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International audience; The different types of instabilities of free cylinders (diameter $D$, length $L$) have been studied in a viscous flow (velocity $U$) between parallel vertical walls of horizontal width $W$ at a distance $H$: the influence of the confinement parameters $D/H$ and $L/W$ has been investigated. As $D/H$ increases, there is a transition from stable flow to oscillations transverse to the walls and then to a fluttering motion with oscillations of the angle of the axis with respect to the horizontal. The two types of oscillations may be superimposed in the transition domain. The frequency $f$ of the transverse oscillations is independent of the lateral confinement $L/W$ in the range: 0.055 \le L/W \le 0.94$ for a given cylinder velocity $V_{cx}$ and increases only weakly with $V_{cx}$. These results are accounted for by assuming a $2D$ local flow over the cylinder with a characteristic velocity independent of $L/W$ for a given $V_{cx}$ value. The experimental values of $f$ are also independent of the transverse confinement $D/H$. The frequency $f_f$ of the fluttering motion is significantly lower than $f$: $f_f$ is also nearly independent of the cylinder diameter and of the flow velocity but decreases significantly as $L/W$ increases. The fluttering instability is then rather a $3D$ phenomenon involving the full length of the cylinder and the clearance between its ends and the side walls.

An oscillatory instability has been observed experimentally on an horizontal cylinder free to move and rotate between two parallel vertical walls of distance H; its characteristics differ both from vortex shedding driven oscillations and from those of tethered cylinders in the same geometry. The vertical motion of the cylinder, its rotation about its axis and its transverse motion across the gap have been investigated as a function of its diameter D, its density s, of the mean vertical velocity U of the fluid and of its viscosity. For a blockage ratio D/H above 0.5 and a Reynolds number Re larger then 14, oscillations of the rolling angle of the cylinder about its axis and of its transverse coordinate in the gap are observed together with periodic variations of the vertical velocity. Their frequency f is the same for the sedimentation of the cylinder in a static fluid (U = 0) and for a non-zero mean flow (U 6= 0). The Strouhal number St associated to the oscillation varies as 1/Re with : St.Re = 3 $\pm$ 0.15. The corresponding period 1/f is then independent of U and corresponds to a characteristic viscous diffusion time over a distance ~ D, implying a strong influence of the viscosity. These characteristics differ from those of vortex shedding and tethered cylinders for which St is instead roughly constant with Re and higher than here.

International audience; A new type of flow induced oscillation has been observed by placing a tethered cylinder in a Hele Shaw cell. This novel instability is studied numerically and experimentally as function of the Reynolds number and as function of the mass of the cylinder in Hele Shaw cell such that the cylinder diameter to cell aperture ratio: $D=0.66$). The cylinder is found to oscillates above a Reynolds number $\Rey_c \simeq 20$. This critical $Re$ is much lower than the threshold for Bénard--Von Kármán vortex shedding behind a fixed cylinder in the same configuration. Close to the threshold, the growth rate of the amplitude varies like $(\Rey - \Rey_c)^{1/2}$ and the lack of hysteresis demonstrate that the process is a supercritical Hopf bifurcation. The adjustement of the position of the cylinder by a Van der Pol equation allows for the identification of the stiffness, the amplification coefficient and to study the effect of the total mass: Forced oscillation is used to study their behavior and their physical meaning is discussed using the pressure field. For dense cylinder, the CIV is observed to end abruptly and new oscillations are observed when the $Re$ is increased above $110$; this oscillation corresponds to Vortex Induced Vibration (VIV). If the mass falls below a critical value, the CIV is not observed to vanish.

International audience; The possible characterization of the heterogeneity of the aperture field in rough fractures by electrical impedance measurement is demonstrated through displacement experiments using two miscible fluids of different electrical resistivity. Two model fractures have been used: their complementary rough walls are identical but have different relative shear displacements creating ``channel'' or `barrier'' structures in the void space, respectively parallel or perpendicular to the mean flow velocity $\vec{U}$. In the (``channel'') geometry, the global electrical resistance displays an initial linear variation followed by a ``tail'' part reflecting the contrast between slow and fast flow channels. In the (``barrier'') geometry, the existence of a change in the slope between two linear zones suggests the appearance of domains of different permeabilities along the fracture. These variations are well reproduced theoretically and numerically either by assuming independent flow channels parallel to $\vec{U}$ (channel case) or an aperture that varies only along the flow (barrier case). For each configuration, we present a specific inversion procedure that allows one to extract the key features of the heterogeneity from the resistance variation.

International audience; We propose a method for calculating the effective permeability of two-dimensional self-affine permeability fields based on generalizing the one-dimensional concept of a bottleneck. We test the method on fracture faults where the local permeability field is given by the cube of the aperture field. The method remains accurate even when there is substantial mechanical overlap between the two fracture surfaces. The computational efficiency of the method is comparable to calculating a simple average and is more than two orders of magnitude faster than solving the Reynolds equations using a finite-difference scheme.

International audience; Dispersion experiments are compared for two transparent model fractures with identical complementary rough walls but with a relative shear displacement $\vec{\delta}$ parallel ($\vec{\delta}\parallel \vec{U}$) or perpendicular ($\vec{\delta} \perp \vec{U}$) to the flow velocity $\vec{U}$. The structure of the mixing front is characterized by mapping the local normalized local transit time $\bar t(x,y)$ and dispersivity $\alpha(x,y)$. For $\vec{\delta} \perp \vec{U}$, displacement fronts display large fingers: their geometry and the distribution of $\bar t(x,y)U/x$ are well reproduced by assuming parallel channels of hydraulic conductance deduced from the aperture field. For $\vec{\delta} \parallel \vec{U}$, the front is flatter and $\alpha(x,y)$ displays a narrow distribution and a Taylor-like variation with $Pe$.

Miscible tracer dispersion measurements in transparent model fractures with different types of wall roughness are reported. The nature (Fickian or not) of dispersion is determined by studying variations of the mixing front as a function of the traveled distance but also as a function of the lateral scale over which the tracer concentration is averaged. The dominant convective dispersion mechanisms (velocity profile in the gap, velocity variations in the fracture plane) are established by comparing measurements using Newtonian and shear thinning fluids. For small monodisperse rugosities, front spreading is diffusive with a dominant geometrical dispersion (dispersion coefficient $D \propto Pe$) at low P\'eclet numbers $Pe$; at higher $Pe$ values one has either $D \propto Pe^2$ ({\it i.e.} Taylor dispersion) for obstacles of height smaller than the gap or $D \propto Pe^{1.35}$ for obstacles bridging the gap. For a self affine multiscale roughness like in actual rocks and a relative shear displacement $\vec{\delta}$ of complementary walls, the aperture field is channelized in the direction perpendicular to $\delta$. For a mean velocity $\vec{U}$ parallel to the channels, the global front geometry reflects the velocity contrast between them and is predicted from the aperture field. For $\vec{U}$ perpendicular to the channels, global front spreading is much reduced. Local spreading of the front thickness remains mostly controlled by Taylor dispersion except in the case of a very strong channelization parallel to $\vec U$.

The influence of a small relative density difference on the displacement of two miscible liquids is studied experimentally in transparent 2D networks of micro channels. Both stable displacements in which the denser fluid enters at the bottom of the cell and displaces the lighter one and unstable displacements in which the lighter fluid is injected at the bottom and displaces the denser one are realized. Except at the lowest mean flow velocity U, the average $C(x,t)$ of the relative concentration satisfies a convection-dispersion equation. The dispersion coefficient is studied as function of the relative magnitude of fluid velocity and of the velocity of buoyancy driven fluid motion. A model is suggested and its applicability to previous results obtained in $3D$ media is discussed.

Flow and transport are studied in transparent model fractures with rough complementary self-affine walls with a relative shear displacement $\vec{u}$. The aperture field is shown to display long range correlations perpendicular to $\vec{u}$: for flow in that direction, the width and geometry of the front of a dyed shear-thinning polymer solution displacing a transparent one have been studied as a function of the fluid rheology and flow rate. The front width increases linearly with distance indicating a convection of the fluids with a low transverse mixing between the flow paths. The width also increases with the flow-rate as the fluid rheology shifts from Newtonian at low shear rates $\dot \gamma$ towards a shear thinning behaviour at higher $\dot \gamma$ values. The width also increases with the polymer concentration at high flow-rates. These results demonstrate the enhancement of the flow velocity contrasts between different flow channels for shear thinning fluids. The relative widths at low and high $\dot \gamma$ values for different polymer concentrations are well predicted by an analytical model considering the fracture as a set of parallel ducts of constant hydraulic apertures. The overall geometry of the experimental front geometry is also predicted by the theoretical model from the aperture map.

A change of solute dispersion regime with the flow velocity has been studied both at the macroscopic and pore scales in a transparent array of capillary channels using an optical technique allowing for simultaneous local and global concentration mappings. Two solutions of different polymer concentrations ($500$ and $1000$~ppm) have been used at different Péclet numbers. At the macroscopic scale, the displacement front displays a diffusive spreading: for $Pe\ \leq \ 10$, the dispersivity $l_d$ is constant with $Pe$ and increases with the polymer concentration; for $Pe \ > \ 10$, $l_d$ increases as $Pe^{1.35}$ and is similar for the two concentrations. At the local scale, a time lag between the saturations of channels parallel and perpendicular to the mean flow has been observed and studied as a function of the flow rate. These local measurements suggest that the change of dispersion regime is related to variations of the degree of mixing at the junctions. For $Pe \ \leq \ 10$, complete mixing leads to pure geometrical dispersion enhanced for shear thinning fluids; for $Pe >10$ weaker mixing results in higher correlation lengths along flow paths parallel to the mean flow and in a combination of geometrical and Taylor dispersion.

The permeability anisotropy that results from a shear displacement ${\vec u}$ between the complementary self-affine walls of a rough fracture is investigated. Experiments in which a dyed fluid radially injected into a transparent fracture displaces a transparent one are presented. A clear anisotropy is observed in the presence of shear displacements and allows us to estimate the ratio of the permeabilities for flows parallel and perpendicular to ${\vec u}$. A simple model which accounts for the development of channels perpendicular to ${\vec u}$ qualitatively explains these results, and predicts a permeability decreasing (increasing) linearly with the variance of the aperture field for flow parallel (perpendicular) to the shear displacement. These predictions are then compared to the results of numerical simulations performed using a lattice-Boltzmann technique and to the anisotropies measured in displacement experiments.

Passive tracer dispersion in oscillating Poiseuille liquid flows of zero net velocity is studied experimentally in a Hele-Shaw cell and numerically by 2D simulations: this study is particularly focused on the time dependence and local properties of the dispersion. The dispersion mechanism is found to be controlled by the ratio τm/T of the molecular diffusion time across the gap and the oscillation period (when molecular diffusion parallel to the flow is negligible). The 2D numerical simulations complement the experiments by providing the local concentration c(x,z,t) at a given distance z from the cell walls (instead of only the average over z). Above a time lapse scaling like τm, the variation of c with the distance x along the flow becomes a Gaussian of width constant with z while the mean distance ¯x may depend both on z and t. For τm/T . 2, the front spreads through Taylor-like dispersion and the normalized dispersivity scales as τm/T. The front oscillates parallel to the flow with an amplitude constant across the gap; its width increases monotonically at a rate modulated at twice the flow frequency, due to variations of the instantaneous dispersivity. For τm/T & 20, the molecular diffusion distance during a period of the flow is smaller than the gap and the normalized dispersivity scales as (τm/T)−1 . The oscillations of the different points of the front follow the local fluid velocity: this produces a reversible modulation of the global front width at twice the flow frequency and in quadrature with that in the Taylor-like regime. Fil: Roht, Yanina Lucrecia. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Física. Grupo de Medios Porosos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Auradou, H.. Université Paris Sud; Francia Fil: Hulin, J. P.. Université Paris Sud; Francia Fil: Salin, D.. Université Paris Sud; Francia Fil: Chertcoff, Ricardo Héctor. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Física. Grupo de Medios Porosos; Argentina Fil: Ippolito, Irene Paula. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Física. Grupo de Medios Porosos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina