Fingering of chemical fronts in porous media

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.

Autocatalytic flow chemistry

Autocatalysis is a crucial process of nonequilibrium self-organization in nature and is assumed to play a role in the origin of life. The essential dynamical phenomena of an autocatalytic reaction network are bistability and the development of propagating front when combined with diffusion. The presence of bulk fluid motion may widen the range of emerging behavior in those systems. Many aspects of the dynamics of autocatalytic reactions in a continuous flow have already been studied, especially the shape and dynamics of the chemical front and the influence of the chemical reactions on hydrodynamic instabilities. This paper aims to provide experimental evidence of bistability and related dynamical phenomena, such as excitability and oscillations in autocatalytic reactions performed in a tubular flow reactor, where the flow is laminar and advection is the dominating transport process. We show that the linear residence time ramp may result in the simultaneous appearance of different dynamic states along the length of the pipe. Therefore, long tubular reactors offer a unique opportunity to quickly explore the dynamics of reaction networks. These findings enhance our understanding of nonlinear flow chemistry and its role in natural pattern formation.

Stability of a layered reactive channel flow

We analyse the linear stability of a reactive plane Poiseuille flow, where a reactant fluid A overlies another reactant B in a layered fashion within a two-dimensional channel. Both reactants are miscible and have the same viscosity, while upon reaction, they produce either a less or more-viscous product fluid C . The reaction kinetics is of simple A + B → C type, and the production of C occurs across the initial contact line of reactants A and B in a mixed zone of small and finite width. All three fluids have the same density. We demonstrate the effects of various controlling parameters such as the log-mobility ratio, Damköhler number, Schmidt number, Reynolds number, position and thicknesses of the reactive zone on the stability characteristics. We show that a tiny viscosity stratification by the reaction destabilizes the flow at a moderate (10–1000) and even at low Reynolds numbers (0.01–1). The maximum growth occurs for shorter waves than for the Tollmien–Schlichting eigenmode, and the ranges of unstable wavenumbers are wider than that known for non-reactive channel flow systems. In most cases, the instability occurs due to the overlap of the critical layer with the viscosity-stratified layer. Surprisingly for some parameters, it is observed that the reaction can make σ M decrease with increasing Reynolds number.

Buoyancy-Induced Convection Driven by Frontal Polymerization

In this Letter, we study the interaction between a self-sustaining exothermic reaction front propagating in a direction perpendicular to that of gravity and the buoyancy-driven convective flow during frontal polymerization (FP) of a low-viscosity monomer resin. As the polymerization front transforms the liquid monomer into the solid polymer, the large thermal gradients associated with the propagating front sustain a natural convection of the fluid ahead of the front. The fluid convection in turn affects the reaction-diffusion (RD) dynamics and the shape of the front. Detailed multiphysics numerical analyses and particle image velocimetry experiments reveal this coupling between natural convection and frontal polymerization. The frontal Rayleigh (Ra) number affects the magnitude of the velocity field and the inclination of the front. A higher Ra number drives instability during FP, leading to the observation of thermal-chemical patterns with tunable wavelengths and magnitudes.

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.

Interaction of Pure Marangoni Convection with a Propagating Reactive Interface under Microgravity

A reactive interface in the form of an autocatalytic reaction front propagating in a bulk phase can generate a dynamic contact line upon reaching the free surface when a surface tension gradient builds up due to the change in chemical composition. Experiments in microgravity evidence the existence of a self-organized autonomous and localized coupling of a pure Marangoni flow along the surface with the reaction in the bulk. This dynamics results from the advancement of the contact line at the surface that acts as a moving source of the reaction, leading to the reorientation of the front propagation. Microgravity conditions allow one to isolate the transition regime during which the surface propagation is enhanced, whereas diffusion remains the main mode of transport in the bulk with negligible convective mixing, a regime typically concealed on Earth because of buoyancy-driven convection.

Control of viscous fingering by nanoparticles

A substantial viscosity increase by the addition of a low dose of nanoparticles to the base fluids can well influence the dynamics of viscous fingering. There is a lack of detailed theoretical studies that address the effect of the presence of nanoparticles on unstable miscible displacements. In this study, the impact of nonreactive nanoparticle presence on the stability and subsequent mixing of an originally unstable binary system is examined using linear stability analysis (LSA) and pseudospectral-based direct numerical simulations (DNS). We have parametrized the role of both nondepositing and depositing nanoparticles on the stability of miscible displacements using the developed static and dynamic parametric analyses. Our results show that nanoparticles have the potential to weaken the instabilities of an originally unstable system. Our LSA and DNS results also reveal that nondepositing nanoparticles can be used to fully stabilize an originally unstable front while depositing particles may act as temporary stabilizers whose influence diminishes in the course of time. In addition, we explain the existing inconsistencies concerning the effect of the nanoparticle diffusion coefficient on the dynamics of the system. This study provides a basis for further research on the application of nanoparticles for control of viscosity-driven instabilities.

Convection induced by thermal gradients on thin reaction fronts

We present a thin front model for the propagation of chemical reaction fronts in liquids inside a Hele-Shaw cell or porous media. In this model we take into account density gradients due to thermal and compositional changes across a thin interface. The front separating reacted from unreacted fluids evolves following an eikonal relation between the normal speed and the curvature. We carry out a linear stability analysis of convectionless flat fronts confined in a two-dimensional rectangular domain. We find that all fronts are stable to perturbations of short wavelength, but they become unstable for some wavelengths depending on the values of compositional and thermal gradients. If the effects of these gradients oppose each other, we observe a range of wavelengths that make the flat front unstable. Numerical solutions of the nonlinear model show curved fronts of steady shape with convection propagating faster than flat fronts. Exothermic fronts increase the temperature of the fluid as they propagate through the domain. This increment in temperature decreases with increasing speed.

Marangoni flow traveling with reaction fronts: Eikonal approximation

Chemical reaction fronts traveling in liquids generate gradients of surface tension leading to fluid motion. This surface tension driven flow, known as Marangoni flow, modifies the shape and the speed of the reaction front. We model the front propagation using the Eikonal relation between curvature and normal speed of the front, resulting in a front evolution equation that couples to the fluid velocity. The sharp discontinuity between the reactants and products leads to a surface tension gradient proportional to a delta function. The Stokes equations with the surface tension gradient as part of the boundary conditions provide the corresponding fluid velocity field. Considering stress free boundaries at the bottom of the liquid layer, we find an analytical solution for the fluid vorticity leading to the velocity field. Solving numerically the appropriate no-slip boundary condition, we gain insights into the role of the boundary condition at the bottom layer. We compare our results with results from two other models for front propagation: the deterministic Kardar-Parisi-Zhang equation and a reaction-diffusion equation with cubic autocatalysis, finding good agreement for small differences in surface tension.

MRI of chemical reactions and processes

As magnetic resonance imaging (MRI) can spatially resolve a wealth of molecular information available from nuclear magnetic resonance (NMR), it is able to non-invasively visualise the composition, properties and reactions of a broad range of spatially-heterogeneous molecular systems. Hence, MRI is increasingly finding applications in the study of chemical reactions and processes in a diverse range of environments and technologies. This article will explain the basic principles of MRI and how it can be used to visualise chemical composition and molecular properties, providing an overview of the variety of information available. Examples are drawn from the disciplines of chemistry, chemical engineering, environmental science, physics, electrochemistry and materials science. The review introduces a range of techniques used to produce image contrast, along with the chemical and molecular insight accessible through them. Methods for mapping the distribution of chemical species, using chemical shift imaging or spatially-resolved spectroscopy, are reviewed, as well as methods for visualising physical state, temperature, current density, flow velocities and molecular diffusion. Strategies for imaging materials with low signal intensity, such as those containing gases or low sensitivity nuclei, using compressed sensing, para-hydrogen or polarisation transfer, are discussed. Systems are presented which encapsulate the diversity of chemical and physical parameters observable by MRI, including one- and two-phase flow in porous media, chemical pattern formation, phase transformations and hydrodynamic (fingering) instabilities. Lastly, the emerging area of electrochemical MRI is discussed, with studies presented on the visualisation of electrochemical deposition and dissolution processes during corrosion and the operation of batteries, supercapacitors and fuel cells.

Eigenvector centrality for geometric and topological characterization of porous media

Solving flow and transport through complex geometries such as porous media is computationally difficult. Such calculations usually involve the solution of a system of discretized differential equations, which could lead to extreme computational cost depending on the size of the domain and the accuracy of the model. Geometric simplifications like pore networks, where the pores are represented by nodes and the pore throats by edges connecting pores, have been proposed. These models, despite their ability to preserve the connectivity of the medium, have difficulties capturing preferential paths (high velocity) and stagnation zones (low velocity), as they do not consider the specific relations between nodes. Nonetheless, network theory approaches, where a complex network is a graph, can help to simplify and better understand fluid dynamics and transport in porous media. Here we present an alternative method to address these issues based on eigenvector centrality, which has been corrected to overcome the centralization problem and modified to introduce a bias in the centrality distribution along a particular direction to address the flow and transport anisotropy in porous media. We compare the model predictions with millifluidic transport experiments, which shows that, albeit simple, this technique is computationally efficient and has potential for predicting preferential paths and stagnation zones for flow and transport in porous media. We propose to use the eigenvector centrality probability distribution to compute the entropy as an indicator of the "mixing capacity" of the system.

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'.

Thermodynamic coarsening arrested by viscous fingering in partially miscible binary mixtures

We study the evolution of binary mixtures far from equilibrium, and show that the interplay between phase separation and hydrodynamic instability can arrest the Ostwald ripening process characteristic of nonflowing mixtures. We describe a model binary system in a Hele-Shaw cell using a phase-field approach with explicit dependence of both phase fraction and mass concentration. When the viscosity contrast between phases is large (as is the case for gas and liquid phases), an imposed background flow leads to viscous fingering, phase branching, and pinch off. This dynamic flow disorder limits phase growth and arrests thermodynamic coarsening. As a result, the system reaches a regime of statistical steady state in which the binary mixture is permanently driven away from equilibrium.

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.

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.

Interface evolution during radial miscible viscous fingering

We study experimentally the miscible radial displacement of a more viscous fluid by a less viscous one in a horizontal Hele-Shaw cell. For the range of tested injection rates and viscosity ratios we observe two regimes for the evolution of the fluid-fluid interface. At early times the interface length increases linearly with time, which is typical of the Saffman-Taylor instability for this radial configuration. However, as time increases, the interface growth slows down and scales as ∼t(1/2), as one expects in a stable displacement, indicating that the overall flow instability has shut down. Surprisingly, the crossover time between these two regimes decreases with increasing injection rate. We propose a theoretical model that is consistent with our experimental results, explains the origin of this second regime, and predicts the scaling of the crossover time with injection rate and the mobility ratio. The key determinant of the observed scalings is the competition between advection and diffusion time scales at the displacement front, suggesting that our analysis can be applied to other interfacial-evolution problems such as the Rayleigh-Bénard-Darcy instability.

Spontaneous formation of complex structures made from elastic membranes in an aluminum-hydroxide-carbonate system

A popular playground for studying chemo-hydrodynamic patterns and instabilities is chemical gardens, also known as silicate gardens. In these systems, complex structures spontaneously form, driven by buoyant forces and either osmotic or mechanical pumps. Here, we report on systems that differ somewhat from classical chemical gardens in that the membranes are much more deformable and soluble. These properties lead to structures that self-construct and evolve in new ways. For example, they exhibit the formation of chemical balloons, a new growth mechanism for tubes, and also the homologous shrinking of these tubes. The stretching mechanism for the membranes is probably different than for other systems by involving membrane "self-healing." Other unusual properties are osmosis that sometimes occurs out of the structure and also small plumes that flow away from the structure, sometimes upwards, and sometimes downwards. Mathematical models are given that explain some of the observed phenomena.

Three-dimensional convection-driven fronts of the exothermic chlorite-tetrathionate reaction

Horizontally propagating autocatalytic reaction fronts in fluids are often accompanied by convective motion in the presence of gravity. We experimentally and numerically investigate the stable complex three-dimensional pattern arising in the exothermic chlorite-tetrathionate reaction as a result of the antagonistic thermal and solutal contribution to the density change. By particle image velocimetry measurements, we construct the flow field that stabilizes the front structure. The calculations applied for incompressible fluids using the empirical rate-law model reproduce the experimental observations with good agreement.

Impact of pressure, salt concentration, and temperature on the convective dissolution of carbon dioxide in aqueous solutions

The convective dissolution of carbon dioxide (CO2) in salted water is theoretically studied to determine how parameters such as CO2 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 CO2 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 CO2 pressure, or decreasing salt concentration or temperature destabilizes the system with regard to convection, leading to a faster dissolution of CO2 into salted water.

Convective dynamics of traveling autocatalytic fronts in a modulated gravity field

Modulation of the gravity field, spanning from the hyper-gravity to micro-gravity of a parabolic flight, reveals the contribution of Marangoni flow in a propagating reaction front with an open air–liquid interface.

Mixing and reaction kinetics in porous media: an experimental pore scale quantification

We propose a new experimental set up to characterize mixing and reactive transport in porous media with a high spatial resolution at the pore scale. The analogous porous medium consists of a Hele-Shaw cell containing a single layer of cylindrical solid grains built by soft lithography. On the one hand, the measurement of the local, intrapore, conservative concentration field is done using a fluorescent tracer. On the other hand, considering a fast bimolecular reaction A + B → C occurring as A displaces B, we quantify the rate of product formation from the spatially resolved measurement of the pore scale reaction rate, using a chemiluminescent reaction. The setup provides a dynamical measurement of the local concentration field over 3 orders of magnitude and allows investigating a wide range of Péclet and Damköhler numbers by varying the flow rate within the cell and the local reaction rate. We use it to study the kinetics of the reaction front between A and B. While the advection-dispersion (Fickian) theory, applied at the continuum scale, predicts a scaling of the cumulative mass of product C as MC ∝ √t, the experiments exhibit two distinct regimes in which the produced mass MC evolves faster than the Fickian behavior. In both regimes the front rate of product formation is controlled by the geometry of the mixing interface between the reactants. Initially, the invading solute is organized in stretched lamellae and the reaction is limited by mass transfer across the lamella boundaries. At longer times the front evolves into a second regime where lamellae coalesce and form a mixing zone whose temporal evolution controls the rate of product formation. In this second regime, the produced mass of C is directly proportional to the volume of the mixing zone defined from conservative species. This interesting property is indeed verified from a comparison of the reactive and conservative data. Hence, for both regimes, the direct measurement of the spatial distribution of the pore scale reaction rate and conservative component concentration is shown to be crucial to understanding the departure from the Fickian scaling as well as quantifying the basic mechanisms that govern the mixing and reaction dynamics at the pore scale.

Synergetic fluid mixing from viscous fingering and alternating injection

We study mixing of two fluids of different viscosity in a microfluidic channel or porous medium. We show that the synergetic action of alternating injection and viscous fingering leads to a dramatic increase in mixing efficiency at high Péclet numbers. Based on observations from high-resolution simulations, we develop a theoretical model of mixing efficiency that combines a hyperbolic mixing model of the channelized region ahead and a mixing-dissipation model of the pseudosteady region behind. Our macroscopic model quantitatively reproduces the evolution of the average degree of mixing along the flow direction and can be used as a design tool to optimize mixing from viscous fingering in a microfluidic channel.

Interface dynamics of immiscible two-phase lattice-gas cellular automata: a model with random dynamic scatterers and quenched disorder in two dimensions

We use a lattice gas cellular automata model in the presence of random dynamic scattering sites and quenched disorder in the two-phase immiscible model with the aim of producing an interface dynamics similar to that observed in Hele-Shaw cells. The dynamics of the interface is studied as one fluid displaces the other in a clean lattice and in a lattice with quenched disorder. For the clean system, if the fluid with a lower viscosity displaces the other, we show that the model exhibits the Saffman-Taylor instability phenomenon, whose features are in very good agreement with those observed in real (viscous) fluids. In the system with quenched disorder, we obtain estimates for the growth and roughening exponents of the interface width in two cases: viscosity-matched fluids and the case of unstable interface. The first case is shown to be in the same universality class of the random deposition model with surface relaxation. Moreover, while the early-time dynamics of the interface behaves similarly, viscous fingers develop in the second case with the subsequent production of bubbles in the context of a complex dynamics. We also identify the Hurst exponent of the subdiffusive fractional Brownian motion associated with the interface, from which we derive its fractal dimension and the universality classes related to a percolation process.

CO2 sequestration in a radial Hele-Shaw cell via an interfacial chemical reaction

In this manuscript, experimental data for the displacement of a finite volume of aqueous Ca(OH)(2) using CO(2) gas in a radial Hele-Shaw cell will be presented. This chemical reaction is known to generate CaCO(3) precipitate along the gas-liquid interface and we seek to understand the influence of the reactive process on fluid displacement. The reactive experiment is compared with the non-reactive case to determine if there are any measurable differences between the two in the range of parameters: CO(2) pressures (1%-10% of an atmosphere measured in gage pressure), liquid volumes (either 50 or 70 μl), and Ca(OH)(2) concentrations (0, 10, or 20 mM) studied. Analysis is performed by measuring the displacing fluid area A(gas) and total fluid area A(tot) to determine several quantities (gas expansion rate, quasi-equilibrium film rate and value, and presence of fingering instability) used to distinguish the experiments. In general there appears to be little effect of the chemical reaction on most of the measured quantities.

Influence of temperature on linear stability in buoyancy-driven fingering of reaction-diffusion fronts

A vertical Hele-Shaw cell was used to study the influence of temperature on Rayleigh-Taylor instabilities on reaction-diffusion fronts. The propagation of the chemical front can thus be observed, and experimental results can be obtained via image treatment. A chemical front produced by the coupling between molecular diffusion and the auto-catalysis of the chlorite-tetrathionate reaction, descends through the cell, consuming the reactants below while the product is formed above. Buoyancy-driven instabilities are formed due to the density difference between reactants and products, and the front takes a fingering pattern, whose growth rate has temperature dependence. In this study, the effect of temperature on the linear regime of the instability (that is, when the effects of such instability start to appear) was analyzed. To measure the instability, Fourier transform analysis is performed, in order to obtain the different wave numbers and their power as a function of time. Thus, the growth rate for each wave number and the most unstable wave number is obtained for each of the temperatures under study. Based on repeated experiments, a decrease in the growth rate for the most unstable wave number can be observed with the increase of temperature.

CHEMO-hydrodynamic coupling between forced advection in porous media and self-sustained chemical waves

Autocatalytic reaction fronts between two reacting species in the absence of fluid flow, propagate as solitary waves. The coupling between autocatalytic reaction front and forced simple hydrodynamic flows leads to stationary fronts whose velocity and shape depend on the underlying flow field. We address the issue of the chemico-hydrodynamic coupling between forced advection in porous media and self-sustained chemical waves. Towards that purpose, we perform experiments over a wide range of flow velocities with the well characterized iodate arsenious acid and chlorite-tetrathionate autocatalytic reactions in transparent packed beads porous media. The characteristics of these porous media such as their porosity, tortuosity, and hydrodynamics dispersion are determined. In a pack of beads, the characteristic pore size and the velocity field correlation length are of the order of the bead size. In order to address these two length scales separately, we perform lattice Boltzmann numerical simulations in a stochastic porous medium, which takes into account the log-normal permeability distribution and the spatial correlation of the permeability field. In both experiments and numerical simulations, we observe stationary fronts propagating at a constant velocity with an almost constant front width. Experiments without flow in packed bead porous media with different bead sizes show that the front propagation depends on the tortuous nature of diffusion in the pore space. We observe microscopic effects when the pores are of the size of the chemical front width. We address both supportive co-current and adverse flows with respect to the direction of propagation of the chemical reaction. For supportive flows, experiments and simulations allow observation of two flow regimes. For adverse flow, we observe upstream and downstream front motion as well as static front behaviors over a wide range of flow rates. In order to understand better these observed static state fronts, flow experiments around a single obstacle were used to delineate the range of steady state behavior. A model using the "eikonal thin front limit" explains the observed steady states.

Horizontally propagating three-dimensional chemo-hydrodynamic patterns in the chlorite-tetrathionate reaction

Planar reaction fronts resulting from the coupling of exothermic autocatalytic reactions and transport processes can be deformed by convection in the presence of gravity field. We have experimentally investigated how buoyancy affects the spatiotemporal pattern formation at various solution thicknesses in three-dimensional medium. In the chlorite-tetrathionate reaction, a stable structure propagating horizontally with constant velocity and geometry develops when appropriately thick solutions are studied. Both the horizontal and the vertical projections of the resulting three-dimensional structures are quantitatively characterized: the smooth leading edge of the front is independent of the solution thickness and the structured trailing edge ends in a center cusp with a constant angle.

Convection and reaction in a diffusive boundary layer in a porous medium: nonlinear dynamics

We study numerically the nonlinear interactions between chemical reaction and convective fingering in a diffusive boundary layer in a porous medium. The reaction enhances stability by consuming a solute that is unstably distributed in a gravitational field. We show that chemical reaction profoundly changes the dynamics of the system, by introducing a steady state, shortening the evolution time, and altering the spatial patterns of velocity and concentration of solute. In the presence of weak reaction, finger growth and merger occur effectively, driving strong convective currents in a thick layer of solute. However, as the reaction becomes stronger, finger growth is inhibited, tip-splitting is enhanced and the layer of solute becomes much thinner. Convection enhances the mass flux of solute consumed by reaction in the boundary layer but has a diminishing effect as reaction strength increases. This nonlinear behavior has striking differences to the density fingering of traveling reaction fronts, for which stronger chemical kinetics result in more effective finger merger owing to an increase in the speed of the front. In a boundary layer, a strong stabilizing effect of reaction can maintain a long-term state of convection in isolated fingers of wavelength comparable to that at onset of instability.

Introduction to the focus issue: chemo-hydrodynamic patterns and instabilities

Pattern forming instabilities are often encountered in a wide variety of natural phenomena and technological applications, from self-organization in biological and chemical systems to oceanic or atmospheric circulation and heat and mass transport processes in engineering systems. Spatio-temporal structures are ubiquitous in hydrodynamics where numerous different convective instabilities generate pattern formation and complex spatiotemporal dynamics, which have been much studied both theoretically and experimentally. In parallel, reaction-diffusion processes provide another large family of pattern forming instabilities and spatio-temporal structures which have been analyzed for several decades. At the intersection of these two fields, "chemo-hydrodynamic patterns and instabilities" resulting from the coupling of hydrodynamic and reaction-diffusion processes have been less studied. The exploration of the new instability and symmetry-breaking scenarios emerging from the interplay between chemical reactions, diffusion and convective motions is a burgeoning field in which numerous exciting problems have emerged during the last few years. These problems range from fingering instabilities of chemical fronts and reactive fluid-fluid interfaces to the dynamics of reaction-diffusion systems in the presence of chaotic mixing. The questions to be addressed are at the interface of hydrodynamics, chemistry, engineering or environmental sciences to name a few and, as a consequence, they have started to draw the attention of several communities including both the nonlinear chemical dynamics and hydrodynamics communities. The collection of papers gathered in this Focus Issue sheds new light on a wide range of phenomena in the general area of chemo-hydrodynamic patterns and instabilities. It also serves as an overview of the current research and state-of-the-art in the field.

The heads and tails of buoyant autocatalytic balls

Buoyancy produced by autocatalytic reaction fronts can produce fluid flows that advect the front position, giving rise to interesting feedback between chemical and hydrodynamic effects. In this paper, we numerically investigate the evolution of autocatalytic iodate-arsenous acid reaction fronts initialized in spherical configurations. Deformation of these "autocatalytic balls" is driven by buoyancy produced by the reaction. In our simulations, we have found that depending on the initial ball radius, the reaction front will develop in one of three different ways. In an intermediate range of ball size, the flow can evolve much like an autocatalytic plume: the ball develops a reacting head and tail that is akin to the head and conduit of an autocatalytic plume. In the limit of large autocatalytic balls, however, growth of a reacting tail is suppressed and the resemblance to plumes disappears. Conversely, very small balls of product solution fail to initiate sustained fronts and eventually disappear.

Marangoni-driven convection around exothermic autocatalytic chemical fronts in free-surface solution layers

Gradients of concentration and temperature across exothermic chemical fronts propagating in free-surface solution layers can initiate Marangoni-driven convection. We investigate here the dynamics arising from such a coupling between exothermic autocatalytic reactions, diffusion, and Marangoni-driven flows. To this end, we numerically integrate the incompressible Navier-Stokes equations coupled through the tangential stress balance to evolution equations for the concentration of the autocatalytic product and for the temperature. A solutal and a thermal Marangoni numbers measure the coupling between reaction-diffusion processes and surface-driven convection. In the case of an isothermal system, the asymptotic dynamics is characterized by a steady fluid vortex traveling at a constant speed with the front, deforming and accelerating it [L. Rongy and A. De Wit, J. Chem. Phys. 124, 164705 (2006)]. We analyze here the influence of the reaction exothermicity on the dynamics of the system in both cases of cooperative and competitive solutal and thermal effects. We show that exothermic fronts can exhibit new unsteady spatio-temporal dynamics when the solutal and thermal effects are antagonistic. The influence of the solutal and thermal Marangoni numbers, of the Lewis number (ratio of thermal diffusivity over molecular diffusivity), and of the height of the liquid layer on the spatio-temporal front evolution are investigated.

Hot spots in density fingering of exothermic autocatalytic chemical fronts

Measurements of two-dimensional (2D) temperature fields are performed by an interferometric method during density fingering of the autocatalytic chlorite-tetrathionate reaction in a Hele-Shaw cell. These measures confirm that, because of heat losses through the glass walls of the reactor, the temperature profile across the front is a pulse rather than a front. Moreover, the full 2D temperature field shows the presence in the reactive zone of hot spots where the temperature exceeds the maximum temperature measured in a stable planar front. We investigate here experimentally the increase of temperature in the hot spots when the composition of the reactants is varied to increase the exothermicity of the reaction. We back up these experimental observations by nonlinear simulations of a reaction-diffusion-convection model which show that the maximum temperature reached in the system depends on the intensity of convection.

Buoyancy-driven convection may switch between reactive states in three-dimensional chemical waves

Traveling waves in an extended reactor, whose width cannot be neglected, represent a three-dimensional (3D) reaction-diffusion-convection system. We investigate the effects of buoyancy-driven convection in such a setting. The 3D waves traveled through horizontal layers of the iodate-arsenous acid (IAA) reaction solution containing excess of arsenous acid. The depth of the reaction solution was the examined parameter. An increase in the intensity of buoyancy-driven flow caused an increase of the traveling wave velocities. Convection distorted the front of the chemical waves. For layers deeper than h>13 mm, heat release became smaller than heat production causing the emergence of Rayleigh-Bénard convection cells. At the interface, a dependency of wave shape on solution depth was observed. For h<7 mm, the waves adopted a stable V-like shape, while for h>13 mm a parabolic shape dominated. For 7<h<13 mm, both shapes were realized with the same probability. Finally, an intermittent switch between stoichiometric regimes is observed as an unexpected effect of the buoyancy-driven convection. The switch is expressed by iodine enrichment in the product. Hence, the experiments demonstrate that the buoyancy-driven convective flow can cause long-lived, but nevertheless transient, changes in the chemical composition by inducing a local transition between different regimes of the IAA reaction.

Spatiotemporal chaos in the dynamics of buoyantly and diffusively unstable chemical fronts

Nonlinear dynamics resulting from the interplay between diffusive and buoyancy-driven Rayleigh-Taylor (RT) instabilities of autocatalytic traveling fronts are analyzed numerically for various values of the relevant parameters. These are the Rayleigh numbers of the reactant A and autocatalytic product B solutions as well as the ratio D=D(B)/D(A) between the diffusion coefficients of the two key chemical species. The interplay between the coarsening dynamics characteristic of the RT instability and the constant short wavelength modulation of the diffusive instability can lead in some regimes to complex dynamics dominated by irregular succession of birth and death of fingers. By using spectral entropy measurements, we characterize the transition between order and spatial disorder in this system. The analysis of the power spectrum and autocorrelation function, moreover, identifies similarities between the various spatial patterns. The contribution of the diffusive instability to the complex dynamics is discussed.

Quantifying mixing in viscously unstable porous media flows

Viscous fingering is a well-known hydrodynamic instability that sets in when a less viscous fluid displaces a more viscous fluid. When the two fluids are miscible, viscous fingering introduces disorder in the velocity field and exerts a fundamental control on the rate at which the fluids mix. Here we analyze the characteristic signature of the mixing process in viscously unstable flows, by means of high-resolution numerical simulations using a computational strategy that is stable for arbitrary viscosity ratios. We propose a reduced-order model of mixing, which, in the spirit of turbulence modeling and in contrast with previous approaches, recognizes the fundamental role played by the mechanical dissipation rate. The proposed model captures the nontrivial interplay between channeling and creation of interfacial area as a result of viscous fingering.

Onset of convection in a porous medium in the presence of chemical reaction

Using scaling, we show that the stability of a buoyant boundary layer in a porous medium in the presence of a first-order chemical reaction is fully determined by the nondimensional number Da/Ra(2)=k(r)aDϕμ(2)/(kΔρ(0)g)(2), where Da=k(r)aL(Z)(2)/k(r)aL(Z)(2)(Dϕ) is the Damköhler number and Ra=kΔρ(0)gL(Z)/kΔρ(0)gL(Z)(μDϕ) is the solutal Rayleigh number. The time for onset of convection is shown to increase with rising Da/Ra(2). Above a critical Da/DaRa(2)≈2×10(-3) Ra(2)≈2×10(-3), no convection occurs as reaction stabilizes the diffusive layer at a finite thickness. This thickness decreases with increasing Da/Ra(2), becoming zero at Da/Ra(2)≈O(1). As applied to CO(2) geostorage, our results suggest distinct regimes for CO(2) transport in saline aquifers.

Suppression of viscous fluid fingering: a piecewise-constant injection process

The injection of a fluid into another of larger viscosity in a Hele-Shaw cell usually results in the formation of highly branched patterns. Despite the richness of these structures, in many practical situations such convoluted shapes are quite undesirable. In this Brief Report, we propose an efficient and easily reproducible way to restrain these instabilities based on a simple piecewise-constant pumping protocol. It results in a reduction in the size of the viscous fingers by one order of magnitude.

Stability of convective patterns in reaction fronts: a comparison of three models

Autocatalytic reaction fronts generate density gradients that may lead to convection. Fronts propagating in vertical tubes can be flat, axisymmetric, or nonaxisymmetric, depending on the diameter of the tube. In this paper, we study the transitions to convection as well as the stability of different types of fronts. We analyze the stability of the convective reaction fronts using three different models for front propagation. We use a model based on a reaction-diffusion-advection equation coupled to the Navier-Stokes equations to account for fluid flow. A second model replaces the reaction-diffusion equation with a thin front approximation where the front speed depends on the front curvature. We also introduce a new low-dimensional model based on a finite mode truncation. This model allows a complete analysis of all stable and unstable fronts.

Hydrodynamic instability in the transport of miscible reactive slices through porous media

Miscible displacement of a slice of a pollutant solution by a carrier solution in homogeneous porous media is examined. The carrier solution reacts with the slice solution to generate a chemical product, and as a result of differences in viscosities of the three species, a hydrodynamic instability known as viscous fingering is observed. The dynamics of the instability and the rate of consumption as well as spread of the pollutant are examined through numerical simulations. The study shows that the rate of consumption of the pollutant is the highest when the chemical product is the most or the least viscous solution in the system. It was also found that displacements in which the pollutant viscosity is the smallest or the largest of all three species lead to the widest spread of the pollutant in the porous media. In addition, the most complex finger structures are observed when the carrier solution has the smallest or largest viscosity in the flow. Furthermore, a mechanism of channeling whereby the carrier is able to break through the slice, therefore bypassing the pollutant, is found in cases where the chemical product is more viscous than the carrier solution. The dynamics of the displacement are analyzed and physical interpretations of their development are presented.