arXiv subjects

Harold Auradou

Publications and source records attributed to Harold Auradou.

34 records · Page 2Linked to original sources

arXiv2010

Analytical shape determination of fiber-like objects with Virtual Image Correlation

This paper reports a method allowing for the determination of the shape of deformed fiber-like objects. Compared to existing methods, it provides analytical results including the local slope and curvature which are of first importance, for instance, in beam mechanics. The presented VIC (Virtual Image Correlation) method consists in looking for the best correlation between the image of the fiber-like object and a virtual beam image, using an algorithm close to the Digital Image Correlation method developed in experimental solid mechanics. The computation only involves the part of the image in the vicinity of the fiber: the method is thus insensitive to the picture background and the computational cost remains low. Two examples are reported: the first proves the precision of the method, the second its ability to identify a complex shape with multiple loops.

cs.CV↗

arXiv2009

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 $λ_{||}$ and $λ_{\bot}$ corresponding respectively to a mean flow parallel and perpendicular to the cylinder length $L$. In the parallel configuration, the variation of $λ_{||}$ with the normalized diameter $β= d/h_0$ of the cylinder is close to that for a 2D flow invariant in the direction of the cylinder axis and does not diverge when $β= 1$. The variation of $λ_{||}$ with the distance from the midplane of the model reflects the parabolic Poiseuille profile between the plates for $β\ll 1$ while it remains almost constant for $β\sim 1$. In the perpendicular configuration, the value of $λ_{\bot}$ is close to that corresponding to a 2D system only if $β\ll 1$ and/or if the clearance between the ends of the cylinder and the side walls is very small: in that latter case, $λ_{\bot}$ diverges as $β\to 1$ 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 $λ_{\bot}$: a full 3D description of the flow is needed to account for these effects.

physics.flu-dyn↗

arXiv2009

Geometrical and transport properties of single fractures: influence of the roughness of the fracture walls

This article reviews the main features of the transport properties of single fractures. A particular attention paid to fractures in geological materials which often display a roughness covering a broad range of length scales. Because of the small distance separating the fracture walls, the surface roughness is a key parameter influencing the structure of the void space. Studies devoted to the characterization of the surface roughness are presented as well as works aimed at characterizing the void space geometry. The correlation of the free space is found to be crucially function of the failure mechanism (brittle, quasi brittle or plastic...) but also of possible shear displacements during the failure. The influence of the surface roughness on the mechanical behavior of fractures under a normal load and a shear stress is also described. Finally, experimental, numerical and theoretical works devoted to the study of the influence of the fracture void geometry on the permeability and on the hydrodynamic dispersion of a dissolved species are discussed.

physics.geo-ph↗

arXiv2009

Miscible transfer of solute in different types of rough fractures: from random to multiscale fracture walls heights

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 Péclet 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 $\vecδ$ of complementary walls, the aperture field is channelized in the direction perpendicular to $δ$. 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 $\vec U$.

physics.flu-dyn↗

arXiv2008

Anisotropy of tracer dispersion in rough model fractures with sheared walls

Dispersion experiments are compared for two transparent model fractures with identical complementary rough walls but with a relative shear displacement $\vecδ$ parallel ($\vecδ\parallel \vec{U}$) or perpendicular ($\vecδ \perp \vec{U}$) 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 $α(x,y)$. For $\vecδ \perp \vec{U}$, 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 $\vecδ \parallel \vec{U}$, the front is flatter and $α(x,y)$ displays a narrow distribution and a Taylor-like variation with $Pe$.

physics.geo-ph↗

arXiv2008

Single fiber transport by a fluid flow in a fracture with rough walls: influence of the fluid rheology

The possible transport of fibers by fluid flow in fractures is investigated experimentally in transparent models using flexible polyester thread (mean diameter $280 μ\mathrm{m}$) and Newtonian and shear thinning fluids. In the case of smooth parallel walls, fibers of finite length $\ell = 20-150 \mathrm{mm}$ move at a constant velocity of the order of the maximum fluid velocity in the aperture. In contrast, for fibers lying initially at the inlet side of the model and dragged by the flow inside it, the velocity increases with the depth of penetration (this results from the lower velocity - and drag - in the inlet part). In both cases, the friction of the fiber with the smooth walls is weak. For rough self-affine walls and a continuous gradient of the local mean aperture transverse to the flow, transport of the fibers by a water flow is only possible in the region of larger aperture ($\bar{a} \gtrsim 1.1 \mathrm{mm}$) and is of "stop and go" type at low velocities. Time dependent distorsions of the fiber are also often observed. When water is replaced by a shear thinning polymer solution, the fibers move faster and continuously in high aperture regions and their friction with the walls is reduced. Fiber transport becomes also possible in narrower regions where irreversible pinning occurred for water. In a third rough model with no global aperture gradient but with rough walls and a channelization parallel to the mean flow, fiber transport was only possible in shear-thinning flows and pinning and entanglement effects were studied.

physics.flu-dyn↗

arXiv2008

Dispersion enhancement and damping by buoyancy driven flows in 2D networks of capillaries

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.

physics.flu-dyn↗

arXiv2007

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 ξ= 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).

cond-mat.stat-mech↗

arXiv2007

Velocity contrasts enhancement for shear thinning solutions flowing in a rough fracture

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 $\dot γ$ towards a shear thinning behaviour at higher $\dot γ$ 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 $\dot γ$ 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.

physics.flu-dyn↗

arXiv2006

Pore scale mixing and macroscopic solute dispersion regimes in polymer flows inside 2D model networks

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.

physics.flu-dyn↗

arXiv2006

Influence of the disorder on tracer dispersion in a flow channel

Tracer dispersion is studied experimentally in periodic or disordered arrays of beads in a capillary tube. Dispersion is measured from light absorption variations near the outlet following a steplike injection of dye at the inlet. Visualizations using dye and pure glycerol are also performed in similar geometries. Taylor dispersion is dominant both in an empty tube and for a periodic array of beads: the dispersivity $l\_d$ increases with the Péclet number $Pe$ respectively as $Pe$ and $Pe^{0.82}$ and is larger by a factor of 8 in the second case. In a disordered packing of smaller beads (1/3 of the tube diameter) geometrical dispersion associated to the disorder of the flow field is dominant with a constant value of $l\_d$ reached at high Péclet numbers. The minimum dispersivity is slightly higher than in homogeneous nonconsolidated packings of small grains, likely due heterogeneities resulting from wall effects. In a disordered packing with the same beads as in the periodic configuration, $l\_d$ is up to 20 times lower than in the latter and varies as $Pe^α$ with $α= 0.5$ or $= 0.69$ (depending on the fluid viscosity). A simple model accounting for this latter result is suggested.

physics.flu-dyn↗

arXiv2006

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 Péclet 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.

physics.flu-dyn↗

arXiv2006

Low self-affine exponents of fracture surfaces of glass ceramics

The geometry of post mortem rough fracture surfaces of porous glass ceramics made of sintered glass beads is shown experimentally to be self-affine with an exponent zeta=0.40 (0.04) remarkably lower than the 'universal' value zeta=0.8 frequently measured for many materials. This low value of zeta is similar to that found for sandstone samples of similar micro structure and is also practically independent on the porosity phi in the range investigated (3% < phi < 26%) as well as on the bead diameter d and of the crack growth velocity. In contrast, the roughness amplitude normalized by d increases linearly with phi while it is still independent, within experimental error, of d and of the crack propagation velocity. An interpretation of this variation is suggested in terms of a transition from transgranular to intergranular fracture propagation with no influence, however, on the exponent zeta.

cond-mat.stat-mech↗

arXiv2006

Flow channelling in a single fracture induced by shear displacement

The effect on the transport properties of fractures of a relative shear displacement $\vec u$ of rough walls with complementary self-affine surfaces has been studied experimentally and numerically. The shear displacement $\vec u$ induces an anisotropy of the aperture field with a correlation length scaling as $u$ and significantly larger in the direction perpendicular to $\vec u$. This reflects the appearance of long range channels perpendicular to $\vec u$ resulting in a higher effective permeability for flow in the direction perpendicular to the shear. Miscible displacements fronts in such fractures are observed experimentally to display a self affine geometry of characteristic exponent directly related to that of the rough wall surfaces. A simple model based on the channelization of the aperture field allows to reproduces the front geometry when the mean flow is parallel to the channels created by the shear displacement.

physics.flu-dyn↗

arXiv2006

Anisotropic self-affine properties of experimental fracture surfaces

The scaling properties of post-mortem fracture surfaces of brittle (silica glass), ductile (aluminum alloy) and quasi-brittle (mortar and wood) materials have been investigated. These surfaces, studied far from the initiation, were shown to be self-affine. However, the Hurst exponent measured along the crack direction is found to be different from the one measured along the propagation direction. More generally, a complete description of the scaling properties of these surfaces call for the use of the 2D height-height correlation function that involves three exponents zeta = 0.75, beta = 0.6 and z = 1.25 independent of the material considered as well as of the crack growth velocity. These exponents are shown to correspond to the roughness, growth and dynamic exponents respectively, as introduced in interface growth models. They are conjectured to be universal.

cond-mat.stat-mech↗

arXiv2005

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 $ζ= 0.59 \pm 0.07$ 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.

physics.class-ph↗