Laminar-turbulent cycles in inclined lock-exchange flows

Peer reviewedPublisher PD

Tracer Dispersion in Rough Open Cracks

Tracer dispersion is studied in an open crack where the two rough crack faces have been translated with respect to each other. The different dispersion regimes encountered in rough-wall Hele-Shaw cell are first introduced, and the geometric dispersion regime in the case of self-affine crack surfaces is treated in detail through perturbation analysis. It is shown that a line of tracer is progressively wrinkled into a self-affine curve with an exponent equal to that of the crack surface.This leads to a global dispersion coefficient which depends on the distance from the tracer inlet, but which is still proportional to the mean advection velocity. Besides, the tracer front is subjected to a local dispersion (as could be revealed by point measurements or echo experiments) very different from the global one. The expression of this anomalous local dispersion coefficient is also obtained

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.Comment: 4 page

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

Dynamical Janssen effect on granular packings with moving walls

Apparent mass measurements at the bottom of granular packings inside a vertical tube in relative motion are reported. They demonstrate that Janssen's model is valid over a broad range of velocities v. The variability of the measurements is lower than for static packings and the theoretical exponential increase of the apparent mass with the height of the packing is precisely followed (the corresponding characteristic screening length is of the order of the tube diameter). The limiting apparent mass at large heights is independent of v and significantly lower than the static value.Comment: 4 pages, 6 figures. accepted for publication in Phys. Rev. Lett. (2003

Experimental study of the transport properties of rough self-affine fractures

An experimental study of the transport properties of fluid-saturated joints composed of two complementary rough fracture surfaces, translated with respect to each other and brought in contact, is reported. Quantitative roughness measurements on different fractured granite samples show that the surfaces have a self-affine geometry from which the dependence of the mean aperture on the relative displacement of fracture surfaces kept in contact can be predicted. Variations of the hydraulic and electrical conductances of the joint are measured as functions of its mean aperture. A simple parallel plane model accounts for the global trend of the measurements, but significant deviations are observed when a relative lateral displacement of the surfaces is introduced. A theoretical analysis of their origin shows that they are due both to the randomness of the aperture field and to a nonzero local slope of the surface near the injection hole; the corresponding conductivity fluctuation amplitudes have power law and linear variations with the lateral displacement, and are enhanced by the radial injection geometry

Numerical study of geometrical dispersion in self-affine rough fractures

We report a numerical study of passive tracer dispersion in fractures with rough walls modeled as the space between two complementary self-affine surfaces rigidly translated with respect to each other. Geometrical dispersion due to the disorder of the velocity distribution is computed using the lubrication approximation. Using a spectral perturbative scheme to solve the flow problem and a mapping coordinate method to compute dispersion, we perform extensive ensemble averaged simulations to test theoretical predictions on the dispersion dependence on simple geometrical parameters. We observe the expected quadratic dispersion coefficient dependence on both the mean aperture and the relative shift of the crack as of well as the anomalous dispersion dependence on tracer traveling distance. We also characterize the anisotropy of the dispersion front, which progressively wrinkles into a self-affine curve whose exponent is equal to that of the fracture surface

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 $\dot \gamma$ 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