Self-Sustained Reaction Fronts in Porous Media

We analyze experimentally chemical waves propagation in the disordered flow field of a porous medium. The reaction fronts travel at a constant velocity which drastically depends on the mean flow direction and rate. The fronts may propagate either downstream and upstream but, surprisingly, they remain static over a range of flow rate values. Resulting from the competition between the chemical reaction and the disordered flow field, these frozen fronts display a particular sawtooth shape. The frozen regime is likely to be associated with front pinning in low velocity zones, the number of which varies with the ratio of the mean flow and the chemical front velocities.Comment: 4 pages, 5 figure

Anisotropic Particles Focusing Effect in Complex Flows

The dispersion of a tracer in a fluid flow is influenced by the Lagrangian motion of fluid elements. Even in laminar regimes, the irregular chaotic behavior of a fluid flow can lead to effective stirring that rapidly redistributes a tracer throughout the domain. When the advected particles possess a finite size and nontrivial shape, however, their dynamics can differ markedly from passive tracers, thus affecting the dispersion phenomena. Here we investigate the behavior of neutrally buoyant particles in 2-dimensional chaotic flows, combining numerical simulations and laboratory experiments. We show that depending on the particles shape and size, the underlying Lagrangian coherent structures can be altered, resulting in distinct dispersion phenomena within the same flow field. Experiments performed in a two-dimensional cellular flow, exhibited a focusing effect in vortex cores of particles with anisotropic shape. In agreement with our numerical model, neutrally buoyant ellipsoidal particles display markedly different trajectories and overall organization than spherical particles, with a clustering in vortices that changes accordingly with the aspect ratio of the particles

Using braids to quantify interface growth and coherence in a rotor-oscillator flow

The growth rate of material interfaces is an important proxy for mixing and reaction rates in fluid dynamics, and can also be used to identify regions of coherence. Estimating such growth rates can be difficult, since they depend on detailed properties of the velocity field, such as its derivatives, that are hard to measure directly. When an experiment gives only sparse trajectory data, it is natural to encode planar trajectories as mathematical braids, which are topological objects that contain information on the mixing characteristics of the flow, in particular through their action on topological loops. We test such braid methods on an experimental system, the rotor-oscillator flow, which is well-described by a theoretical model. We conduct a series of laboratory experiments to collect particle tracking and particle image velocimetry data, and use the particle tracks to identify regions of coherence within the flow that match the results obtained from the model velocity field. We then use the data to estimate growth rates of material interface, using both the braid approach and numerical simulations. The interface growth rates follow similar qualitative trends in both the experiment and model, but have significant quantitative differences, suggesting that the two are not as similar as first seems. Our results shows that there are challenges in using the braid approach to analyze data, in particular the need for long trajectories, but that these are not insurmountable.Comment: 18 pages including Supplementary Material, 16 figures. RevTeX 4.1 document clas

Propagation de fronts d onde chimique en écoulement désordonné

La propagation d'ondes de réaction constitue un exemple générique d'auto-organisation dans les systèmes de réaction-diffusion. Générées par une réaction chimique non-linéaire, ces fronts auto-entretenues peuvent être observés dans de nombreux systèmes comme la croissance de colonies de bactéries ou lors de la propagation de fronts de combustion. Dans ce travail de thèse, nous aborderons la question de l'effet d'un écoulement hétérogène sur la propagation d'un front de réaction. Dans le cas d'un courant moyen de sens opposé à celui de la réaction chimique, le couplage d'un tel système de nature auto-entretenue, avec un écoulement désordonné, peut conduire à l'apparition spontanée de motifs triangulaires statiques. Nous montrerons quelles sont les mécanismes à l'origines de la formation de ces états gelés'' des fronts de réaction. Nous montrerons ensuite, l'existence de fluctuations en loi d'échelles sur les fronts de réaction. Nous déterminerons les exposants de rugosité et de croissance associés à ces structures. Ces fronts d'onde chimique peuvent par ailleurs présenter une dynamique de nature critique, matérialisée par l'apparition de phénomènes d'avalanches. Nous montrerons que ces évènements possèdent des propriétés fractales à l'approche d'un point de transition cinématique. Enfin, un mécanisme de croissance associé au modèle KPZ, sera présenté pour expliquer le facettage des fronts chimiques observés.Reaction waves are an example of self-organization in reaction-diffusion systems. Generated by a nonlinear chemical reaction, these self-sustained fronts are observed in numerous systems such as in bacterial colony growth or flame fronts propagation. In this work, we have investigated the coupling between heterogeneous fluid flow and autocatalytic reaction fronts. When the mean flow opposes the chemical reaction direction, static fronts, with a specific triangular shape can appear. We will show the mechanism at the origin of these frozen pattern formation. We will then show that these reaction fronts exhibit power law spatial fluctuations. We will determine the roughness exponents associated with these structures. These fronts can also display a critical behavior through the onset of burst-like events called avalanches. We will show that these events exhibit fractal properties when approaching a dynamical phase transition. Finally, the faceted morphology of the fronts will be explained through a KPZ-like growth process.PARIS-BIUSJ-Physique recherche (751052113) / SudocSudocFranceF

Band gap formation in internal gravity waves propagating in periodically stratified fluids

International audienceIn the ocean, the interplay between heat diffusion and salt diffusion can drive double diffusive instability and lead to the formation of spatially periodic density profiles. These periodic structures, called thermohaline staircases, can persist over large regions and have also been suggested to exist in astrophysical bodies, such as in giant planet interiors. In this talk, we show that such periodically stratified fluids can host internal gravity waves with properties reminiscent of photonic crystal and topological insulator physics. Combining experimental, numerical and analytical modeling, we show the formation of band gaps and surface states that are exponentially localized near interfaces and controlled by boundary conditions. We also find that these internal wave states are robust to perturbations and can be observed in numerical simulations performed with geophysical stratification profiles from the Arctic Region. Our results suggest that energy transport by internal waves could be profoundly altered by the presence of periodic stratifications naturally occurring in the ocean, and could therefore influence large-scale circulation patterns

Phase diagram of sustained wave fronts opposing the flow in disordered porous media

Using lattice Boltzmann simulations, we analyze the different regimes of propagation of an autocatalytic reaction front in heterogenous porous media. The heterogeneities of the porous medium are characterized by the standard deviation of its log-normal distribution of permeability and its correlation length. We focus on the situation where chemical reaction and flow field act in opposite directions. In agreement with previous experiments we observe upstream, downstream fronts as well as static, frozen ones over a range of flow velocity which depends drastically on the heterogeneities of the flow field. The transition between the static regime and the downstream one account for large enough low-velocity zones, whereas the transition from static to upstream regime is found to be given by a kind of percolation path

Rocket yeast

This paper is associated with a video winner of a 2020 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion,&nbsp;https://doi.org/10.1103/APS.DFD.2020.GFM.V0020.</p