Ostwald-like ripening in the two-dimensional clustering of passive particles induced by swimming bacteria.

Clustering passive particles by active agents is a promising route for fabrication of colloidal structures. Here, we report the dynamic clustering of micrometric beads in a suspension of motile bacteria. We characterize the coarsening dynamics for various bead sizes, surface fractions, and bacterial concentrations. We show that the time scale τ for the onset of clustering is governed by the time of first encounter of diffusing beads. At large time (t≫τ), we observe a robust cluster growth as t^{1/3}, similar to the Ostwald ripening mechanism. From bead tracking measurements, we extract the short-range bacteria-induced attractive force at the origin of this clustering.

Direct measurement of the aerotactic response in a bacterial suspension.

Aerotaxis is the ability of motile cells to navigate toward oxygen. A key question is the dependence of the aerotactic velocity with the local oxygen concentration c. Here we combine simultaneous bacteria tracking and local oxygen concentration measurements using Ruthenium encapsulated in micelles to characterize the aerotactic response of Burkholderia contaminans, a motile bacterium ubiquitous in the environment. In our experiments, an oxygen gradient is produced by the bacterial respiration in a sealed glass capillary permeable to oxygen at one end, producing a bacterial band traveling toward the oxygen source. We compute the aerotactic response χ(c) both at the population scale, from the drift velocity in the bacterial band, and at the bacterial scale, from the angular modulation of the run times. Both methods are consistent with a power-law χ∝c^{-2}, in good agreement with existing models based on the biochemistry of bacterial membrane receptors.

Effect of the porosity on the fracture surface roughness of sintered materials: from anisotropic to isotropic self-affine scaling.

To unravel how the microstructure affects the fracture surface roughness in heterogeneous brittle solids like rocks or ceramics, we characterized the roughness statistics of postmortem fracture surfaces in homemade materials of adjustable microstructure length scale and porosity, obtained by sintering monodisperse polystyrene beads. Beyond the characteristic size of disorder, the roughness profiles are found to exhibit self-affine scaling features evolving with porosity. Starting from a null value and increasing the porosity, we quantitatively modify the self-affine scaling properties from anisotropic (at low porosity) to isotropic (for porosity >10%).

CHEMO-hydrodynamic coupling between forced advection in porous media and self-sustained chemical waves.

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.

Viscometer using drag force measurements.

A robust and precise viscometer using the forces exerted by a laminar flow inside a small duct is presented: the force is measured on a long cylindrical sensor dipped into the flow. Two devices of respective volumes 1.4 and 0.031 ml have been realized, demonstrating that the technique is usable with small fluid volumes. Several Newtonian and non-Newtonian fluids have been tested at shear rates ranging from 0.3 to 10 s(-1) for the first device and from 85 to 2550 s(-1) for the second one. For Newtonian fluids, of viscosities ranging from 10(-3) to 0.1 Pa s, the linear response of the device has been verified and a 90% agreement with the values provided by commercial rheometers is obtained. For non-Newtonian polymer solutions, the variation of the force with the flow velocity allows one to determine the dependence of the viscosity on the shear rate. Two shear thinning polymer solutions with a power law behavior at intermediate shear rates have been investigated and their rheological parameters have been determined.

Characterization of fracture aperture field heterogeneity by electrical resistance measurement.

We use electrical resistance measurements to characterize the aperture field in a rough fracture. This is done by performing displacement experiments using two miscible fluids of different electrical resistivity and monitoring the time variation of the overall fracture resistance. Two fractures have been used: their complementary rough walls are identical but have different relative shear displacements which create "channel" or "barrier" structures in the aperture field, respectively parallel or perpendicular to the mean flow velocity U(→). In the "channel" geometry, the resistance displays an initial linear variation followed by a tail part which reflects the velocity contrast between slow and fast flow channels. In the "barrier" geometry, a change in the slope between two linear zones suggests the existence of domains of different characteristic aperture along the fracture. These variations are well reproduced analytically and numerically using simple flow models. For each geometry, we present then a data inversion procedure that allows one to extract the key features of the heterogeneity from the resistance measurement.

Failure mechanisms and surface roughness statistics of fractured Fontainebleau sandstone.

In an effort to investigate the link between failure mechanisms and the geometry of fractures of compacted grains materials, a detailed statistical analysis of the surfaces of fractured Fontainebleau sandstones has been achieved. The roughness of samples of different widths W is shown to be self-affine with an exponent zeta=0.46+/-0.05 over a range of length scales ranging from the grain size d up to an upper cutoff length xi approximately =0.15 W. This low zeta value is in agreement with measurements on other sandstones and on sintered materials. The probability distributions pi delta z(delta h) of the variations of height over different distances delta z>d can be collapsed onto a single Gaussian distribution with a suitable normalization and do not display multiscaling features. The roughness amplitude, as characterized by the height-height correlation over fixed distances delta z, does not depend on the sample width, implying that no anomalous scaling of the type reported for other materials is present. It is suggested, in agreement with recent theoretical work, to explain these results by the occurrence of brittle fracture (instead of damage failure in materials displaying a higher value of zeta approximately =0.8 ).

Self-affine fronts in self-affine fractures: large and small-scale structure.

The evolution and spatial structure of displacement fronts in fractures with self-affine rough walls are studied by numerical simulations. The fractures are open and the two faces are identical but shifted along their mean plane, either parallel or perpendicular to the flow. An initially flat front advected by the flow is progressively distorted into a self-affine front with a Hurst exponent equal to that of the fracture walls. The lower cutoff of the self-affine regime depends only on the aperture, while the upper cutoff grows with the lateral shift and linearly with the width of the front.

Experimental study of miscible displacement fronts in rough self-affine fractures.

Miscible fluid displacements are studied experimentally in a radial flow between two complementary replica of a self-affine rough granite fracture surface. The displacement front between a dyed fluid and a transparent (but otherwise identical) one is followed optically through one face of the cell. The evolution of its geometry is studied as a function of time, flow-rate, and normal and lateral relative displacements between the two surfaces. For a purely normal displacement, the front is globally smooth, due to the constant local distance between surfaces. For a finite lateral displacement, the front is rough due to spatial variations of this distance; its geometry is fractal and its dimension is directly related to the Hurst exponent H approximately 0.8 of the surface. The fractal regime is observed only above a lower cut-off scale that depends on the normal spacing of the surfaces and an upper one that increases with the injected volume and with the amplitude of the lateral displacement.

Geometry and dynamics of invasion percolation with correlated buoyancy

We study an invasion percolation model for drainage where the disorder comes partly from capillary thresholds and partly from height differences in a rough self-affine landscape. As a function of the buoyancy, the geometry of the invaded clusters changes dramatically. Long-range correlations from the fracture topography induce a double cluster structure with strings and compact blobs. A characteristic length is introduced comparing the width of the capillary threshold distribution and gravity effects at the pore scale. We study electrical properties of percolating clusters. Current distributions along percolating clusters are shown to be multifractal and sensitive to the buoyancy.

Competition between correlated buoyancy and uncorrelated capillary effects during drainage.

We study drainage in a horizontally oriented rough fracture joint filled with glass beads. The shape and structure of the drained areas is the result of competition between two effects: (1) variations in the capillary thresholds necessary to be overcome in order to drain the pores and (2) the height variations due to the roughness of the fracture joint. These height variations have long range correlations due to the self-affine nature of the fracture. The capillary thresholds are uncorrelated. We tune the relative strength of these two effects by performing experiments in a centrifuge and thus changing the "strength of gravity." As gravity is increased, the structure of the drained areas change from that of invasion percolation to a structure composed of compact blobs linked together by threadlike links. We study both the geometry and the effect of trapping while changing acceleration of gravity from zero to 6g(0). At high centrifugal acceleration we further observe fragmentation, migration and coalescence of bubbles of fluid inside the drained areas.