Chemoconvection: A chemically driven hydrodynamic instability

Boundary-bound reactions: Pattern formation with and without hydrodynamics

We study chemical pattern formation in a fluid between two flat plates and the effect of such patterns on the formation of convective cells. This patterning is made possible by assuming the plates are chemically reactive or release reagents into the fluid, both of which we model as chemical fluxes. We consider this as a specific example of boundary-bound reactions. In the absence of coupling with fluid flow, we show that the two-reagent system with nonlinear reactions admits chemical instabilities equivalent to diffusion-driven Turing instabilities. In the other extreme, when chemical fluxes at the two bounding plates are constant, diffusion-driven instabilities do not occur but hydrodynamic phenomena analogous to Rayleigh-Bénard convection are possible. Assuming we can influence the chemical fluxes along the domain and select suitable reaction systems, this presents a mechanism for the control of chemical and hydrodynamic instabilities and pattern formation. We study a generic class of models and find necessary conditions for a bifurcation to pattern formation. Afterwards, we present two examples derived from the Schnakenberg-Selkov reaction. Unlike the classical Rayleigh-Bénard instability, which requires a sufficiently large unstable density gradient, a chemohydrodynamic instability based on Turing-style pattern formation can emerge from a state that is uniform in density. We also find parameter combinations that result in the formation of convective cells whether gravity acts upwards or downwards relative to the reactive plate. The wave number of the cells and the direction of the flow at regions of high/low concentration depend on the orientation, hence, different patterns can be elicited by simply inverting the device. More generally, our results suggest methods for controlling pattern formation and convection by tuning reaction parameters. As a consequence, we can drive and alter fluid flow in a chamber without mechanical pumps by influencing the chemical instabilities.

Effect of variable solubility on reactive dissolution in partially miscible systems

When two partially miscible systems are put in contact, one phase, A, can dissolve into the other one with a given solubility. Chemical reactions in the host phase can impact this dissolution by consuming A and by generating products that impact the solubility of A. Here, we study theoretically the optimal conditions for transfer of a reactant A in a host phase containing a species B when a bimolecular A + B → C reaction generates a product C that linearly decreases the solubility of A. We have quantified numerically the influence of this variable solubility on the reaction-diffusion (RD) concentration profiles of all species in the host phase, on the temporal evolution of the position of the reaction front, and on the flux of A through the interface. We have also computed the analytical asymptotic concentration profiles, solutions at long times of the RD governing equations. For a fixed negative effect of C on the solubility of A, an increase in the initial concentration of reactant B or an increase in the diffusion rate of species B and C results in a larger flux of A and hence a larger amount of A dissolved in the host solution at a given time. However, when the influence of C on the solubility increases, the mass transfer decreases. Our results help understand to what extent a chemical reaction can optimize the reactive transfer of a solute to a host phase with application to, among other things, the geological sequestration of carbon dioxide in an aquifer.

Influence of Oxygen on Chemoconvective Patterns in the Iodine Clock Reaction

There is increasing interest in using chemical clock reactions to drive material formation; however, these reactions are often subject to chemoconvective effects, and control of such systems remains challenging. Here, we show how the transfer of oxygen at the air-water interface plays a crucial role in the spatiotemporal behavior of the iodine clock reaction with sulfite. A kinetic model was developed to demonstrate how the reaction of oxygen with sulfite can control a switch from a low-iodine to high-iodine state under well-stirred conditions and drive the formation of transient iodine gradients in unstirred solutions. In experiments in thin layers with optimal depths, the reaction couples with convective instability at the air-water interface forming an extended network-like structure of iodine at the surface that develops into a spotted pattern at the base of the layer. Thus, oxygen drives the spatial separation of iodine states essential for patterns in this system and may influence pattern selection in other clock reaction systems with sulfite.

Spatial programming of self-organizing chemical systems using sustained physicochemical gradients from reaction, diffusion and hydrodynamics

Living organisms employ chemical self-organization to build structures, and inspire new strategies to design synthetic systems that spontaneously take a particular form, via a combination of integrated chemical reactions, assembly pathways and physicochemical processes. However, spatial programmability that is required to direct such self-organization is a challenge to control. Thermodynamic equilibrium typically brings about a homogeneous solution, or equilibrium structures such as supramolecular complexes and crystals. This perspective addresses out-of-equilibrium gradients that can be driven by coupling chemical reaction, diffusion and hydrodynamics, and provide spatial differentiation in the self-organization of molecular, ionic or colloidal building blocks in solution. These physicochemical gradients are required to (1) direct the organization from the starting conditions (e.g. a homogeneous solution), and (2) sustain the organization, to prevent it from decaying towards thermodynamic equilibrium. We highlight four different concepts that can be used as a design principle to establish such self-organization, using chemical reactions as a driving force to sustain the gradient and, ultimately, program the characteristics of the gradient: (1) reaction-diffusion coupling; (2) reaction-convection; (3) the Marangoni effect and (4) diffusiophoresis. Furthermore, we outline their potential as attractive pathways to translate chemical reactions and molecular/colloidal assembly into organization of patterns in solution, (dynamic) self-assembled architectures and collectively moving swarms at the micro-, meso- and macroscale, exemplified by recent demonstrations in the literature.

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.

Adaptive Micromixer Based on the Solutocapillary Marangoni Effect in a Continuous-Flow Microreactor

Continuous-flow microreactors are an important development in chemical engineering technology, since pharmaceutical production needs flexibility in reconfiguring the synthesis system rather than large volumes of product yield. Microreactors of this type have a special vessel, in which the convective vortices are organized to mix the reagents to increase the product output. We propose a new type of micromixer based on the intensive relaxation oscillations induced by a fundamental effect discovered recently. The mechanism of these oscillations was found to be a coupling of the solutal Marangoni effect, buoyancy and diffusion. The phenomenon can be observed in the vicinity of an air⁻liquid (or liquid⁻liquid) interface with inhomogeneous concentration of a surface-active solute. Important features of the oscillations are demonstrated experimentally and numerically. The periodicity of the oscillations is a result of the repeated regeneration of the Marangoni driving force. This feature is used in our design of a micromixer with a single air bubble inside the reaction zone. We show that the micromixer does not consume external energy and adapts to the medium state due to feedback. It switches on automatically each time when a concentration inhomogeneity in the reaction zone occurs, and stops mixing when the solution becomes sufficiently uniform.

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.

Enhanced steady-state dissolution flux in reactive convective dissolution

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 CO₂ geological sequestration where quantifying the storage rate of CO₂ dissolving into the host oil or aqueous phase is crucial to assess the efficiency and the safety of the project.

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 control of dissolution-driven convection in partially miscible systems: theoretical classification

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 in solution 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 RA,B,C of chemical species A, B, C and by the ratio β of initial concentrations of the reactants. For RA > 0, the non reactive dissolution of A in the host phase is buoyantly unstable. In that case, we show that the 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 (RA≤ 0), reactions can create in time an unstable density stratification and trigger convection if RC > RB. Our theoretical approach allows classifying previous results in a unifying picture and developing strategies for the chemical control of convective dissolution.

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.

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.