Influence of thermal effects on buoyancy-driven convection around autocatalytic chemical fronts propagating horizontally

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.

Front instabilities in the presence of convection due to thermal and compositional gradients

Reaction fronts separate fluids of different densities due to thermal and compositional gradients that may lead to convection. The stability of convectionless flat fronts propagating in the vertical direction depends not only on fluid properties but also in the dynamics of a front evolution equation. In this work, we analyze fronts described by the Kuramoto-Sivashinsky (KS) equation coupled to hydrodynamics. Without density gradients, the KS equation has a flat front solution that is unstable to perturbations of long wavelengths. Buoyancy enhances this instability if a fluid of lower density is underneath a denser fluid. In the reverse situation, with the denser fluid underneath, the front can be stabilized with appropriate thermal and compositional gradients. However, in this situation, a different instability develops for large enough thermal gradients. We also solve numerically the nonlinear KS equation coupled to the Navier-Stokes equations to analyze the front propagation in two-dimensional rectangular domains. As convection takes place, the reaction front curves, increasing its velocity.

Marangoni- vs. buoyancy-driven flows: competition for spatio-temporal oscillations in A + B → C systems

The emergence of self-organized behaviors such as spatio-temporal oscillations is well-known for complex reactions involving nonlinear chemical or thermal feedback. Recently, it was shown that local oscillations of the chemical species concentration can be induced under isothermal batch conditions for simple bimolecular A + B → C reactions, provided they are actively coupled with hydrodynamics. When two reactants A and B, initially separated in space, react upon diffusive contact, damped spatio-temporal oscillations could develop when the surface tension increases sufficiently in the reaction zone. Additionally, if the density decreases, the coupling of both surface tension- and buoyancy-driven contributions to the flow can further sustain this oscillatory instability. Here, we investigate the opposite case of a reaction inducing a localized decrease in surface tension and an increase in density in the reacting zones. In this case, the competition arising from the two antagonistic flows is needed to create oscillatory dynamics, i.e., no oscillations are observed for pure chemically driven Marangoni flows. We study numerically these scenarios in a 2-dimensional system and show how they are controlled by the following key parameters: (i) ΔM and ΔR governing the surface tension and density variation during the reaction, respectively, (ii) the layer thickness of the system, and (iii) its lateral length. This work is a further step toward inducing and controlling chemical oscillations in simple reactions.

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.

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.

Propagating fronts in fluids with solutal feedback

We numerically study the propagation of reacting fronts in a shallow and horizontal layer of fluid with solutal feedback and in the presence of a thermally driven flow field of counterrotating convection rolls. We solve the Boussinesq equations along with a reaction-convection-diffusion equation for the concentration field where the products of the nonlinear autocatalytic reaction are less dense than the reactants. For small values of the solutal Rayleigh number the characteristic fluid velocity scales linearly, and the front velocity and mixing length scale quadratically, with increasing solutal Rayleigh number. For small solutal Rayleigh numbers the front geometry is described by a curve that is nearly antisymmetric about the horizontal midplane. For large values of the solutal Rayleigh number the characteristic fluid velocity, the front velocity, and the mixing length exhibit square-root scaling and the front shape collapses onto an asymmetric self-similar curve. In the presence of counterrotating convection rolls, the mixing length decreases while the front velocity increases. The complexity of the front geometry increases when both the solutal and convective contributions are significant and the dynamics can exhibit chemical oscillations in time for certain parameter values. Last, we discuss the spatiotemporal features of the complex fronts that form over a range of solutal and thermal driving.

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.

Influence of reaction-induced convection on quorum sensing in enzyme-loaded agarose beads

In theory, groups of enzyme-loaded particles producing an acid or base may show complex behavior including dynamical quorum sensing, the appearance of synchronized oscillations above a critical number or density of particles. Here, experiments were performed with the enzyme urease loaded into mm-sized agarose beads and placed in a solution of urea, resulting in an increase in pH. This behavior was found to be dependent upon the number of beads present in the array; however, reaction-induced convection occurred and plumes of high pH developed that extended to the walls of the reactor. The convection resulted in the motion of the mm-sized particles and conversion of the solution to high pH. Simulations in a simple model of the beads demonstrated the suppression of dynamical quorum sensing in the presence of flow.

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.

Surface tension- and buoyancy-driven flows across horizontally propagating chemical fronts

Chemical reactions can interplay with hydrodynamic flows to generate various complex phenomena. Because of their relevance in many research areas, chemically-induced hydrodynamic flows have attracted increasing attention in the last decades. In this context, we propose to give a review of the past and recent theoretical and experimental works which have considered the interaction of such flows with chemical fronts, i.e. reactive interfaces, formed between miscible solutions. We focus in particular on the influence of surface tension- (Marangoni) and buoyancy-driven flows on the dynamics of chemical fronts propagating horizontally in the gravity field.

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.

Control of chemical chaos through medium viscosity in a batch ferroin-catalysed Belousov–Zhabotinsky reaction

A macroscopic parameter, such as medium viscosity, can be used to fine tune chemical chaos in a reaction–diffusion–convection system.

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.

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.

Relation between shape of liquid-gas interface and evolution of buoyantly unstable three-dimensional chemical fronts

Buoyantly unstable 3D chemical fronts were seen traveling through an iodate-arsenous acid reaction solution. The experiments were performed in channel reactors with rectangular cross sections, where the top of the reaction solution was in contact with air. A concave or convex meniscus was pinned to reactor lateral walls. Influence of the meniscus shape on front development was investigated. For the concave meniscus, an asymptotic shape of fronts holding negative curvature was observed. On the other hand, fronts propagating in the solution with the convex meniscus kept only positive curvature. Those fronts were also a bit faster than fronts propagating in the solution with the concave meniscus. A relation between the meniscus shape, flow distribution, velocity, and shape is discussed.

Segmented waves in a reaction-diffusion-convection system

The interaction of traveling waves, with both Marangoni and buoyancy driven flows, can generate an extraordinary rich array of patterns ranging from stationary structures to chaotic waves. However, the inherent complexity of reaction-diffusion-convection (RDC) systems makes the explanation of the patterning mechanisms very difficult, both numerically and experimentally. In this paper, we describe the appearance of segmented waves in a shallow layer of an excitable Belousov-Zhabotinsky solution. The segmentation process was found to be dependent both on the depth of the solution and on the excitability of the reaction. We caught the essential features of the system through a RDC model, where the chemical waves were coupled both with surface and bulk fluid motions and we found that by varying the excitability of the reaction, and in turn the wavelength of the chemical fronts, it is possible to create a sort of hydrodynamic resonance structures (corridors), which are responsible for the segmentation process.

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.

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.

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.