Chemically driven hydrodynamic instabilities

Transport-driven chemical oscillations: a review

Chemical oscillators attract transversal interest not only as useful models for understanding and controlling (bio)chemical complexity far from the equilibrium, but also as a promising means to design smart materials and power synthetic functional behaviors. We review and classify oscillatory phenomena in systems where a periodic variation in the concentration of the constitutive chemical species is induced by transport instabilities either triggered by simple reactions or without any reactive process at play. These phenomena, where the origin of the dynamical complexity is shifted from chemical to physical nonlinearities, can facilitate a variety of processes commonly encountered in chemistry and chemical engineering. We present an excursus through the main examples, discussing phenomenology, properties and modeling of different mechanisms that can lead to these kinds of oscillations. In particular, we reproduce the relevant results reported in the pertinent literature and, in parallel, propose new kinds of proof-of-concept systems substantiated by preliminary studies which can inspire new research lines. In the landscape of physically driven chemical oscillations, we devote particular attention to transport phenomena, actively or passively combined to (reactive or nonreactive) chemical species, which provide multiple pathways towards spontaneous oscillatory instabilities. Though with different specificities, the great part of these systems can be reduced to a common theoretical description. We finally overview possible perspectives in the study of physically driven oscillatory instabilities, showing how the related control can impact fundamental and applied open problems, ranging from origin of life studies to the optimization of processes with environmental relevance.

Thermal and compositional driven convection in thin reaction fronts

Chemical reaction fronts separate regions of reacted and unreacted substances as they propagate in liquids. These fronts may induce density gradients due to different chemical compositions and temperatures across the front. In this paper, we investigate buoyancy-induced convection driven by both types of gradients. We consider a thin front approximation where the normal front velocity depends only on the front curvature. This model applies for small curvature fronts independent of the specific type of chemical reaction. For density changes due only to heat variations near the front, we find that convection can take place for either upward or downward propagating fronts if density gradients are above a threshold. Convection can set in even if the fluid with lower density is above the higher density fluid. Our model consists of Navier-Stokes equations coupled to the front propagation equation. We carry out a linear stability analysis to determine the parameters for the onset of convection. We study the nonlinear front propagation for liquids confined in narrow two-dimensional domains. Convection leads to fronts of steady shape, propagating with constant velocities.

Chemically Enhanced Convective Dissolution of CO_{2}

Convective dissolution, one of the main mechanisms for geological storage of CO_{2}, occurs when supercritical or gas CO_{2} dissolves partially into an aqueous solution, thus triggering downward convection of the denser CO_{2}-enriched liquid. Chemical reaction in the liquid can greatly enhance the process. Here, experimental measurements of convective flow inside a cylinder filled with a sodium hydroxide (NaOH) solution show that the plume's velocity can be increased tenfold as compared to a situation with no NaOH. This tremendous effect is predicted by a model with no adjusting parameters.

Elastic fingering in a rotating Hele-Shaw cell

We consider the steady-state fingering instability of an elastic membrane separating two fluids of different density under external pressure in a rotating Hele-Shaw cell. Both inextensible and highly extensible membranes are considered, and the role of membrane tension is detailed in each case. Both systems exhibit a centrifugally driven Rayleigh-Taylor-like instability when the density of the inner fluid exceeds that of the outer one, and this instability competes with the restoring forces arising from curvature and tension, thereby setting the finger scale. Numerical continuation is used to compute not only strongly nonlinear primary finger states up to the point of self-contact, but also secondary branches of mixed modes and circumferentially localized folds as a function of the rotation rate and the externally imposed pressure. Both reflection-symmetric and symmetry-broken chiral states are computed. The results are presented in the form of bifurcation diagrams. The ratio of system scale to the natural length scale is found to determine the ordering of the primary bifurcations from the unperturbed circle state as well as the solution profiles and onset of secondary bifurcations.

Buoyancy-Driven Chemohydrodynamic Patterns in A + B → Oscillator Two-Layer Stratifications

Chemohydrodynamic patterns due to the interplay of buoyancy-driven instabilities and reaction-diffusion patterns are studied experimentally in a vertical quasi-two-dimensional reactor in which two solutions A and B containing separate reactants of the oscillating Belousov-Zhabotinsky system are placed in contact along a horizontal contact line where excitable or oscillating dynamics can develop. Different types of buoyancy-driven instabilities are selectively induced in the reactive zone depending on the initial density jump between the two layers, controlled here by the bromate salt concentration. Starting from a less dense solution above a denser one, two possible differential diffusion instabilities are triggered depending on whether the fast diffusing sulfuric acid is in the upper or lower solution. Specifically, when the solution containing malonic acid and sulfuric acid is stratified above the one containing the slow-diffusing bromate salt, a diffusive layer convection (DLC) instability is observed with localized convective rolls around the interface. In that case, the reaction-diffusion wave patterns remain localized above the initial contact line, scarcely affected by the flow. If, on the contrary, sulfuric acid diffuses upward because it is initially dissolved in the lower layer, then a double-diffusion (DD) convective mode develops. This triggers fingers across the interface that mix the reactants such that oscillatory dynamics and rippled waves develop throughout the whole reactor. If the denser solution is put on top of the other one, then a fast developing Rayleigh-Taylor (RT) instability induces fast mixing of all reactants such that classical reaction-diffusion waves develop later on in the convectively mixed solutions.

Linear stability analysis and nonlinear simulations of convective dissolution in an inclined porous layer between impermeable surfaces

Convective dissolution can occur in porous media when a given solute dissolves in a host layer from above and increases the density of the host solution. Buoyancy-driven fingering can then develop, which increases the transfer flux of the solute. We investigate here numerically the properties of this convective dissolution when the porous host layer is inclined by an angle θ relative to the horizontal direction. We consider an incompressible flow in porous media governed by Darcy's law, driven by density gradients associated with the concentration of the dissolving solute. The model problem focuses on the case of a very long (infinite) tilted porous layer limited by two parallel impermeable surfaces. A linear stability analysis and nonlinear simulations are performed using the Boussinesq approximation. A vorticity-stream function formulation is adopted to solve the two-dimensional hydrodynamic field through the finite element method. We find that the inclination of the interface decreases the growth rate of the instability and the range of unstable wavenumbers, delaying or even suppressing the onset of the fingering instability. Moreover, it introduces a drift velocity on the perturbations, which is characterized here in both the linear stability analysis and the nonlinear simulations.

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.

A bottom-up approach to construct or deconstruct a fluid instability

Fluid instabilities have been the subject of study for a long time. Despite all the extensive knowledge, they still constitute a serious challenge for many industrial applications. Here, we experimentally consider an interface between two fluids with different viscosities and analyze their relative displacement. We designed the contents of each fluid in such a way that a chemical reaction takes place at the interface and use this reaction to suppress or induce a fingering instability at will. This process describes a road map to control viscous fingering instabilities in more complex systems via interfacial chemical reactions.

Chemo-hydrodynamic pulsations in simple batch A + B → C systems

Spatio-temporal oscillations can be induced under batch conditions with ubiquitous bimolecular reactions in the absence of any nonlinear chemical feedback, thanks to an active interplay between the chemical process and chemically driven hydrodynamic flows. When two reactants A and B, initially separated in space, react upon diffusive contact, they can power convective flows by inducing a localized variation of surface tension and density at the mixing interface. These flows feedback with the reaction-diffusion dynamics, bearing damped or sustained spatio-temporal oscillations of the concentrations and flow field. By means of numerical simulations, we detail the mechanism underlying these chemohydrodynamic oscillations and classify the main dynamical scenarios in the relevant space drawn by parameters ΔM and ΔR, which rule the surface tension- and buoyancy-driven contributions to convection, respectively. The reactor height is found to play a critical role in the control of the dynamics. The analysis reveals the intimate nature of these oscillatory phenomena and the hierarchy among the different phenomena at play: oscillations are essentially hydrodynamic and the chemical process features the localized trigger for Marangoni flows unstable toward oscillatory instabilities. The characteristic size of Marangoni convective rolls mainly determines the critical conditions and properties of the oscillations, which can be further tuned or suppressed by the buoyancy competition. We finally discuss the possible experimental implementation of such a class of chemo-hydrodynamic oscillator and its implications in fundamental and applied terms.

Switching Modes of Mixing Due to an Adjustable Gap in a Continuous-Flow Microreactor

Microreactors are an important development in chemical engineering since the pharmaceutical industry needs flexible production rather than a large amount of product yield. The size of the microreactor may be so small that it requires the development of non-mechanical methods for reagent mixing. In this paper, we propose the design of a continuous-flow microreactor in the form of a narrow cell with a variable gap. By tuning the gap width in time and space, one can control the reaction rate and regulate the product yield. We show that the governing equation for the fluid flow can be reduced to the Darcy equation with permeability varying in space and time. As a test reaction, we consider the neutralization of nitric acid with sodium hydroxide resulting in the solutal convection in the presence of gravity. We show numerically that the prototyping spatially-distributed relief of the reactor walls can successfully separate the incoming and outgoing flows of reagents, control the mixing intensity, increase or decrease the product yield. We demonstrate also the dynamic control of the reactor efficiency via real-time local changes in the gap width.

Spatial analog of the two-frequency torus breakup in a nonlinear system of reactive miscible fluids

We present a theoretical study on pattern formation occurring in miscible fluids reacting by a second-order reaction A+B→C in a vertical Hele-Shaw cell under constant gravity. We have recently reported that the concentration-dependent diffusion of species coupled with a frontal neutralization reaction can produce a multilayer system where low-density depleted zones could be embedded between the denser layers. This leads to the excitation of chemoconvective modes spatially separated from each other by a motionless fluid. In this Rapid Communication, we show that the layers can interact via a diffusion mechanism. Since diffusively coupled instabilities initially have different wavelengths, this causes a long-wave modulation of one pattern by another. We have developed a mathematical model which includes a system of reaction-diffusion-convection equations. The linear stability of a transient base state is studied by calculating the growth rate of the Lyapunov exponent for each unstable layer. Numerical simulations supported by phase portrait reconstruction and Fourier spectra calculation have revealed that nonlinear dynamics consistently passes through (i) a perfect spatially periodic system of chemoconvective cells, (ii) a quasiperiodic system of the same cells, and (iii) a disordered fingering structure. We show that in this system, the coordinate codirected to the reaction front paradoxically plays the role of time, time itself acts as a bifurcation parameter, and a complete spatial analog of the two-frequency torus breakup is observed.

Interface Fingering Instability Triggered by a Density-Coupled Oscillatory Chemical Reaction via Precipitation

A density fingering hydrodynamic instability is triggered by a chemical reaction at the interface between two fluids. The density instability is controlled by the density gradient between both solutions, while the excitability of the bubble-free Belousov-Zhabotinsky-1,4-cyclohexanedione (BZ-CHD) oscillatory chemical reaction controls the importance of the chemistry in the system. Both parameters are thoroughly analyzed, and the mechanism underlying the instability is unveiled. The experimental observations lead us to modify the existing and accepted models for the BZ-CHD reaction within this context. The important role played by precipitation is considered in this context and included into the model. The modified kinetic model once coupled with fluid dynamics along with the precipitation mechanism was able to reproduce the experimental observations.

Intrinsic concentration cycles and high ion fluxes in self-assembled precipitate membranes

Concentration cycles are important for bonding of basic molecular building components at the emergence of life. We demonstrate that oscillations occur intrinsically in precipitation reactions when coupled with fluid mechanics in self-assembled precipitate membranes, such as at submarine hydrothermal vents. We show that, moreover, the flow of ions across one pore in such a prebiotic membrane is larger than that across one ion channel in a modern biological cell membrane, suggesting that proto-biological processes could be sustained by osmotic flow in a less efficient prebiotic environment. Oscillations in nanoreactors at hydrothermal vents may be just right for these warm little pores to be the cradle of life.

Experimental methods for visualization of hydrodynamic instability caused by the neutralization reaction in a miscible two-layer system

This paper focuses on experimental investigations of the spatio-temporal distributions of fluid velocity and temperature and the concentration of reagents and reaction products. We study concentration-dependent diffusion (CDD) convection driven by the neutralization reaction in a two-layer miscible system in a vertical Hele-Shaw cell using the original experimental complex. A comprehensive understanding of the physical mechanisms of convective motion and instabilities requires employing various experimental methods simultaneously. The proposed experimental complex provides simultaneous visualization and facilitates identification of the location of the reaction front, which is of importance to the study of its characteristics.

Making a Simple A+B→C Reaction Oscillate by Coupling to Hydrodynamic Effect

We present a new mechanism through which chemical oscillations and waves can be induced in batch conditions with a simple A+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.

Unpredictable Dynamics of Polymeric Reacting Flow by Comparison between Pre- and Post-Reaction Fluid Properties: Hydrodynamics Involving Molecular Diagnosis via ATR-FTIR Spectroscopy

In reacting flows, changes in fluid properties induced by the chemical reaction can alter the flow dynamics. Generally, these changes in fluid properties are evaluated by comparison between their pre- and post-reaction properties. If a fluid property such as viscosity decreases between pre- and post-reaction, we expect a decrease in viscosity to occur in the reacting flow. However, this study demonstrates a reacting polymeric liquid flow where a remarkable increase in the viscoelasticity temporally occurs despite the viscosity slightly decreasing after the reaction. We elucidated the underlying reaction mechanism, which involves a structural change in the side functional group (carboxyl) in polyacrylamide at ultrahigh molecular weights ( M_w > 10⁶) with ultralow concentrations ([polymer] < 1 wt %) by using ATR-FTIR spectroscopy. This study demonstrates the existence of a reacting flow in which examination of microscopic molecular structure is required to understand the macroscopic flow dynamics. The findings will be valuable not only for industrial application such as reactor designs and rheology control but also for opening a new research area: chemically reacting flow involving the diagnosis of molecule structure.

Surface-Tension-Driven Dynamic Contact Line in Microgravity

We study the effect of Marangoni flow on a dynamic contact line formed by a propagating reaction front and a liquid-air interface. The self-sustained iodate-arsenous acid reaction maintains the production of the weakly surface active iodine leading to an unbalanced surface force along the tip of the reaction front. The experiments, performed in microgravity to exclude the contribution of buoyancy, reveal that the fluid flow generated by the surface tension gradient is localized to the contact line. The penetration depth of the surface stress is measured as 1-2 mm; therefore, with greater fluid height the liquid advancement on the upper surface does not lead to enhanced mixing in the bulk. Because the propagation velocity of the reactive interface remains at that of reaction-diffusion, the leading edge consists of two straight lines; a tilted segment connects the contact line on the surface with the vertical segment on bottom. Modeling calculations of the reaction-diffusion-advection system in three dimensions reconstruct the experimental observations and along with the experiments validate a model based on geometric spreading. According to the calculated flow field, the direction of significant fluid flow follows the concentration gradients and hence coincides with the propagation of the reaction front, allowing only negligible transverse flow in the upper fluid layer.

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.

Magnetically-Actuated Mixing and Merging of Acid-Base Micro-Droplets on Open Surfaces: Preliminary Study

We present the mixing and merging of two reactive droplets on top of an open surface. A mobile droplet (1.0 M HCl solution + iron oxide particles) is magnetically-actuated to merge with a sessile droplet (1.0 M NaOH + phenolphthalein). The heat from the exothermic reaction is detected by a thermocouple. We vary the droplet volume (1, 5 and 10 μL), the magnet speed (1.86, 2.79, 3.72 and 4.65 mm/s) and the iron oxide concentration (0.010, 0.020 and 0.040 g/mL) to study their influences on the mixing time, peak temperature and cooling time. The sampled recording of these processes are provided as ^{supplementary files}. We observe the following trends. First, the lower volume of droplet and higher speed of magnet lead to shorter mixing time. Second, the peak temperature increases and cooling time decreases at the increasing speed of magnet. Third, the peak temperature is similar for bigger droplets, and they take longer to cool down. Finally, we also discuss the limitations of this preliminary study and propose improvements. These observations could be used to improve the sensitivity of the open chamber system in measuring the exothermic reaction of biological samples.

Shock-wave-like structures induced by an exothermic neutralization reaction in miscible fluids

We report shock-wave-like structures that are strikingly different from previously observed fingering instabilities, which occur in a two-layer system of miscible fluids reacting by a second-order reaction A+B→S in a vertical Hele-Shaw cell. While the traditional analysis expects the occurrence of a diffusion-controlled convection, we show both experimentally and theoretically that the exothermic neutralization reaction can also trigger a wave with a perfectly planar front and nearly discontinuous change in density across the front. This wave propagates fast compared with the characteristic diffusion times and separates the motionless fluid and the area with anomalously intense convective mixing. We explain its mechanism and introduce a new dimensionless parameter, which allows to predict the appearance of such a pattern in other systems. Moreover, we show that our governing equations, taken in the inviscid limit, are formally analogous to well-known shallow-water equations and adiabatic gas flow equations. Based on this analogy, we define the critical velocity for the onset of the shock wave which is found to be in the perfect agreement with the experiments.

Lateral movements in Rayleigh-Taylor instabilities due to frontiers. Numerical analysis

Numerical simulations were performed for Rayleigh-Taylor (RT) hydrodynamic instabilities when a frontier is present. The frontier formed by the interface between two fluids prevents the free movement of the fingers created by the instability. As a consequence, transversal movements at the rear of the fingers are observed in this area. These movements produce collapse of the fingers (two or more fingers join in one finger) or oscillations in the case that there is no collapse. The transversal velocity of the fingers, the amplitude of the oscillations, and the wave number of the RT instabilities as a function of the Rayleigh number (Ra) were studied near the frontier. We verified numerically that in classical RT instabilities, without a frontier, these lateral movements do not occur; only with a physical frontier, the transversal displacements of the fingers appear. The transverse displacement velocity and the initial wave number increase with Ra. This leads to the collapse of the fingers, diminishing the wave number of the instabilities at the interface. Instead, no significant changes in the amplitude of the oscillations are observed modifying Ra. The numerical results are independent of the type or origin of the frontier (gas-liquid, liquid-liquid, or solid-liquid). The numerical results are in good agreement with the experimental results reported by Binda et al. [Chaos 28, 013107 (2018)]. Based on these results, it was possible to determine the cause of the transverse displacements, which had not been explained until now.

Dissipative structures: From reaction-diffusion to chemo-hydrodynamic patterns

The interplay of reaction and diffusion processes can trigger localized spatiotemporal patterns when two solutions containing separate reactants A and B of an oscillating reaction are put in contact. Using the Brusselator, a classical model for chemical oscillations, we show numerically that localized waves and Turing patterns as well as reaction-diffusion (RD) patterns due to an interaction between these two kinds of modes can develop in time around the reactive contact zone depending on the initial concentration of reactants and diffusion coefficients of the intermediate species locally produced. We further explore the possible hydrodynamic destabilization of an initially buoyantly stable stratification of such an A + B → oscillator system, when the chemical reaction provides a buoyant periodic forcing via localized density changes. Guided by the properties of the underlying RD dynamics, we predict new chemo-hydrodynamic instabilities on the basis of the dynamic density profiles which are here varying with the concentration of one of the intermediate species of the oscillator. Nonlinear simulations of the related reaction-diffusion-convection equations show how the active coupling between the localized oscillatory kinetics and buoyancy-driven convection can induce pulsatile convective fingering and pulsatile plumes as well as rising or sinking Turing spots, depending on the initial concentration of the reactants and their contribution to the density.

Chlorine dioxide-induced and Congo red-inhibited Marangoni effect on the chlorite-trithionate reaction front

Hydrodynamic flows can exert multiple effects on an exothermal autocatalytic reaction, such as buoyancy and the Marangoni convection, which can change the structure and velocity of chemical waves. Here we report that in the chlorite-trithionate reaction, the production and consumption of chlorine dioxide can induce and inhibit Marangoni flow, respectively, leading to different chemo-hydrodynamic patterns. The horizontal propagation of a reaction-diffusion-convection front was investigated with the upper surface open to the air. The Marangoni convection, induced by gaseous chlorine dioxide on the surface, produced from chlorite disproportionation after the proton autocatalysis, has the same effect as the heat convection. When the Marangoni effect is removed by the reaction of chlorine dioxide with the Congo red (CR) indicator, an oscillatory propagation of the front tip is observed under suitable conditions. Replacing CR with bromophenol blue (BPB) distinctly enhanced the floating, resulting in multiple vortexes, owing to the coexistence between BPB and chlorine dioxide. Using the incompressible Navier-Stokes equations coupled with reaction-diffusion and heat conduction equations, we numerically obtain various experimental scenarios of front instability for the exothermic autocatalytic reaction coupled with buoyancy-driven convection and Marangoni convection.

Chemical control of dissolution-driven convection in partially miscible systems: nonlinear simulations and experiments

Numerical simulations combined with experimental results from two laboratory-scale model systems show how to control convective dissolution by chemical reactions.

Chemo-hydrodynamic patterns in porous media

Chemical reactions can interplay with hydrodynamic flows to generate chemo-hydrodynamic instabilities affecting the spatio-temporal evolution of the concentration of the chemicals. We review here such instabilities for porous media flows. We describe the influence of chemical reactions on viscous fingering, buoyancy-driven fingering in miscible systems, convective dissolution as well as precipitation patterns. Implications for environmental systems are discussed.This article is part of the themed issue 'Energy and the subsurface'.

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.

Localized stationary and traveling reaction-diffusion patterns in a two-layer A+B→ oscillator system

When two solutions containing separate reactants A and B of an oscillating reaction are put in contact in a gel, localized spatiotemporal patterns can develop around the contact zone thanks to the interplay of reaction and diffusion processes. Using the Brusselator model, we explore analytically the deployment in space and time of the bifurcation diagram of such an A+B→ oscillator system. We provide a parametric classification of possible instabilities as a function of the ratio of the initial reactant concentrations and of the reaction intermediate species diffusion coefficients. Related one-dimensional reaction-diffusion dynamics are studied numerically. We find that the system can spatially localize waves and Turing patterns as well as induce more complex dynamics such as zigzag spatiotemporal waves when Hopf and Turing modes interact.

One-Directional Fluidic Flow Induced by Chemical Wave Propagation in a Microchannel

A one-directional flow induced by chemical wave propagation was investigated to understand the origin of its dynamic flow. A cylindrical injection port was connected with a straight propagation channel; the chemical wave was initiated at the injection port. Chemical waves propagated with a constant velocity irrespective of the channel width, indicating that the dynamics of the chemical waves were governed by a geometry-independent interplay between the chemical reaction and diffusion. In contrast, the velocity of the one-directional flow was dependent on the channel width. Furthermore, enlargement of the injection port volume increased the flow velocity and volume flux. These results imply that the one-directional flow in the microchannel is due to a hydrodynamic effect induced in the injection port. Spectroscopic analysis of a pH indicator revealed the simultaneous behavior between the pH increase near the injection port and the one-directional flow. Hence, we can conclude that the one-directional flow in the microchannel with chemical wave propagation was caused by a proton consumption reaction in the injection port, probably through liquid volume expansion by the reaction products and the reaction heat. It is a characteristic feature of the present system that the hydrodynamic flow started from the chemical wave initiation point and not the propagation wavefront, as observed for previous systems.

Convection-Induced Fingering Fronts in the Chlorite-Trithionate Reaction

Based upon a former study, the chlorite-trithionate reaction can avoid the side reactions arising from the well-known alkaline decomposition of polythionates, making it a suitable candidate for investigating spatial front instabilities in a reaction-diffusion-convection system. In this work, the chlorite-trithionate reaction was investigated in a Hele-Shaw cell, in which fingering patterns were observed over a wide range of reactant concentrations. A significant density increment crossing the propagating front indicates that the fingering pattern is generated as a consequence of the buoyancy-driven instability due to the density changes of solute when the gap thickness is less than 4 mm. The velocity of the steepest descent in the propagating front depends almost linearly on the gap thickness but displays a saturation-like profile on the trithionate concentration as well as a maximum on the chlorite concentration. Numerical simulation using the Stokes-Brinkman Equation coupled to the reaction-diffusion processes, including hydrogen ion autocatalysis and consumption, reproduces the observed fingering fronts.

Development of tip-splitting and side-branching patterns in elastic fingering

Elastic fingering supplements the already interesting features of the traditional viscous fingering phenomena in Hele-Shaw cells with the consideration that the two-fluid separating boundary behaves like an elastic membrane. Sophisticated numerical simulations have shown that under maximum viscosity contrast the resulting patterned shapes can exhibit either finger tip-splitting or side-branching events. In this work, we employ a perturbative mode-coupling scheme to get important insights into the onset of these pattern formation processes. This is done at lowest nonlinear order and by considering the interplay of just three specific Fourier modes: a fundamental mode n and its harmonics 2n and 3n. Our approach further allows the construction of a morphology diagram for the system in a wide range of the parameter space without requiring expensive numerical simulations. The emerging interfacial patterns are conveniently described in terms of only two dimensionless controlling quantities: the rigidity fraction C and a parameter Γ that measures the relative strength between elastic and viscous effects. Visualization of the rigidity field for the various pattern-forming structures supports the idea of an elastic weakening mechanism that facilitates finger growth in regions of reduced interfacial bending rigidity.

The efficiency of driving chemical reactions by a physical non-equilibrium is kinetically controlled

A model system illustrates how the coupling efficiency of a physical non-equilibrium to a chemical reaction is affected by the relative timescales of the respective kinetics.

Facile multi-dimensional profiling of chemical gradients at the millimetre scale

Tomography with a LCD/LED screen as the source of light enables multi-dimensional reconstruction of non-homogeneous samples.

Cross-diffusion-driven hydrodynamic instabilities in a double-layer system: General classification and nonlinear simulations

Cross diffusion, whereby a flux of a given species entrains the diffusive transport of another species, can trigger buoyancy-driven hydrodynamic instabilities at the interface of initially stable stratifications. Starting from a simple three-component case, we introduce a theoretical framework to classify cross-diffusion-induced hydrodynamic phenomena in two-layer stratifications under the action of the gravitational field. A cross-diffusion-convection (CDC) model is derived by coupling the fickian diffusion formalism to Stokes equations. In order to isolate the effect of cross-diffusion in the convective destabilization of a double-layer system, we impose a starting concentration jump of one species in the bottom layer while the other one is homogeneously distributed over the spatial domain. This initial configuration avoids the concurrence of classic Rayleigh-Taylor or differential-diffusion convective instabilities, and it also allows us to activate selectively the cross-diffusion feedback by which the heterogeneously distributed species influences the diffusive transport of the other species. We identify two types of hydrodynamic modes [the negative cross-diffusion-driven convection (NCC) and the positive cross-diffusion-driven convection (PCC)], corresponding to the sign of this operational cross-diffusion term. By studying the space-time density profiles along the gravitational axis we obtain analytical conditions for the onset of convection in terms of two important parameters only: the operational cross-diffusivity and the buoyancy ratio, giving the relative contribution of the two species to the global density. The general classification of the NCC and PCC scenarios in such parameter space is supported by numerical simulations of the fully nonlinear CDC problem. The resulting convective patterns compare favorably with recent experimental results found in microemulsion systems.

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.

Concentration-dependent diffusion instability in reactive miscible fluids

We report on chemoconvective pattern formation phenomena observed in a two-layer system of miscible fluids filling a vertical Hele-Shaw cell. We show both experimentally and theoretically that the concentration-dependent diffusion coupled with frontal acid-base neutralization can give rise to the formation of a local unstable zone low in density, resulting in a perfectly regular cell-type convective pattern. The described effect gives an example of yet another powerful mechanism which allows the reaction-diffusion processes to govern the flow of reacting fluids under gravity conditions.

Do dissolving objects converge to a universal shape?

Surprisingly, macroscopic objects such as melting ice cubes and growing stalactites approach nonintuitive geometric ideals. Here we investigate the shape of dissolving cylinders in a large volume of water. The cylinders are oriented vertically and consist of amorphous glucose or poly(ethylene glycol). The dissolution causes density differences in the surrounding fluid, which induce gravity-driven convection downward along the object. The resulting concentration gradient shapes the cylinder according to fast dissolution at the tip and slow dissolution at the base. The contour of the object approaches a power law of the form z ∝ R(2), where z is the vertical distance from the tip and R is the corresponding radius. We suggest that this paraboloidal shape is the geometric attractor for the dissolution of noncrystalline objects in the presence of gravity.

Buoyancy-driven instabilities around miscible A+B→C reaction fronts: a general classification

Upon contact between miscible solutions of reactants A and B along a horizontal interface in the gravity field, various buoyancy-driven instabilities can develop when an A+B→C reaction takes place and the density varies with the concentrations of the various chemicals. To classify the possible convective instability scenarios, we analyze the spatial dependence of the large time asymptotic density profiles as a function of the key parameters of the problem, which are the ratios of diffusion coefficients and of solutal expansion coefficients of species A, B, and C. We find that 62 different density profiles can develop in the reactive problem, whereas only 6 of them can be obtained in the nonreactive one.

Cross-diffusion-induced convective patterns in microemulsion systems

Cross-diffusion phenomena are experimentally and theoretically shown to be able to induce convective fingering around an initially stable stratification of two microemulsions with different compositions.

Geochemistry of silicate-rich rocks can curtail spreading of carbon dioxide in subsurface aquifers

Pools of carbon dioxide are found in natural geological accumulations and in engineered storage in saline aquifers. It has been thought that once this CO2 dissolves in the formation water, making it denser, convection streams will transport it efficiently to depth, but this may not be so. Here, we assess theoretically and experimentally the impact of natural chemical reactions between the dissolved CO2 and the rock formation on the convection streams in the subsurface. We show that, while in carbonate rocks the streaming of dissolved carbon dioxide persists, the chemical interactions in silicate-rich rocks may curb this transport drastically and even inhibit it altogether. These results challenge our view of carbon sequestration and dissolution rates in the subsurface, suggesting that pooled carbon dioxide may remain in the shallower regions of the formation for hundreds to thousands of years. The deeper regions of the reservoir can remain virtually carbon free.

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.