Coupled air/granular flow in a linear Hele-Shaw cell.

We investigate experimentally the pattern formation process during injection of air in a noncohesive granular material confined in a linear Hele-Shaw cell. We characterize the features and dynamics of this pattern formation on the basis of fast image analysis and sensitive pressure measurements. Behaviors are classified using two parameters--injection pressure and plate opening--and four hydrodynamic regimes are defined. For some regions of the parameter space, flows of air and grains are shown to be strongly coupled and instable, and lead to channelization within the granular material with obvious large-scale permeability variations.

Revolving rivers in sandpiles: from continuous to intermittent flows.

In a previous paper [E. Altshuler, Phys. Rev. Lett. 91, 014501 (2003)], the mechanism of "revolving rivers" for sandpile formation is reported: As a steady stream of dry sand is poured onto a horizontal surface, a pile forms which has a river of sand on one side flowing from the apex of the pile to the edge of the base. For small piles the river is steady, or continuous. For larger piles, it becomes intermittent. In this paper we establish experimentally the "dynamical phase diagram" of the continuous and intermittent regimes, and give further details of the piles' "topography," improving the previous kinematic model to describe it and shedding further light on the mechanisms of river formation. Based on experiments in Hele-Shaw cells, we also propose that a simple dimensionality reduction argument can explain the transition between the continuous and intermittent dynamics.

Decompaction and fluidization of a saturated and confined granular medium by injection of a viscous liquid or gas.

We compare quantitatively two experimental situations concerning injection of a miscible fluid into an initially jammed granular medium saturated with the same fluid, confined in a Hele-Shaw cell. The two experiments are identical, apart from the interstitial and injected fluid, which is in one case air injected into a dry granular packing, and in the other case silicone oil injected into a dense suspension. In spite of the strong differences regarding the nature of the two fluids, strikingly similar dynamical and geometrical features are identified as functions of the control parameters: cell thickness and applied fluid injection pressure. In both cases an initial hydrodynamically driven decompaction process controls the unjamming and prepares the final displacement process characterized by fingerlike patterns empty of grains. The pattern shapes are comparable. In addition, the mobilities of the coupled fluid-grain flow, rescaled by the interstitial fluid viscosity and grain diameter squared, are of the same range and behave comparably. The mobility proves to depend on the initial solid fraction of the medium. Subtle differences are observed in geometrical aspects like the finger width with respect to the control parameters.

Scaling of crack surfaces and implications for fracture mechanics

The scaling laws describing the roughness development of crack surfaces are incorporated into the Griffith criterion. We show that, in the case of a Family-Vicsek scaling, the energy balance leads to a purely elastic brittle behavior. On the contrary, it appears that an anomalous scaling reflects an R-curve behavior associated with a size effect of the critical resistance to crack growth in agreement with the fracture process of heterogeneous brittle materials exhibiting a microcracking damage.

Distinguishing fractional and white noise in one and two dimensions.

We discuss the link between uncorrelated noise and the Hurst exponent for one- and two-dimensional interfaces. We show that long range correlations cannot be observed using one-dimensional cuts through two-dimensional self-affine surfaces whose height distributions are characterized by a Hurst exponent H lower than -1/2. In this domain, fractional and white noise are not distinguishable. A method analyzing the correlations in two dimensions is necessary. For H>-1/2, a crossover regime leads to an systematic overestimate of the Hurst exponent.

Shear with comminution of a granular material: microscopic deformations outside the shear band.

A correlation imaging velocimetry technique is applied to recover displacement fields in a granular material subjected to extended shear. A thick (10 cm) annular sand sample (grain size: 1 mm) is confined at constant pressure (sigma=0.5 MPa) against a rough moving wall displacing at very low speed (delta=83 microm s(-1)). Localization of the strain rapidly forms a shear band (seven particles wide) in which comminution develops. We focused on the strain field outside this shear band and observed a rich dynamics of large and intermittent mechanical clusters (up to 50 particles wide). Quantitative description of the radial velocity profile outside the shear band reveals an exponential decrease. However, a significant slip evolution of the associated characteristic length is observed, indicative of a slow decoupling between the shear band and the rest of the sample. This slow evolution is shown to be well described by power laws with the imposed slip, and has important implications for friction laws and earthquake physics.

Hydrothermal coupling in a self-affine rough fracture.

The influence of the multiscale fracture roughness on the heat exchange when a cold fluid enters a fractured hot solid is studied numerically on the basis of the Stokes equation and in the limit of both hydrolubrication and thermolubrication. The geometrical complexity of the fracture aperture is modeled by small self-affine perturbations added to a uniform aperture field. Thermal and hydraulic properties are characterized via the definition of hydraulic and thermal apertures both at microscopic and macroscopic scales and obtained by comparing the fluxes to the ones of flat fractures. Statistics over a large number of fracture configurations provide an estimate of the average behavior and its variability. We show that the long-range correlations of the fracture roughness induces strong channeling effects that significantly influence the hydraulic and thermal properties. An important parameter is the aspect ratio (length over width) of the fracture: we show, for example, that a downstream elongated rough fracture is more likely to inhibit the hydraulic flow and subsequently to enhance the thermal exchange. Fracture roughness might, in the opposite configuration, favor strong channeling which inhibits heating of the fluid. The thermal behavior is in general shown to be mainly dependent on the hydraulic one, which is expressed through a simple law.

Dynamical event during slow crack propagation.

We address the role of material heterogeneities on the propagation of a slow rupture at laboratory scale. With a high speed camera, we follow an in-plane crack front during its propagation through a transparent heterogeneous Plexiglas block. We obtain two major results. First, the slip along the interface is strongly correlated over scales much larger than the asperity sizes. Second, the dynamics is scale dependent. Locally, mechanical instabilities are triggered during asperity depinning and propagate along the front. The intermittent behavior at the asperity scale is in contrast with the large scale smooth creeping evolution of the average crack position. The dynamics is described on the basis of a Family-Vicsek scaling.

High resolution description of a crack front in a heterogeneous Plexiglas block.

We study experimentally the propagation of an in-plane fracture into a transparent and heterogeneous Plexiglas block. A stable crack propagation in mode I is monitored by an imposed displacement. The experimental setup allows a high resolution observation of the crack front in situ. Self-affine properties of the crack front are described over more than three decades using several techniques: variable bandwidth, return probability, Fourier spectrum, and wavelet analysis. The different methods lead to a roughness exponent of 0.63+/-0.03, consistent with a previous work.

Roughness of stylolites: implications of 3D high resolution topography measurements.

Stylolites are natural pressure-dissolution surfaces in sedimentary rocks. We present 3D high resolution measurements at laboratory scales of their complex roughness. The topography is shown to be described by a self-affine scaling invariance. At large scales, the Hurst exponent is zeta(1) approximately 0.5 and very different from that at small scales where zeta(2) approximately 1.2. A crossover length scale at around L(c)=1 mm is well characterized. Measurements are consistent with a Langevin equation that describes the growth of a stylolitic interface as a competition between stabilizing long range elastic interactions at large scales or local surface tension effects at small scales and a destabilizing quenched material disorder.

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.

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.