Downscaling of fracture energy during brittle creep experiments

We present mode 1 brittle creep fracture experiments along fracture surfaces that contain strength heterogeneities. Our observations provide a link between smooth macroscopic time-dependent failure and intermittent microscopic stress-dependent processes. We find the large-scale response of slow-propagating subcritical cracks to be well described by an Arrhenius law that relates the fracture speed to the energy release rate. At the microscopic scale, high-resolution optical imaging of the transparent material used (PMMA) allows detailed description of the fracture front. This reveals a local competition between subcritical and critical propagation (pseudo stick-slip front advances) independently of loading rates. Moreover, we show that the local geometry of the crack front is self-affine and the local crack front velocity is power law distributed. We estimate the local fracture energy distribution by combining high-resolution measurements of the crack front geometry and an elastic line fracture model. We show that the average local fracture energy is significantly larger than the value derived from a macroscopic energy balance. This suggests that homogenization of the fracture energy is not straightforward and should be taken cautiously. Finally, we discuss the implications of our results in the context of fault mechanics

Revolving rivers in sandpiles: from continuous to intermittent flows

In a previous paper [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 owing 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.Comment: 8 pages, 11 figures, submitted to Phys Rev

Influence of pore-scale disorder on viscous fingering during drainage

We study viscous fingering during drainage experiments in linear Hele-Shaw cells filled with a random porous medium. The central zone of the cell is found to be statistically more occupied than the average, and to have a lateral width of 40% of the system width, irrespectively of the capillary number $Ca$. A crossover length $w_f \propto Ca^{-1}$ separates lower scales where the invader's fractal dimension $D\simeq1.83$ is identical to capillary fingering, and larger scales where the dimension is found to be $D\simeq1.53$. The lateral width and the large scale dimension are lower than the results for Diffusion Limited Aggregation, but can be explained in terms of Dielectric Breakdown Model. Indeed, we show that when averaging over the quenched disorder in capillary thresholds, an effective law $v\propto (\nabla P)^2$ relates the average interface growth rate and the local pressure gradient.Comment: 4 pages, 4 figures, submitted to Phys Rev Letter

Numerical studies of aerofractures in porous media / Estudios numericos de aerofractures en medios porosos

During the hydraulically induced compaction of a granular layer fracture patterns arise. In numerical simulations we study how these patterns depend on the gas properties as well as on the properties of the porous medium. In particular the relation between the speed of fracture propagation and injection pressure is here studied in detail.Comment: Revista Cubana de Fisica, volume following the MarchCoMeeting'12 access on: http://www.fisica.uh.cu/biblioteca/revcubfis/index.php/component/content/article?id=3

Roughness and multiscaling of planar crack fronts

We consider numerically the roughness of a planar crack front within the long-range elastic string model, with a tunable disorder correlation length $\xi$. The problem is shown to have two important length scales, $\xi$ and the Larkin length $L_c$. Multiscaling of the crack front is observed for scales below $\xi$, provided that the disorder is strong enough. The asymptotic scaling with a roughness exponent $\zeta \approx 0.39$ is recovered for scales larger than both $\xi$ and $L_c$. If $L_c > \xi$, these regimes are separated by a third regime characterized by the Larkin exponent $\zeta_L \approx 0.5$. We discuss the experimental implications of our results.Comment: 8 pages, two figure

Simulating temporal evolution of pressure in two-phase flow in porous media

We have simulated the temporal evolution of pressure due to capillary and viscous forces in two-phase drainage in porous media. We analyze our result in light of macroscopic flow equations for two-phase flow. We also investigate the effect of the trapped clusters on the pressure evolution and on the effective permeability of the system. We find that the capillary forces play an important role during the displacements for both fast and slow injection rates and both when the invading fluid is more or less viscous than the defending fluid. The simulations are based on a network simulator modeling two-phase drainage displacements on a two-dimensional lattice of tubes.Comment: 12 pages, LaTeX, 14 figures, Postscrip

Intercalation-enhanced electric polarization and chain formation of nano-layered particles

Microscopy observations show that suspensions of synthetic and natural nano-layered smectite clay particles submitted to a strong external electric field undergo a fast and extended structuring. This structuring results from the interaction between induced electric dipoles, and is only possible for particles with suitable polarization properties. Smectite clay colloids are observed to be particularly suitable, in contrast to similar suspensions of a non-swelling clay. Synchrotron X-ray scattering experiments provide the orientation distributions for the particles. These distributions are understood in terms of competing (i) homogenizing entropy and (ii) interaction between the particles and the local electric field; they show that clay particles polarize along their silica sheet. Furthermore, a change in the platelet separation inside nano-layered particles occurs under application of the electric field, indicating that intercalated ions and water molecules play a role in their electric polarization. The resulting induced dipole is structurally attached to the particle, and this causes particles to reorient and interact, resulting in the observed macroscopic structuring. The macroscopic properties of these electro-rheological smectite suspensions may be tuned by controlling the nature and quantity of the intercalated species, at the nanoscale.Comment: 7 pages, 5 figure

Viscous stabilization of 2D drainage displacements with trapping

We investigate the stabilization mechanisms due to viscous forces in the invasion front during drainage displacement in two-dimensional porous media using a network simulator. We find that in horizontal displacement the capillary pressure difference between two different points along the front varies almost linearly as function of height separation in the direction of the displacement. The numerical result supports arguments taking into account the loopless displacement pattern where nonwetting fluid flow in separate strands (paths). As a consequence, we show that existing theories developed for viscous stabilization, are not compatible with drainage when loopless strands dominate the displacement process.Comment: The manuscript has been substantially revised. Accepted in Phys. Rev. Let

Burst dynamics during drainage displacements in porous media: Simulations and experiments

We investigate the burst dynamics during drainage going from low to high injection rate at various fluid viscosities. The bursts are identified as pressure drops in the pressure signal across the system. We find that the statistical distribution of pressure drops scales according to other systems exhibiting self-organized criticality. The pressure signal was calculated by a network model that properly simulates drainage displacements. We compare our results with corresponding experiments.Comment: 7 pages, 4 figures. Submitted to Europhys. Let

Determination of the Hurst Exponent by Use of Wavelet Transforms

We propose a new method for (global) Hurst exponent determination based on wavelets. Using this method, we analyze synthetic data with predefined Hurst exponents, fracture surfaces and data from economy. The results are compared with those obtained from Fourier spectral analysis. When many samples are available, the wavelet and Fourier methods are comparable in accuracy. However, when one or only a few samples are available, the wavelet method outperforms the Fourier method by a large margin.Comment: 10 pages RevTeX, 13 Postscript figures. Some additional material compared to previous versio