted by linear stability analysis. We further show that the asymptotic dissolution flux of A can be increased in the convective regime by increasing the difference ΔR_CB = R_C-R_B between the Rayleigh numbers of the product C and reactant B above a critical value and by increasing the ratio β = B₀/A₀ between the initial concentration B₀ of reactant B and the solubility A₀ of A. Our results indicate that chemical reactions can not only initiate convective mixing but can also give rise to large dissolution fluxes, which is advantageous for various geological applications.

Glucose Oxidase Micropumps: Multi-Faceted Effects of Chemical Activity on Tracer Particles Near the Solid–Liquid Interface

We report the development of glucose oxidase pumps characterized by small lateral dimensions (≈200 μ m). We studied the effects of the activity of the enzyme pump on silica particles (“tracers”) sedimented around the enzyme pump/patch. Once the activity of the pump was turned on (i.e., the glucose substrate was added to the solution), in-plane motion of the tracers away from the enzyme patch, as well as the emergence of an in-plane region around the patch which was depleted by tracers, was observed. The lateral extent of this depletion zone increased in time at a rate dependent both on the glucose concentration and on the areal density of the enzyme in the patch. We argue that, when the tracers were very near the wall, their motion and the emergence of the depletion zone were most likely the result of diffusiophoresis and drag by osmotic flows induced at the wall, rather than that of drag by a solutal buoyancy driven convective flow. We infer that, for the glucose oxidase enzymatic pumps, bulk (solutal buoyancy), as previously reported, as well as surface (osmotic) driven flows coexist and have to be explicitly accounted for. It seems plausible to assume that this is the case in general for enzyme pumps, and these complementary effects should be considered in the design of applications, e.g., stirring or sensing inside microfluidic systems, based on such pumps.

A DFT investigation of the blue bottle experiment: E∘half-cell analysis of autoxidation catalysed by redox indicators

The blue bottle experiment is a collective term for autoxidation reactions catalysed by redox indicators. The reactions are characterized by their repeatable cycle of colour changes when shaken/left to stand and intricate chemical pattern formation. The blue bottle experiment is studied based on calculated solution-phase half-cell reduction potential of related reactions. Our investigation confirms that the reaction in various versions of the blue bottle experiment published to date is mainly the oxidation of an acyloin to a 1,2-dicarbonyl structure. In the light of the calculations, we also propose new non-acyloin reducing agents for the experiment. These results can help guide future experimental studies on the blue bottle experiment.

Density profiles around A+B→C reaction-diffusion fronts in partially miscible systems: A general classification

Various spatial density profiles can develop in partially miscible stratifications when a phase A dissolves with a finite solubility into a host phase containing a dissolved reactant B. We investigate theoretically the impact of an A+B→C reaction on such density profiles in the host phase and classify them in a parameter space spanned by the ratios of relative contributions to density and diffusion coefficients of the chemical species. While the density profile is either monotonically increasing or decreasing in the nonreactive case, reactions combined with differential diffusivity can create eight different types of density profiles featuring up to two extrema in density, at the reaction front or below it. We use this framework to predict various possible hydrodynamic instability scenarios inducing buoyancy-driven convection around such reaction fronts when they propagate parallel to the gravity field.

Chemical convection in the methylene-blue-glucose system: Optimal perturbations and three-dimensional simulations

A case of convection driven by chemical reactions is studied by linear stability theory and direct numerical simulations. In a plane aqueous layer of glucose, the methylene-blue-enabled catalytic oxidation of glucose produces heavier gluconic acid. As the oxygen is supplied through the top surface, the production of gluconic acid leads to an overturning instability. Our results complement earlier experimental and numerical work by Pons et al. First, we extend the model by including the top air layer with diffusive transport and Henry's law for the oxygen concentration at the interface to provide a more realistic oxygen boundary condition. Second, a linear stability analysis of the diffusive basic state in the layers is performed using an optimal perturbation approach. This method is appropriate for the unsteady basic state and determines the onset time of convection and the associated wavelength. Third, the nonlinear evolution is studied by the use of three-dimensional numerical simulations. Three typical parameters sets are explored in detail showing significant differences in pattern formation. One parameter set for which the flow is dominated by viscous forces, displays persistently growing convection cells. The other set with increased reaction rate displays a different flow regime marked by local chaotic plume emission. The simulated patterns are then compared to experimental observations.

Control of convective dissolution by chemical reactions: general classification and application to CO(2) dissolution in reactive aqueous solutions

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.

Convective mixing induced by acid-base reactions

When two miscible solutions, each containing a reactive species, are put in contact in the gravity field, local variations in the density due to the reaction can induce convective motion and mixing. We characterize here both experimentally and theoretically such buoyancy-driven instabilities induced by the neutralization of a strong acid by a strong base in aqueous solutions. The diverse patterns obtained are shown to depend on the type of reactants used and on their relative concentrations. They have their origin in a combination of classical hydrodynamic instabilities including differential diffusion of the solutes involved while temperature effects only play a marginal role.

Nonlinear chemoconvection in the methylene-blue-glucose system: two-dimensional shallow layers

Interfacial hydrodynamic instabilities arise in a range of chemical systems. One mechanism for instability is the occurrence of unstable density gradients due to the accumulation of reaction products. In this paper we conduct two-dimensional nonlinear numerical simulations for a member of this class of system: the methylene-blue-glucose reaction. The result of these reactions is the oxidation of glucose to a relatively, but marginally, dense product, gluconic acid, that accumulates at oxygen permeable interfaces, such as the surface open to the atmosphere. The reaction is catalyzed by methylene-blue. We show that simulations help to disassemble the mechanisms responsible for the onset of instability and evolution of patterns, and we demonstrate that some of the results are remarkably consistent with experiments. We probe the impact of the upper oxygen boundary condition, for fixed flux, fixed concentration, or mixed boundary conditions, and find significant qualitative differences in solution behavior; structures either attract or repel one another depending on the boundary condition imposed. We suggest that measurement of the form of the boundary condition is possible via observation of oxygen penetration, and improved product yields may be obtained via proper control of boundary conditions in an engineering setting. We also investigate the dependence on parameters such as the Rayleigh number and depth. Finally, we find that pseudo-steady linear and weakly nonlinear techniques described elsewhere are useful tools for predicting the behavior of instabilities beyond their formal range of validity, as good agreement is obtained with the simulations.

Chemoconvection patterns in the methylene-blue-glucose system: weakly nonlinear analysis

The oxidation of solutions of glucose with methylene-blue as a catalyst in basic media can induce hydrodynamic overturning instabilities, termed chemoconvection in recognition of their similarity to convective instabilities. The phenomenon is due to gluconic acid, the marginally dense product of the reaction, which gradually builds an unstable density profile. Experiments indicate that dominant pattern wavenumbers initially increase before gradually decreasing or can even oscillate for long times. Here, we perform a weakly nonlinear analysis for an established model of the system with simple kinetics, and show that the resulting amplitude equation is analogous to that obtained in convection with insulating walls. We show that the amplitude description predicts that dominant pattern wavenumbers should decrease in the long term, but does not reproduce the aforementioned increasing wavenumber behavior in the initial stages of pattern development. We hypothesize that this is due to horizontally homogeneous steady states not being attained before pattern onset. We show that the behavior can be explained using a combination of pseudo-steady-state linear and steady-state weakly nonlinear theories. The results obtained are in qualitative agreement with the analysis of experiments.