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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., 18 pages including Supplementary Material, 16 figures. RevTeX 4.1 document class

Despite the importance of fluid flow for transporting and organizing populations, few laboratory systems exist to systematically investigate the impact of advection on their spatial evolutionary dynamics. To address this problem, we study the morphology and genetic spatial structure of microbial colonies growing on the surface of a nutrient-laden fluid 10^{4} to 10^{5} times more viscous than water in Petri dishes; the extreme but finite viscosity inhibits undesired thermal convection and allows populations to effectively live at the air-liquid interface due to capillary forces. We discover that S. cerevisiae (baker’s yeast) growing on a viscous liquid behave like “active matter”: They metabolically generate fluid flows many times larger than their unperturbed colony expansion speed, and that flow, in turn, can dramatically impact their colony morphology and spatial population genetics. We show that yeast cells generate fluid flows by consuming surrounding nutrients and decreasing the local substrate density, leading to misaligned fluid pressure and density contours, which ultimately generates vorticity via a thresholdless baroclinic instability. Numerical simulations with experimentally measured parameters demonstrate that an intense vortex ring is produced below the colony’s edge. As the viscosity of the substrate is lowered and the self-induced flow intensifies, we observe three distinct morphologies: At the highest viscosity, cell proliferation and movement produces compact circular colonies with, however, a stretched regime of exponential expansion; intermediate viscosities give rise to compact colonies with “fingers” that are usually monoclonal and then break into smaller cell clusters; at the lowest viscosity, the expanding colony fractures into many genetically diverse, mutually repelling, islandlike fragments that can colonize an entire 94-mm-diameter Petri dish within 36 hours. We propose a simple phenomenological model that predicts the early colony dynamics. Our results provide rich opportunities to study the interplay between fluid flow and spatial population genetics for future investigations.

We report on numerical studies of avalanches of an autocatalytic reaction front in a porous medium. The front propagation is controlled by an adverse flow resulting in upstream, static, or downstream regimes. In an earlier study focusing on front shape, we identified three different universality classes associated with this system by following the front dynamics experimentally and numerically. Here, using numerical simulations in the vicinity of the second-order transition, we identify an avalanche dynamics characterized by power-law distributions of avalanche sizes, durations, and lateral extensions. The related exponents agree well with the quenched-Kardar-Parisi-Zhang theory, which describes the front dynamics. However, the geometry of the propagating front differs slightly from that of the theoretical one. We show that this discrepancy can be understood in terms of the nonquasistatic correction induced by the finite front velocity.

International audience; Self-sustained reaction fronts in a disordered medium subject to an external flow display self-affine roughening, pinning and depinning transitions. We measure spatial and temporal fluctuations of the front in $1+1$ dimensions, controlled by a single parameter, the mean flow velocity. Three distinct universality classes are observed, consistent with the Kardar-Parisi-Zhang (KPZ) class for fast advancing or receding fronts, the quenched KPZ class (positive-qKPZ) when the mean flow approximately cancels the reaction rate, and the negative-qKPZ class for slowly receding fronts. Both quenched KPZ classes exhibit distinct depinning transitions, in agreement with the theory.

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. PACS numbers

Autocatalytic reaction fronts between two reacting species in the absence of fluid flow, propagate as solitary waves. The coupling between autocatalytic reaction front and forced simple hydrodynamic flows leads to stationary fronts whose velocity and shape depend on the underlying flow field. We address the issue of the chemico-hydrodynamic coupling between forced advection in porous media and self-sustained chemical waves. Towards that purpose, we perform experiments over a wide range of flow velocities with the well characterized iodate arsenious acid and chlorite-tetrathionate autocatalytic reactions in transparent packed beads porous media. The characteristics of these porous media such as their porosity, tortuosity, and hydrodynamics dispersion are determined. In a pack of beads, the characteristic pore size and the velocity field correlation length are of the order of the bead size. In order to address these two length scales separately, we perform lattice Boltzmann numerical simulations in a stochastic porous medium, which takes into account the log-normal permeability distribution and the spatial correlation of the permeability field. In both experiments and numerical simulations, we observe stationary fronts propagating at a constant velocity with an almost constant front width. Experiments without flow in packed bead porous media with different bead sizes show that the front propagation depends on the tortuous nature of diffusion in the pore space. We observe microscopic effects when the pores are of the size of the chemical front width. We address both supportive co-current and adverse flows with respect to the direction of propagation of the chemical reaction. For supportive flows, experiments and simulations allow observation of two flow regimes. For adverse flow, we observe upstream and downstream front motion as well as static front behaviors over a wide range of flow rates. In order to understand better these observed static state fronts, flow experiments around a single obstacle were used to delineate the range of steady state behavior. A model using the "eikonal thin front limit" explains the observed steady states.

Spontaneous symmetry breaking and bifurcations can be observed in highly turbulent flows. Such phenomena are particularly interesting because they may be considered as laboratory models for changes of states in far-fromequilibrium complex and/or large natural systems. The von Karman flow is a closed swirling shear flow produced by two counterrotating impellers in a cylindrical vessel which allows to easily access high Reynolds numbers Re up to 106. In this study, we have used water-glycerol mixtures to scan a wide range of Re from 102 to 106. Using stereoscopic PIV, we have been able to measure the three components of the velocity field in a meridian plane of the flow. Our acquisition frequency is moderate, around 10 Hz, but our system is able to record up to 32 000 velocity fields providing a large statistics and highly converged averages.

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.