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The competition between chemically induced Marangoni-driven and buoyancy-driven flows is at the core of a new mechanism through which autonomous chemical oscillations can arise for simple A + B → C reactions.

Networks of diffusively coupled inorganic oscillators, confined in nano- and microcompartments, are effective for predicting and understanding the global dynamics of those systems where the diffusion of activatory or inhibitory signals regulates the communication among different individuals. By taking advantage of a microfluidic device, we study the dynamics of arrays of diffusively coupled Belousov-Zhabotinsky (BZ) oscillators encapsulated in water-in-oil single emulsions. New synchronization patterns are induced and controlled by modulating the structural and chemical properties of the phospholipid-based biomimetic membranes via the introduction of specific dopants. Doping molecules do not alter the membrane basic backbone, but modify the lamellarity (and, in turn, the permeability) or interact chemically with the reaction intermediates. A transition from two-period clusters showing 1:2 period-locking to one-period antiphase synchronization is observed by decreasing the membrane lamellarity. An unsynchronized scenario is found when the dopant is able to interfere with chemical communication by reacting with the chemical messengers.

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 Δ M and Δ R, 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.

The purpose of this work is to introduce time delays in an Oregonator-based model [11] to describe molecular communication in a system of coupled chemical oscillators [5]. With this approach we assume that the molecules responsible for communication (signal molecules) take a non-zero time to cross the barrier (phospholipid membrane) which physically separate the oscillators. In particular, here we present numerical results and we discuss and highlight the differences between delayed and non-delayed models.

We study the impact of delayed feedbacks in the collective synchronization of ensembles of identical and autonomous micro-oscillators. To this aim, we consider linear arrays of Belousov–Zhabotinsky (BZ) oscillators confined in micro-compartmentalised systems, where the delayed feedback mimics natural lags that can arise due to the confinement properties and mechanisms driving the inter-oscillator communication. The micro-oscillator array is modeled as a set of Oregonator-like kinetics coupled via mass exchange of the chemical messengers. Changes in the synchronization patterns are explored by varying the delayed feedback introduced in the messenger species Br2. A direct transition from anti-phase to in-phase synchronization and back to the initial anti-phase scheme is observed by progressively increasing the time delay from zero to the value T0, which is the oscillation period characterising the system without any delayed coupling. The route from anti- to in-phase oscillations (and back) consists of regimes where windows of in-phase oscillations are periodically broken by anti-phase beats. Similarities between these phase transition dynamics and synchronization scenarios characterising the coordination of oscillatory limb movements are finally discussed.

International audience; Stable cell like multisomes encapsulating the inorganic chemical oscillator Belousov-Zhabotinsky were engineered and organized in a linear network of diffusively-coupled chemical oscillators by using microlfuidics. The multi-compartmentalization and the spatial configuration resulted in a new global synchronization scenario. After an initial induction interval, all the oscillators started to pulsate in phase with a halved period respect to the natural one.

In this work we studied the effect of spectator ions in the prototype of far-from-equilibrium self-organized chemical systems, the Belousov-Zhabotinsky (BZ) reaction. In particular, we investigated...

We present a discrete-generation model to study the effect of a seasonally asynchronous alien host on the population dynamics of a native host/parasitoid system. We assume that i) the native host and parasitoid are seasonally synchronous; ii) there is no direct competition for resources between the two host species (one native, one alien); and iii) the introduced alien host population (the alternative host) is in an invasive stage and, consequently, it is not subject to any density-dependent regulation. In our model, variations in the annual number of generations (voltinism) of the alien host greatly alter the dynamics of the native host/parasitoid interaction. When the alien host is synchronous with the native host, the parasitoid is favoured, and the native host population decreases until reaching a new, lower equilibrium or becoming extinct. By contrast, when alien and native hosts are asynchronous with each other, there are population oscillations of the native community members compatible with the pulsating availability of the alien host and, under specific conditions, the parasitoid may rapidly become extinct.

We studied the effect of spectator ions in the prototype of far-from-equilibrium self-organized chemical systems, the Belousov-Zhabotinsky (BZ) reaction. In particular, we investigated the specific ion effect of alkali metal cations, connoted for their kosmotropic and chaotropic properties. By means of combined experimental and numerical approaches, we could show a neat and robust evidence for the Hofmeister effect in this system. Spectator cations induce a marked increment of the induction period that preludes regular oscillations and decrease the oscillation amplitude following the sequence Li

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.

The hydrolysis of borohydride salts is a promising process for the generation in situ of pure molecular hydrogen that can be used as an alternative fuel. One of the obstacles toward its concrete application in the realm of green energy resides in nonlinear behaviors of H2 delivery during the reaction development. In particular, we have recently shown that this system behaves like a chemical oscillator in a wide range of experimental conditions, exhibiting nondesirable fluctuations in the production of molecular hydrogen. Despite the potential of NaBH4 hydrolysis in applicative terms, a deep understanding of the reaction mechanisms leading to these nonlinear dynamics is still left to a primary stage. Here we show how to control a typical bursting-like oscillatory scenario occurring in the gas development from NaBH4 hydrolysis. Bursting transients are isolated and stabilized by using highly concentrated solutions of dihydrogen-phosphate/hydrogen-phosphate buffers with an initial pH value around 7. The lengt...

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

Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterisation of empirical data. Here we investigate the effects of the (multi)fractal properties of a time signal, common in sequences arising from chaotic or strange attractors, on the topology of a suitably projected network. Relying on the box counting formalism, we map boxes into the nodes of a network and establish analytic expressions connecting the natural measure of a box with its degree in the graph representation. We single out the conditions yielding to the emergence of a scale-free topology, and validate our findings with extensive numerical simulations., 8 pages, 5 figures

Chemical reactions can impact mixing in partially miscible stratifications by affecting buoyancy-driven convection developing when one phase dissolves into the other one in the gravity field. By means of combined nonlinear simulations and experiments, we explore the power of an A + B → C type of reaction to either enhance or refrain convective dissolution with respect to the nonreactive system depending on the relative contribution to density of the dissolving species A, of the reactant B initially dissolved in the host phase and of the product C. Nonlinear simulations are performed by solving reaction–diffusion–convection equations describing the dissolution and reactive dynamics when a less dense phase of A is layered on top of a reactive denser solution of B, in which A is partially miscible with a given solubility. The spatio-temporal dynamics and convective patterns observed in the numerical study compare favorably with experiments carried out with (i) a liquid alkyl-formate stratified on top of an aqueous solution in which the ester dissolves and undergoes a hydrolysis reaction and (ii) gaseous CO2 dissolving into an aqueous solution of NaOH. We show that the same reaction type can induce a different effect on the convective dynamics depending on the reactant in the host phase. The efficiency of convective dissolution in partially miscible systems can hence be controlled by the chemicals present in the host fluid and their concentration. The direct comparison between the convective dynamics observed during CO2 dissolution in an aqueous phase and in the ester/water stratification validates the latter as a convenient liquid–liquid model system for the interpretation of the impact of chemical reactivity in geological CO2 sequestration.

Depensation in a population growth rate, well-known as Allee effect , has dramatic implications for the dynamics and conservation of small or sparse populations, as it can drive low-density populations to extinction when their demographic size is below a critical threshold. Although rarely detected, depensation effects are believed to be common in nature. Here we present experimental evidence for Allee effect in one Mediterranean endemic plant: Anchusa sardoa . Depensation in the population growth rate is demonstrated through a density-based approach by showing the fingerprinting relationship which ties the population density to its per capita growth rate ( pgr ) during specific stages of the plant life-cycle. The pgr –density plots derived from observational data qualitatively compare with a general 2nd order polynomial function which features one of the peculiar trends underlying an Allee mechanism. We found strong evidence for depensation in the seedling and sapling classes, whereas no-depensation effect could be clearly observed in the adult classes. We also point out a characteristic demographic structure of A. sardoa (i.e. number of juveniles > number of adults) which reflects a not common life strategy with respect to Mediterranean endemic plants. By combining dynamical and demographic information, the results of this study suggest a possible scenario by which A. sardoa population could go extinct, and are discussed in the context of the increasing mass tourism in Mediterranean coastal environments.

In this paper we show that the active interplay of nonlinear kinetics and transport phenomena in a chemical oscillator can be exploited to induce and control chaos. To this aim we use as a model system the ferroin-catalysed Belousov-Zhabotinsky (BZ) oscillating reaction, which is known to evolve to characteristic chaotic transient dynamics when carried out under batch and unstirred conditions. In particular, chemical chaos was found to appear and disappear by following a Ruelle-Takens-Newhouse (RTN) scenario. Here we use medium viscosity as a bifurcation parameter to tune the reaction-diffusion-convection (RDC) interplay and force the reaction in a specific sequence of dynamical regimes: either (i) periodic → quasi-periodic → chaotic or (ii) periodic → quasi-periodic or (iii) only periodic. The medium viscosity can be set by adding different amounts of surfactant (sodium dodecyl sulphate), known to have a little impact on the reaction mechanism, above its critical micelle concentration. Experimental results are supported by means of numerical simulations of a RDC model, which combines self-sustained oscillations to the related chemically-induced buoyancy convection.

Studying the interplay between hydrodynamic instabilities and chemical reactions is attracting increasing interest because of its transversal impact ranging from fundamental to applied science. Depending on the case of study, the exploration of Reaction-Diffusion-Convection (RDC) dynamics over a significant spatio-temporal domain can be computationally expensive and convergence issues may arise in the presence of steep gradients of the chemical or the hydrodynamic fields. Cloud automation techniques allow to create in an easy and dynamical way an arbitrarily large number of virtual nodes, tailored on the specific problem at hands. In this work we show the first steps towards a fully automated and flexible platform for the simulation of chemo-hydrodynamic problems in a cloud environment.

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

In ecological and population dynamics, the coupling between random perturbations and the Allee effect could drive small and confined populations of rare species to extinction. In this paper, we propose a general model for describing spatio-temporal dynamics characterized by demographic Allee growth. In this approach, we include the combined contribution of stochasticity and spatial processes, typically dispersal, which is scarcely explored in the literature. The model is formulated in a reaction-diffusion framework, where the dynamics is regulated by a typical Allee–dispersal evolution and the resilience to white noise is probed at different perturbation amplitudes. Preliminary results show that dispersal processes can compensate random fluctuations to favor the stabilization of the species establishment.

Fractal worlds with limited connectivity are the topological result of growing graphs from chaotic series. We show how this model presents original characteristics which cannot be detected by means of the standard network descriptors. In detail, intrinsic inaccessibility to the fully connected configuration is demonstrated to be a universal feature associated with this family of graphs and strictly related to the fractality of a specific “chaotic source”. Here we discuss the potential of our model to be a generator of fractal graphs and also a self-consistent tool for differentiating chaotic dynamics from stochastic processes.

We investigate the origin of deterministic chaos in the Belousov–Zhabotinsky (BZ) reaction carried out in closed and unstirred reactors (CURs). In detail, we develop a model on the idea that hydrodynamic instabilities play a driving role in the transition to chaotic dynamics. A set of partial differential equations were derived by coupling the two variable Oregonator–diffusion system to the Navier–Stokes equations. This approach allows us to shed light on the correlation between chemical oscillations and spatial–temporal dynamics. In particular, numerical solutions to the corresponding reaction-diffusion-convection (RDC) problem show that natural convection can change the evolution of the concentration distribution as well as oscillation patterns. The results suggest a new way of perceiving the BZ reaction when it is conducted in CURs. In conflict with the common experience, chemical oscillations are no longer a mere chemical process. Within this framework the evolution of all dynamical observables are demonstrated to converge to the regime imposed by the RDC coupling: chemical and spatial–temporal chaos are genuine manifestations of the same phenomenon.

The Belousov–Zhabotinsky (BZ) reaction is the best known example of far from equilibrium self-organizing chemical reaction. Among the many dynamical behaviors that this reaction can exhibit, spatio-temporal chaos attracted particular interest, both for the ferroin and cerium catalyzed systems. In recent years transient chaos was found in the cerium catalyzed BZ reaction, when conducted in batch and unstirred reactors. It was established that the chaotic oscillations, originated by the coupling among chemical kinetics and transport phenomena, appeared and disappeared following a Ruelle–Takens–Newhouse scenario. In this Letter, we show results about the ferroin catalyzed system conducted in batch and unstirred reactors. An aperiodic transient regime was detected and we show that this is a genuine manifestation of spatio-temporal chaos.

When two gels, each loaded with a different set of reactants A and B of an oscillatory reaction, are brought into contact, reaction-diffusion patterns such as waves or Turing patterns can develop in the reactive contact zone. The initial condition which separates the reactants at the beginning leads to a localization in space of the different dynamical regimes accessible to the chemical oscillator. We study here both numerically and experimentally the composite traveling structures resulting from the interaction between chemical fronts and localized waves in the case in which the reactants of such an A + B → oscillator system are those of the canonical Belousov-Zhabotinsky (BZ) oscillating reaction. A transition between different dynamics is obtained by varying the initial concentration of the organic substrate of the BZ reactants, which is one of the parameters controlling the local excitability. We show that the dynamical regime (excitable or oscillatory) characterizing the BZ oscillator in the initial contact area is the key feature which determines the spatiotemporal evolution of the system. The experimental results are in qualitative agreement with the theoretical predictions.

Can we exploit hydrodynamic instabilities to trigger an efficient, selective and spontaneous flow of encapsulated chemical information? One possible answer to this question is presented in this paper where cross-diffusion, which commonly characterizes compartmentalized dispersed systems, is shown to initiate buoyancy-driven hydrodynamic instabilities. A general theoretical framework allows us to predict and classify cross-diffusion-induced convection in two-layer stratifications under the action of the gravitational field. The related nonlinear dynamics is described by a cross-diffusion-convection (CDC) model where fickian diffusion is coupled to the Stokes equations. We identify two types of hydrodynamic modes (the negative cross-diffusion-driven convection, NCC, and the positive cross-diffusion-driven convection, PCC) corresponding to the sign of the cross-diffusion term dominating the system dynamics. We finally show how AOT water-in-oil reverse microemulsions are an ideal model system to confirm the general theory and to approach experimentally cross-diffusion-induced hydrodynamic scenarios.

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

Cross-diffusion phenomena are experimentally shown to be able to induce convective fingering around an initially stable stratification of two microemulsions with different compositions. Upon diffusion of a salt that entrains water and AOT micelles by cross-diffusion, the miscible interface deforms into fingers following the build-up of a non-monotonic density profile in the gravitational field. A diffusion model incorporating cross-diffusion effects provides an explanation for the mechanism of the buoyancy-driven hydrodynamic instability and for the properties of the convective fingers., SCOPUS: ar.j, info:eu-repo/semantics/published

When two microemulsions are put in contact in the gravity field along a horizontal contact line, cross-diffusion can trigger the transport of one species in the presence of a gradient in concentration of another species. We show here theoretically that such cross-diffusion effects can induce buoyancy-driven convective instabilities at the interface between two solutions of different compositions even when initially the less dense solution lies on top of the denser one. Two different sources of convective modes are identified depending whether positive or negative cross-diffusion is involved. We evidence the two predicted cross-diffusion driven instabilities experimentally using a two-layer stratification of Aerosol-OT (AOT) water-in-oil microemulsions solutions with different water or AOT composition.

Understanding the transition from planar fronts, trigger waves, or solitary waves to spirals in excitable media has attracted increasing interest in the past few decades, mainly because of its relevance for biological and medical applications. In this paper, we introduce a new mechanism for the formation of rotating spiral waves based on the collision between a phase reduction front and trigger waves propagating in the oscillatory Belousov–Zhabotinsky (BZ) medium. The phase reduction front is triggered by imposing a heterogeneous spatial gradient of a chemical agent S able to temporarily sequester an inhibitory species of the oscillatory mechanism. This determines an initial oxidized transient over the whole reactor and, successively, a phase desynchronization by which the system recovers the excitable condition. The resulting reduction front can induce and control the transition from phase to trigger waves, whose properties depend upon the concentration profile of S along the spatial coordinate. By means...

Pulsatile chemo-hydrodynamic patterns due to a coupling between an oscillating chemical reaction and buoyancy-driven hydrodynamic flows can develop when two solutions of separate reactants of the Belousov-Zhabotinsky reaction are put in contact in the gravity field and conditions for chemical oscillations are met in the contact zone. In regular oscillatory conditions, localized periodic changes in the concentration of intermediate species induce pulsatile density gradients, which, in turn, generate traveling convective fingers breaking the transverse symmetry. These patterns are the self-organized result of a genuine coupling between chemical and hydrodynamic modes. © 2014 American Chemical Society., SCOPUS: ar.j, info:eu-repo/semantics/published

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., SCOPUS: ar.j, info:eu-repo/semantics/published

The hydrolysis of borohydride salts represents one of the most promising processes for the generation of high purity molecular hydrogen under mild conditions. In this work we show that the sodium borohydride hydrolysis exhibits a fingerprinting periodic oscillatory transient in the hydrogen flow over a wide range of experimental conditions. We disproved the possibility that flow oscillations are driven by supersaturation phenomena of gaseous bubbles in the reactive mixture or by a nonlinear thermal feedback according to a thermokinetic model. Our experimental results indicate that the NaBH4 hydrolysis is a spontaneous inorganic oscillator, in which the hydrogen flow oscillations are coupled to an “oscillophor” in the reactive solution. The discovery of this original oscillator paves the way for a new class of chemical oscillators, with fundamental implications not only for testing the general theory on oscillations, but also with a view to chemical control of borohydride systems used as a source of hydrogen based green fuel.

We introduce a reaction-diffusion-convection (RDC) model to study the combined effect of buoyancy- and Marangoni-driven flows around a traveling front. The model allows for a parametric control of the two contributions via the solutal Rayleigh number, Ra c , which rules the buoyancy component and the solutal Marangoni number, Ma c , governing the intensity of the velocity field at the interface between the reacting solution and air. Complex dynamics may arise when the bulk and the surface flows describe an antagonistic interplay. Typically, spatiotemporal oscillations are observed in the parameter region (Ra c 0).

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 (Ra0, Ma0). 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.

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.

A reaction–diffusion–convection (RDC) model is introduced as a convenient framework for studying instability scenarios by which chemical oscillators are driven to chaos. Distinct bifurcations in the oscillating patterns are found as diffusion coefficients or Grashof numbers are varied. Singularly there emerge peculiar bifurcation paths in which quasi-periodicity transmutes into a period-doubling sequence to chemical chaos. The opposite influence exhibited by the two parameters in these transitions clearly indicate that diffusion and natural convection are in ‘competition’ for the stability of ordered dynamics: the former has a stabilizing effect while the latter exerts a destabilizing role.

Chemical oscillations generated by the Belousov–Zhabotinsky reaction in batch unstirred reactors, show a characteristic chaotic transient in their dynamical regime, which is generally found between two periodic regions. Chemical chaos starts and finishes by following a direct and an inverse Ruelle–Takens–Newhouse scenario, respectively. In previous works we showed, both experimentally and theoretically, that the complex oscillations are generated by the coupling among the nonlinear kinetics and the transport phenomena, the latter due to concentration and density gradients. In particular, convection was found to play a fundamental role. In this paper, we develop a reaction–diffusion–convection model to explore the influence of the reagents consumption (BrO−3 in particular) in the inverse transition from chaos to periodicity. We demonstrated that, on the route towards thermodynamic equilibrium, the reagents concentration directly modulates the strength of the coupling between chemical kinetics and mass transport phenomena. An effective sequential decoupling (reaction–diffusion–convection → reaction–diffusion → reaction) takes place upon the reagents consumption and this is at the basis of the transition from chaos to periodicity.

The transition to spatial-temporal complexity exhibited by spiral waves under the effect of gravitational field in the Belousov-Zhabotinsky reaction is numerically studied on the basis of spiral tip dynamics. Successive transformations in tip trajectories are characterized as a function of the hydrodynamical parameter and attributed to a Ruelle-Takens-Newhouse scenario to chaos. The analysis describes the emergence of complexity in terms of the interplay between the evolution of the velocity field and concentration waves. In particular, (i) by mapping the tip motion in relation to some hydrodynamical pseudopotentials, the general mechanism by which the velocity field affects the tip trajectory is pointed out, and, (ii) by comparing the dynamical evolutions of local and mean properties associated with the inhomogeneous structures and to the velocity field, a surprising correlation is found. The results suggest that the reaction-diffusion-convection (RDC) coupling addresses the system to some general regimes, whose nature is imposed by the hydrodynamical contribution. More generally, RDC coupling would be formalized as the phenomenon that governs the system and drives it to chaos.

Direct numerical simulations of the transition process from periodic to chaotic dynamics are presented for two variable Oregonator-diffusion model coupled with convection. Numerical solutions to the corresponding reaction-diffusion-convection system of equations show that natural convection can change in a qualitative way, the evolution of concentration distribution, as compared with convectionless conditions. The numerical experiments reveal distinct bifurcations as the Grashof number is increased. A transition to chaos similar to Ruelle-Takens-Newhouse scenario is observed. Numerical results are in agreement with the experiments.

This work focuses on the dynamics of a ball inside the reactor of a ball mill. We show that the distribution of collisions at the reactor walls exhibits multifractal properties in a wide region of the parameter space defining the geometrical characteristics of the reactor and the collision elasticity. This feature points to the presence of restricted self-organized zones of the reactor walls where the ball preferentially collides and the mechanical energy is mainly dissipated.

Buoyancy-driven flows induced by the hydrodynamic Rayleigh-Taylor or double-diffusive instabilities develop symmetrically around the initial contact line when two solutions of given solutes with different densities are put in contact in the gravitational field. If the solutes affecting the densities of these solutions are involved in chemical reactions, changes in composition due to the underlying reaction-diffusion processes can modify the density profile in space and time, and affect the hydrodynamic patterns. In particular, if the density difference between the two reactant solutions is not too large, the resulting chemo-hydrodynamic patterns are asymmetric with regard to the initial contact line. We quantify both experimentally and numerically this asymmetry showing that fingers here preferentially develop above the reaction zone and not across the mixing zone as in the non reactive situation. In some cases, the reaction can even lead to the onset of a secondary double-diffusive instability between the product of the reaction, dynamically generated in situ, and one of the reactants.