Miscible displacement fronts of shear thinning fluids inside rough fractures

The miscible displacement of a shear-thinning fluid by another of same rheological properties is studied experimentally in a transparent fracture by an optical technique imaging relative concentration distributions. The fracture walls have complementary self-affine geometries and are shifted laterally in the direction perpendicular to the mean flow velocity {\bf U} : the flow field is strongly channelized and macro dispersion controls the front structure for P\'{e}clet numbers above a few units. The global front width increases then linearly with time and reflects the velocity distribution between the different channels. In contrast, at the local scale, front spreading is similar to Taylor dispersion between plane parallel surfaces. Both dispersion mechanisms depend strongly on the fluid rheology which shifts from Newtonian to shear-thinning when the flow rate increases. In the latter domain, increasing the concentration enhances the global front width but reduces both Taylor dispersion (due to the flattening of the velocity profile in the gap of the fracture) and the size of medium scale front structures

Deformation of a flexible fiber in a viscous flow past an obstacle

We study the deformation and transport of elastic fibers in a viscous Hele-Shaw flow with curved streamlines. The variations of the global velocity and orientation of the fiber follow closely those of the local flow velocity. The ratios of the curvatures of the fibers by the corresponding curvatures of the streamlines reflect a balance between elastic and viscous forces: this ratio is shown experimentally to be determined by a dimensionless {\it Sperm number} $Sp$ combining the characteristic parameters of the flow (transverse velocity gradient, viscosity, fiber diameter/cell gap ratio) and those of the fiber (diameter, effective length, Young's modulus). For short fibers, the effective length is that of the fiber; for long ones, it is equal to the transverse characteristic length of the flow. For $S\_p \lesssim 250$, the ratio of the curvatures increases linearly with $Sp$; For $S\_p \gtrsim 250$, the fiber reaches the same curvature as the streamlines

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 cut-off length \xi = 0.15 W. This low zeta value is in agreement with measurements on other sandstones and on sintered materials. The probability distributions P(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 normalisation and do not display multifractal 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 occurence of brittle fracture (instead of damage failure in materials displaying a higher value of zeta = 0.8).Comment: 7 page

Oscillations and translation of a free cylinder in a confined flow

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

Numerical study of the temperature and porosity effects on the fracture propagation in a 2D network of elastic bonds

This article reports results concerning the fracture of a 2d triangular lattice of atoms linked by springs. The lattice is submitted to controlled strain tests and the influence of both porosity and temperature on failure is investigated. The porosity is found on one hand to decrease the stiffness of the material but on the other hand it increases the deformation sustained prior to failure. Temperature is shown to control the ductility due to the presence of cavities that grow and merge. The rough surfaces resulting from the propagation of the crack exhibit self-affine properties with a roughness exponent $\zeta = 0.59 \pm 0.07$ over a range of length scales which increases with temperature. Large cavities also have rough walls which are found to be fractal with a dimension, $D$, which evolves with the distance from the crack tip. For large distances, $D$ is found to be close to 1.5, and close to 1.0 for cavities just before their coalescence with the main crack

Influence of flow confinement on the drag force on a static cylinder

The influence of confinement on the drag force $F$ on a static cylinder in a viscous flow inside a rectangular slit of aperture $h_0$ has been investigated from experimental measurements and numerical simulations. At low enough Reynolds numbers, $F$ varies linearly with the mean velocity and the viscosity, allowing for the precise determination of drag coefficients $\lambda_{||}$ and $\lambda_{\bot}$ corresponding respectively to a mean flow parallel and perpendicular to the cylinder length $L$. In the parallel configuration, the variation of $\lambda_{||}$ with the normalized diameter $\beta = d/h_0$ of the cylinder is close to that for a 2D flow invariant in the direction of the cylinder axis and does not diverge when $\beta = 1$. The variation of $\lambda_{||}$ with the distance from the midplane of the model reflects the parabolic Poiseuille profile between the plates for $\beta \ll 1$ while it remains almost constant for $\beta \sim 1$. In the perpendicular configuration, the value of $\lambda_{\bot}$ is close to that corresponding to a 2D system only if $\beta \ll 1$ and/or if the clearance between the ends of the cylinder and the side walls is very small: in that latter case, $\lambda_{\bot}$ diverges as $\beta \to 1$ due to the blockage of the flow. In other cases, the side flow between the ends of the cylinder and the side walls plays an important part to reduce $\lambda_{\bot}$: a full 3D description of the flow is needed to account for these effects

Shaping gels and gels mixture to create helices

In cooking, food gels, such as agar-agar or alginate, are often prepared and presented in the form of spheres or spaghetti. While experimenting in our kitchen, we realized that it is quite difficult to make more advanced shapes. In this study, we sought to develop new methods to obtain more complex shapes. Our first challenge was to obtain helices. The best method we selected was to deposit the solutions before their gelation in a thread. The robustness of the method is tested by systematically changing the thread pitch, diameter, and depth. From the deformation under its own weight, we propose to deduce the mechanical characteristics of the helix. These values are compared to those obtained in the laboratory using indentation testing. Finally, we experimented with mixed gels obtained by combining agar-agar and alginate.Fil: D'angelo, María Verónica. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Física. Grupo de Medios Porosos; ArgentinaFil: Pauchard, L.. Centre National de la Recherche Scientifique; FranciaFil: Auradou, H.. Centre National de la Recherche Scientifique; FranciaFil: Darbois Texier, B.. Centre National de la Recherche Scientifique; Franci

Relation Between First Arrival Time and Permeability in Self-Affine Fractures with Areas in Contact

We demonstrate that the first arrival time in dispersive processes in self-affine fractures are governed by the same length scale characterizing the fractures as that which controls their permeability. In one-dimensional channel flow this length scale is the aperture of the bottle neck, i.e., the region having the smallest aperture. In two dimensions, the concept of a bottle neck is generalized to that of a minimal path normal to the flow. The length scale is then the average aperture along this path. There is a linear relationship between the first arrival time and this length scale, even when there is strong overlap between the fracture surfaces creating areas with zero permeability. We express the first arrival time directly in terms of the permeability.Comment: EPL (2012)