Marcello A. Budroni

Asymmetric Rayleigh-Taylor and double-diffusive fingers in reactive systems

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 th...

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.

Chemical Control of Hydrodynamic Instabilities in Partially Miscible Two-Layer Systems.

Hydrodynamic instabilities at the interface between two partially miscible liquids impact numerous applications, including CO2 sequestration in saline aquifers. We introduce here a new laboratory-scale model system on which buoyancy- and Marangoni-driven convective instabilities of such partially miscible two-layer systems can easily be studied. This system consists of the stratification of a pure alkyl formate on top of a denser aqueous solution in the gravitational field. A rich spectrum of convective dynamics is obtained upon partial dissolution of the ester into the water followed by its hydrolysis. The properties of the convective patterns are controlled by the miscibility of the ester in water, the feedback of the dissolved species on its own miscibility, as well as the reactivity of given chemicals in the aqueous solution with the solubilized ester.

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.

Bifurcations in spiral tip dynamics induced by natural convection in the Belousov–Zhabotinsky reaction

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.

Ruelle–Takens–Newhouse scenario in reaction-diffusion-convection system

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.

Interfacial hydrodynamic instabilities driven by cross-diffusion in reverse microemulsions

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.

Self-Organized Traveling Chemo-Hydrodynamic Fingers Triggered by a Chemical Oscillator

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.

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.

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

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