Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications

There is a special reason for reviewing this book at this time: it is the 50th edition of a compendium that is known and used frequently in most chemical and physical laboratories in many parts of the world. Surely, a publication that has been published for 56 years, withstanding the vagaries of science in this century, must have had something to offer. There is another reason: while the book is a standard fixture in most chemical and physical laboratories, including those in medical centers, it is not as frequently seen in the laboratories of physician's offices (those either in solo or group practice). I believe that the Handbook can be useful in those laboratories. One of the reasons, among others, is that the various basic items of information it offers may be helpful in new tests, either physical or chemical, which are continuously being published. The basic information may relate

Handbook of Chemistry and Physics

The behaviour of dense assemblies of dry grains submitted to continuous shear deformation has been the subject of many experiments and discrete particle simulations. This paper is a collective work carried out among the French research group Groupement de Recherche Milieux Divises (GDR MiDi). It proceeds from the collection of results on steady uniform granular flows obtained by different groups in six different geometries both in experiments and numerical works. The goal is to achieve a coherent presentation of the relevant quantities to be measured i.e. flowing thresholds, kinematic profiles, effective friction, etc. First, a quantitative comparison between data coming from different experiments in the same geometry identifies the robust features in each case. Second, a transverse analysis of the data across the different configurations, allows us to identify the relevant dimensionless parameters, the different flow regimes and to propose simple interpretations. The present work, more than a simple juxtaposition of results, demonstrates the richness of granular flows and underlines the open problem of defining a single rheology.

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On dense granular flows.

1. Place animal in induction chamber and anesthetize the mouse and ensure sedation. 2. Once the animal is sedated, move it to a nose cone for hair removal using cream. Only apply cream to the area of the chest that will be utilized for imaging. Once the hair is removed, wipe area with wet gauze to ensure all hair is removed. 3. Move the animal to the imaging platform and tape its paws to the ECG lead plates and insert rectal probe. Body temperature should be maintained at 36-37°C. During imaging, reduce anesthesia to maintain proper heart rate. If the animal shows signs of being awake, use a higher concentration of anesthetic.

人唾液天疱疮抗原的纯化

The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

/pdf/validity-of-cubic-law-for-fluid-flow-in-a-deformable-rock-2ynq4id3hq.pdf

VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

The displacement of water molecules associated with the flow of water inside a nonconsolidated packing of 800 μm OD glass spheres has been measured by a pulsed gradient NMR technique. Using a stimulated spin‐echo sequence, mean displacements of up to 300 μm corresponding to measurement times of up to 200 ms can be analyzed. The measurement can be quantitatively calibrated using the pure molecular self‐diffusion of water at zero flow conditions. For molecular displacements much smaller than the pore size, the distribution of the flow velocity component along the mean flow direction is determined at Reynolds numbers high enough so that longitudinal molecular diffusion is negligible. An exponential decay of the probability distribution of the displacements is observed at large distances. The results are very similar to those obtained by numerical solution of the Stokes equation in random sphere packings. At longer displacement distances, a secondary peak of the displacement distribution is observed: It is interpreted as the first step toward the transition toward classical dispersion at displacements much larger than the pore size. The influence of molecular diffusion and of the heterogeneities of the magnetic permeability also are discussed.

Pulsed gradient NMR measurements and numerical simulation of flow velocity distribution in sphere packings

[1] The permeability anisotropy that results from a shear displacement between the complementary self-affine walls of a rough fracture is investigated. Experiments in which a dyed fluid radially injected into a transparent fracture displaces a transparent one are presented. A clear anisotropy is observed in the presence of shear displacements and allows us to estimate the ratio of the permeabilities for flows parallel and perpendicular to . A simple model which accounts for the development of channels perpendicular to qualitatively explains these results and predicts a permeability decreasing (increasing) linearly with the variance of the aperture field for flow parallel (perpendicular) to the shear displacement. These predictions are then compared to the results of numerical simulations performed using a lattice Boltzmann technique and to the anisotropies measured in displacement experiments.

https://hal.archives-ouvertes.fr/hal-00003775/document

Permeability anisotropy induced by the shear displacement of rough fracture walls

http://www.fast.u-psud.fr/~hulin/papers/geothermics_sfili_06.pdf

Flow channeling in a single fracture induced by shear displacement

We compare high resolution roughness measurements on fractured granite, basalt and sandstone samples. For granite and basalt, the fractures display over the full experimental length scale range a self-affine geometry with a characteristic Hurst exponent consistent with the value 0.8 suggested to be universal by several authors. For sandstone, the rugosity spectrum reMayns independent on the fracturation velocity but displays self-affine characteristics only for characteristic length scales roughly larger than the grain size: furthermore, the corresponding Hurst exponent takes a value 0.47 ± 0.05 distinctly smaller than the previous one. At characteristic length scales below the grain size, a clear cutoff is observed in the spectrum. This cut-off is shown through numerical simulations to be largely explainable by the faceted shape of the sand grains and to a minor degree by the finite size of the profilometer sensor tip. None of these factors seems to influence the low frequency part of the spectrum from which Hurst's exponent is determined. The differences between the values of Hurst's exponent may reflect the intergranular nature of fracture in the sandstone samples while no effect of structural heterogeneities on fracture propagation is observed in granite.

Jean-Pierre Hulin

Papers

Pulsed gradient NMR measurements and numerical simulation of flow velocity distribution in sphere packings

Permeability anisotropy induced by the shear displacement of rough fracture walls

Flow channeling in a single fracture induced by shear displacement

Experimental analysis of fracture rugosity in granular and compact rocks

Physical Hydrodynamics, 2nd Edn