Autocatalytic Fronts Research Articles

Effect of radial advection on autocatalytic reaction-diffusion fronts.

The reaction-diffusion-advection properties of autocatalytic fronts are studied both theoretically and experimentally in the case where the autocatalytic species is injected radially into the reactant at a constant flow rate. The theoretical part analyzes both polar and spherical cases. At long times or equivalently large radius from the injection point, the well-known properties of one-dimensional reaction-diffusion autocatalytic fronts are logically recovered as the influence of the advection field decreases radially. At earlier times however, the radial advection impacts the dynamics of the front. We characterize numerically the influence in this transient regime of the injection flow rate and of the ratio of initial concentration of reactant and autocatalytic product on the position of the front, the reaction rate and the amount of product generated. We confirm experimentally the theoretical predictions in polar geometries using the autocatalytic chlorite-tetrathionate reaction.

Spatiotemporal Regulation of Hydrogel Actuators by Autocatalytic Reaction Networks (Adv. Mater. 13/2022)

Hydrogel Actuators Biochemical circuits regulate the movement of living organisms. In article number 2106816, Sergey N. Semenov and co-workers use a synthetic chemical reaction network based on thiols to regulate hydrogel actuators. The signal inducing the actuation is propagated by the autocatalytic front of the thiols. It can jump from one actuator to another or be initiated by the chemical circuit with preprogrammed delay.

Spatiotemporal Regulation of Hydrogel Actuators by Autocatalytic Reaction Networks.

Regulating hydrogel actuators with chemical reaction networks is instrumental for constructing life-inspired smart materials. Herein, hydrogel actuators are engineered that are regulated by the autocatalytic front of thiols. The actuators consist of two layers. The first layer, which is regular polyacrylamide hydrogel, is in a strained conformation. The second layer, which is polyacrylamide hydrogel with disulfide crosslinks, maintains strain in the first layer. When thiols released by the autocatalytic front reduce disulfide crosslinks, the hydrogel actuates by releasing the mechanical strain in the first layer. The autocatalytic front is sustained by the reaction network, which uses thiouronium salts, disulfides of β-aminothiols, and maleimide as starting components. The gradual actuation by the autocatalytic front enables movements such as gradual unrolling, screwing, and sequential closing of "fingers." This actuation also allows the transmission of chemical signals in a relay fashion and the conversion of a chemical signal to an electrical signal. Locations and times of spontaneous initiation of autocatalytic fronts can be preprogrammed in the spatial distribution of the reactants in the hydrogel. To approach the functionality of living matter, the actuators triggered by an autocatalytic front can be integrated into smart materials regulated by chemical circuits.

Autocatalytic Cycles in a Copper-Catalyzed Azide-Alkyne Cycloaddition Reaction.

This work describes the autocatalytic copper-catalyzed azide-alkyne cycloaddition (CuAAC) reaction between tripropargylamine and 2-azidoethanol in the presence of Cu(II) salts. The product of this reaction, tris-(hydroxyethyltriazolylmethyl)amine (N(C3N3)3), accelerates the cycloaddition reaction (and thus its own production) by two mechanisms: (i) by coordinating Cu(II) and promoting its reduction to Cu(I) and (ii) by enhancing the catalytic reactivity of Cu(I) in the cycloaddition step. Because of the cooperation of these two processes, a rate enhancement of >400× is observed over the course of the reaction. The kinetic profile of the autocatalysis can be controlled by using different azides and alkynes or ligands (e.g., ammonia) for Cu(II). When carried out in a layer of 1% agarose gel, and initiated by ascorbic acid, this autocatalytic reaction generates an autocatalytic front. This system is prototypical of autocatalytic reactions where the formation of a product, which acts as a ligand for a catalytic metal ion, enhances the production and activity of the catalyst.

Spatiotemporal control of DNA-based chemical reaction network via electrochemical activation in microfluidics

In recent years, DNA computing frameworks have been developed to create dynamical systems which can be used for information processing. These emerging synthetic biochemistry tools can be leveraged to gain a better understanding of fundamental biology but can also be implemented in biosensors and unconventional computing. Most of the efforts so far have focused on changing the topologies of DNA molecular networks or scaling them up. Several issues have thus received little attention and remain to be solved to turn them into real life technologies. In particular, the ability to easily interact in real-time with them is a key requirement. The previous attempts to achieve this aim have used microfluidic approaches, such as valves, which are cumbersome. We show that electrochemical triggering using DNA-grafted micro-fabricated gold electrodes can be used to give instructions to these molecular systems. We demonstrate how this approach can be used to release at specific times and locations DNA- based instructions. In particular, we trigger reaction-diffusion autocatalytic fronts in microfluidic channels. While limited by the stability of the Au-S bond, this easy to implement, versatile and scalable technique can be used in any biology laboratory to provide new ways to interact with any DNA-based computing framework.

Self-Assembly of Charged Nanoparticles by an Autocatalytic Reaction Front.

In this work we present that aggregation of charged and pH sensitive nanoparticles can be spatiotemporally controlled by an autonomous way using the chlorite-tetrathionate autocatalytic front, where the front regulates the electrostatic interaction between nanoparticles due to protonation of the capping (carboxylate-terminated) ligand. We found that the aggregation and sedimentation of nanoparticles in liquid phase with the effect of reversible binding of the autocatalyst (H(+)) play important roles in changing the front stability (mixing length) and the velocity of the front in both cases when the fronts propagate upward and downward. Calculation of interparticle interactions (electrostatic and van der Waals) with the measurement of front velocity revealed that the aggregation process occurs fast (within a few seconds) at the front position.

Convective dynamics of traveling autocatalytic fronts in a modulated gravity field.

When traveling in thin solution layers, autocatalytic chemical fronts may be deformed and accelerated by convective currents that develop because of density and surface tension gradients related to concentration and thermal gradients across the front. On earth, both buoyancy and Marangoni related flows can act in solution layers open to the air while only buoyancy effects operate in covered liquid layers. The respective effects of density and surface tension induced convective motions are analysed here by studying experimentally the propagation of autocatalytic fronts in uncovered and covered liquid layers during parabolic flights in which the gravity field is modulated periodically. We find that the velocity and deformation of the front are increased during hyper-gravity phases and reduced in the micro-gravity phase. The experimental results compare well with numerical simulations of the evolution of the concentration of the autocatalytic product coupled to the flow field dynamics described by Navier-Stokes equations.

Influence of a simple magnetic bar on buoyancy-driven fingering of traveling autocatalytic reaction fronts

Magnetic fields have been shown experimentally to modify convective dynamics developing around traveling chemical fronts in presence of unfavorable density gradients. To understand the conditions in which such magnetic fields affect autocatalytic fronts, we study theoretically the influence of a simple magnetic bar on buoyancy-driven density fingering of a chemical front by numerical simulations of a reaction-diffusion-convection system. The model couples Darcy's law for the flow velocity to an evolution equation for the concentration of the autocatalytic product, which affects both the density of the solution and the magnetic force. The solutions of both products and reactants are assumed to be diamagnetic (i.e., negative magnetic susceptibility) and the magnetization is oriented perpendicularly to the plane in which the front travels. We show that, when aligned along the direction of front propagation, the magnetic force is able to suppress or enhance the convective instability depending on the value of the magnetic Rayleigh number of the problem. If the magnetic force is oriented transversely to the front propagation direction, tilted drifting convective patterns are obtained.

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.

Dynamics due to combined buoyancy- and Marangoni-driven convective flows around autocatalytic fronts

A reaction-diffusion-convection (RDC) model is introduced to analyze convective dynamics around horizontally traveling fronts due to combined buoyancy- and surface tension-driven flows in vertical solution layers open to the air. This isothermal model provides a means for a comparative study of the two effects via tuning two key parameters: the solutal Rayleigh number Ra, which rules the buoyancy influence, and the solutal Marangoni number Ma governing the intensity of surface effects at the interface between the reacting solution and air. The autocatalytic front dynamics is probed by varying the relative importance of Ra and Ma and the resulting RDC patterns are quantitatively characterized through the analysis of the front mixing length and the topology of the velocity field. Steady asymptotic regimes are found when the bulk and the surface contributions to fluid motions act cooperatively i.e. when Ra and Ma have the same sign. Complex dynamics may arise when these numbers are of opposite signs and the two effects thus compete in an antagonistic configuration. Typically, spatiotemporal oscillations are observed as the control parameters are set in the region (Ra < 0, Ma > 0). Periodic behaviour develops here even in the absence of any double-diffusive interplay, which in previous literature was identified as a possible source of complexity.

Stability of exothermic autocatalytic fronts with regard to buoyancy-driven instabilities in presence of heat losses

Across traveling autocatalytic fronts, density differences due to composition and temperature changes can lead to buoyancy-driven hydrodynamic instabilities deforming the front by convective motions. We study here the influence of heat losses through the walls of the reactor on the stability of such exothermic fronts in the gravity field. The stability domain is computed numerically in a parameter space spanned by the solutal R c and thermal R T Rayleigh numbers of the problem for various values of the Newton's coefficient α quantifying the intensity of heat losses.

Buoyancy-driven convection around exothermic autocatalytic chemical fronts traveling horizontally in covered thin solution layers

Spatial variations of concentrations and temperature across exothermic chemical fronts can initiate buoyancy-driven convection. We investigate here theoretically the spatiotemporal dynamics arising from such a coupling between exothermic autocatalytic reactions, diffusion, and buoyancy-driven flows when an exothermic autocatalytic front travels perpendicularly to the gravity field in a thin solution layer. To do so, we numerically integrate the incompressible Stokes equations coupled to evolution equations for the concentration of the autocatalytic product and temperature through buoyancy terms proportional to, respectively, a solutal R(C) and a thermal R(T) Rayleigh number. We show that exothermic fronts can exhibit new types of dynamics in the presence of convection with regard to the isothermal system. In the cooperative case (R(C) and R(T) are of the same sign), the dynamics asymptotes to one vortex surrounding, deforming, and accelerating the front much like in the isothermal case. However, persistent local stratification of heavy zones over light ones can be observed at the rear of the front when the Lewis number Le (ratio of thermal diffusivity over molecular diffusion) is nonzero. When the solutal and thermal effects are antagonistic (R(C) and R(T) of opposite sign), temporal oscillations of the concentration, temperature, and velocity fields can, in some cases, be observed in a reference frame moving with the front. The various dynamical regimes are discussed as a function of R(C), R(T), and Le.

Comparison of the oxidation of two porphyrin complexes by bromate with respect to wave propagation

The kinetics and mechanism of the oxidation of iron(III) protoporphyrin IX (hemin) and iron(III) meso-tetra(4-sulfonatophenyl)porphine (TPPSFe) were compared. Both reactions exhibit sigmoid-shaped time dependence of the absorbance of the porphyrin complexes during the course of the reaction. The oxidation of hemin was proved to be an autocatalytic reaction resembling very much the autocatalytic subset reaction of the BZ oscillators. The oxidation of TPPSFe was proved not to be autocatalytic. It consists of consecutive reaction steps without any feedback. One of the intermediates absorbing in the same region as TPPSFe could be identified as an iron(V)-oxo complex of TPPS. According to the kinetic differences, single autocatalytic wave fronts could be observed in the autocatalytic hemin–bromate reaction if hemin was fixed and stabilized in silica gels, while no wave formation appeared in the TPPSFe-bromate system. The kinetic differences are in agreement with the different structures of the two porphyrin complexes.

Influence of heat losses on nonlinear fingering dynamics of exothermic autocatalytic fronts

Across traveling exothermic autocatalytic fronts, a density jump can be observed due to changes in composition and temperature. These density changes are prone to induce buoyancy-driven convection around the front when the propagation takes place in absence of gel within the gravity field. Most recent experiments devoted to studying such reaction-diffusion-convection dynamics are performed in Hele–Shaw cells, two glass plates separated by a thin gap width and filled by the chemical solutions. We investigate here the influence of heat losses through the walls of such cells on the nonlinear fingering dynamics of exothermic autocatalytic fronts propagating in vertical Hele–Shaw cells. We show that these heat losses increase tip splittings and modify the properties of the flow field. A comparison of the differences between the dynamics in reactors with respectively insulating and conducting walls is performed as a function of the Lewis number L e , the Newton cooling coefficient α quantifying the amplitude of heat losses and the width of the system. We find that tip splitting is enhanced for intermediate values of α while coarsening towards one single finger dominates for insulated systems or large values of α leading to situations equivalent to isothermal ones.

Front propagation in the bromate–sulfite–ferrocyanide–aluminum (III) system: Autocatalytic front in a buffer system

We study the propagation of pH fronts in a narrow, pseudo-one-dimensional strip of gel containing bromate, sulfite, ferrocyanide and aluminum ions. The front propagation speed v decreases with [ Al 3+] as 1 / v = 1 / v 0 + c [ Al 3 + ] , where c is a constant. We determine the diffusion coefficients of protons and ferricyanide ions and find that Al(OH) 3 loaded in agarose or acrylamide gels binds protons reversibly, thereby slowing the propagating fronts without significantly affecting the diffusion of ferricyanide ions. We present a model that qualitatively reproduces the experimental behavior, and we suggest some general principles governing autocatalytic fronts in buffered systems.

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

The spatiotemporal dynamics of vertical autocatalytic fronts traveling horizontally in thin solution layers closed to the air can be influenced by buoyancy-driven convection induced by density gradients across the front. We perform here a combined experimental and theoretical study of the competition between solutal and thermal effects on such convection. Experimentally, we focus on the antagonistic chlorite-tetrathionate reaction for which solutal and thermal contributions to the density jump across the front have opposite signs. We show that in isothermal conditions the heavier products sink below the lighter reactants, providing an asymptotic constant finger shape deformation of the front by convection. When thermal effects are present, the hotter products, on the contrary, climb above the reactants for strongly exothermic conditions. These various observations as well as the influence of the relative weight of the solutal and thermal effects and of the thickness of the solution layer on the dynamics are discussed in terms of a two-dimensional reaction-diffusion-convection model parametrized by a solutal R(C) and a thermal R(T) Rayleigh number.

Hot spots revealed by simultaneous experimental measurement of the two-dimensional concentration and temperature fields of an exothermic chemical front during finger-pattern formation

A noninvasive optical technique combining digital interferometry in transmission and transparency measurement of concentration is developed to analyze spatiotemporal dynamics of physicochemical systems. This technique allows one to measure simultaneously the two-dimensional (2D) dynamics of concentration and temperature fields in both reactive and nonreactive systems contained inside a transparent cell. When used to experimentally analyze buoyancy-driven fingering of an exothermic autocatalytic chemical front, this method reveals in the 2D temperature field the presence of hot spots where the temperature locally exceeds the adiabatic one.

Buoyancy-driven convection around chemical fronts traveling in covered horizontal solution layers

Density differences across an autocatalytic chemical front traveling horizontally in covered thin layers of solution trigger hydrodynamic flows which can alter the concentration profile. We theoretically investigate the spatiotemporal evolution and asymptotic dynamics resulting from such an interplay between isothermal chemical reactions, diffusion, and buoyancy-driven convection. The studied model couples the reaction-diffusion-convection evolution equation for the concentration of an autocatalytic species to the incompressible Stokes equations ruling the evolution of the flow velocity in a two-dimensional geometry. The dimensionless parameter of the problem is a solutal Rayleigh number constructed upon the characteristic reaction-diffusion length scale. We show numerically that the asymptotic dynamics is one steady vortex surrounding, deforming, and accelerating the chemical front. This chemohydrodynamic structure propagating at a constant speed is quite different from the one obtained in the case of a pure hydrodynamic flow resulting from the contact between two solutions of different density or from the pure reaction-diffusion planar traveling front. The dynamics is symmetric with regard to the middle of the layer thickness for positive and negative Rayleigh numbers corresponding to products, respectively, lighter or heavier than the reactants. A parametric study shows that the intensity of the flow, the propagation speed, and the deformation of the front are increasing functions of the Rayleigh number and of the layer thickness. In particular, the asymptotic mixing length and reaction-diffusion-convection speed both scale as square root Ra for Ra>5. The velocity and concentration fields in the asymptotic dynamics are also found to exhibit self-similar properties with Ra. A comparison of the dynamics in the case of a monostable versus bistable kinetics is provided. Good agreement is obtained with experimental data on the speed of iodate-arsenous acid fronts propagating in horizontal capillaries. We furthermore compare the buoyancy-driven dynamics studied here to Marangoni-driven deformation of traveling chemical fronts in solution open to the air in the absence of gravity previously studied in the same geometry [L. Rongy and A. De Wit, J. Chem. Phys. 124, 164705 (2006)].

Marangoni flow around chemical fronts traveling in thin solution layers: influence of the liquid depth

Surface-tension gradients, which can exist across autocatalytic chemical fronts propagating in thin layers of solution in contact with air, can induce capillary flows that are also called Marangoni flows. These flows in turn affect the spatio–temporal evolution of the concentration fields. This paper addresses the influence of the thickness of the solution layer on the chemo–hydrodynamic pattern resulting from such a coupling between autocatalytic reactions, diffusion and Marangoni effects, neglecting any buoyancy-driven effect. The system reaches an asymptotic dynamics characterized by a steady fluid vortex traveling at a constant speed with the front and deforming it. When the thickness of the fluid layer is increased, Marangoni effects are increasing, thus leading to a larger deformation of the chemical front, larger traveling speed, and more intense convection.