The statistics of particle velocities in dense granular flows

We present measurements of the particle velocity distribution in the flow of granular material through vertical channels. Our study is confined to dense, slow flows where the material shears like a fluid only in thin layers adjacent to the walls, while a large core moves without continuous deformation, like a solid. We find the velocity distribution to be non-Gaussian, anisotropic, and to follow a power law at large velocities. Remarkably, the distribution is identical in the fluid-like and solid-like regions. The velocity variance is maximum at the core, defying predictions of hydrodynamic theories. We show evidence of spatially correlated motion, and propose a mechanism for the generation of fluctuational motion in the absence of shear.Comment: Submitted to Phys. Rev. Let

Evidence of Sulfur Non-Innocence in [CoII(dithiacyclam)]2+-Mediated Catalytic Oxygen Reduction Reactions

In many metalloenzymes, sulfur-containing ligands participate in catalytic processes, mainly via the involvement in electron transfer reactions. In a biomimetic approach, we now demonstrate the implication of S-ligation in cobalt mediated oxygen reduction reactions (ORR). A comparative study between the catalytic ORR capabilities of the four-nitrogen bound [Co(cyclam)]2+ (1; cyclam=1,5,8,11-tetraaza-cyclotetradecane) and the S-containing analog [Co(S2N2-cyclam)]2+ (2; S2N2-cyclam=1,8-dithia-5,11-diaza-cyclotetradecane) reveals improved catalytic performance once the chalcogen is introduced in the Co coordination sphere. Trapping and characterization of the intermediates formed upon dioxygen activation at the CoII centers in 1 and 2 point to the involvement of sulfur in the O2 reduction process as the key for the improved catalytic ORR capabilities of 2

Analysis of pore-fluid pressure gradient and effective vertical-stress gradient distribution in layered hydrodynamic systems

A theoretical analysis is carried out to investigate the pore-fluid pressure gradient and effective vertical-stress gradient distribution in fluid saturated porous rock masses in layered hydrodynamic systems. Three important concepts, namely the critical porosity of a porous medium, the intrinsic Fore-fluid pressure and the intrinsic effective vertical stress of the solid matrix, are presented and discussed. Using some basic scientific principles, we derive analytical solutions and explore the conditions under which either the intrinsic pore-fluid pressure gradient or the intrinsic effective vertical-stress gradient can be maintained at the value of the lithostatic pressure gradient. Even though the intrinsic pore-fluid pressure gradient can be maintained at the value of the lithostatic pressure gradient in a single layer, it is impossible to maintain it at this value in all layers in a layered hydrodynamic system, unless all layers have the same permeability and porosity simultaneously. However, the intrinsic effective vertical-stress gradient of the solid matrix can be maintained at a value close to the lithostatic pressure gradient in all layers in any layered hydrodynamic system within the scope of this study

Interface modeling in incompressible media using level sets in Escript

We use a finite element (FEM) formulation of the level set method to model geological fluid flow problems involving interface propagation. Interface problems are ubiquitous in geophysics. Here we focus on a Rayleigh-Taylor instability, namely mantel plumes evolution, and the growth of lava domes. Both problems require the accurate description of the propagation of an interface between heavy and light materials (plume) or between high viscous lava and low viscous air (lava dome), respectively. The implementation of the models is based on Escript which is a Python module for the solution of partial differential equations (PDEs) using spatial discretization techniques such as FEM. It is designed to describe numerical models in the language of PDEs while using computational components implemented in C and C++ to achieve high performance for time-intensive, numerical calculations. A critical step in the solution geological flow problems is the solution of the velocity-pressure problem. We describe how the Escript module can be used for a high-level implementation of an efficient variant of the well-known Uzawa scheme. We begin with a brief outline of the Escript modules and then present illustrations of its usage for the numerical solutions of the problems mentioned above

Convective instability of 3-D fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the convective instability of 3-D fluid-saturated geological fault zones when they are heated uniformly from below. In particular, we have derived exact analytical solutions for the critical Rayleigh numbers of different convective flow structures. Using these critical Rayleigh numbers, three interesting convective flow structures have been identified in a geological fault zone system. It has been recognized that the critical Rayleigh numbers of the system have a minimum value only for the fault zone of infinite length, in which the corresponding convective flow structure is a 2-D slender-circle flow. However, if the length of the fault zone is finite, the convective flow in the system must be 3-D. Even if the length of the fault zone is infinite, since the minimum critical Rayleigh number for the 2-D slender-circle flow structure is so close to that for the 3-D convective flow structure, the system may have almost the same chance to pick up the 3-D convective flow structures. Also, because the convection modes are so close for the 3-D convective flow structures, the convective flow may evolve into the 3-D finger-like structures, especially for the case of the fault thickness to height ratio approaching zero. This understanding demonstrates the beautiful aspects of the present analytical solution for the convective instability of 3-D geological fault zones, because the present analytical solution is valid for any value of the ratio of the fault height to thickness. Using the present analytical solution, the conditions, under which different convective flow structures may take place, can be easily determined

Signatures of granular microstructure in dense shear flows

Granular materials react to shear stresses differently than do ordinary fluids. Rather than deforming uniformly, materials such as dry sand or cohesionless powders develop shear bands: narrow zones containing large relative particle motion leaving adjacent regions essentially rigid[1,2,3,4,5]. Since shear bands mark areas of flow, material failure and energy dissipation, they play a crucial role for many industrial, civil engineering and geophysical processes[6]. They also appear in related contexts, such as in lubricating fluids confined to ultra-thin molecular layers[7]. Detailed information on motion within a shear band in a three-dimensional geometry, including the degree of particle rotation and inter-particle slip, is lacking. Similarly, only little is known about how properties of the individual grains - their microstructure - affect movement in densely packed material[5]. Combining magnetic resonance imaging, x-ray tomography, and high-speed video particle tracking, we obtain the local steady-state particle velocity, rotation and packing density for shear flow in a three-dimensional Couette geometry. We find that key characteristics of the granular microstructure determine the shape of the velocity profile.Comment: 5 pages, incl. 4 figure

Shearing of loose granular materials: A statistical mesoscopic model

A two-dimensional lattice model for the formation and evolution of shear bands in granular media is proposed. Each lattice site is assigned a random variable which reflects the local density. At every time step, the strain is localized along a single shear-band which is a spanning path on the lattice chosen through an extremum condition. The dynamics consists of randomly changing the `density' of the sites only along the shear band, and then repeating the procedure of locating the extremal path and changing it. Starting from an initially uncorrelated density field, it is found that this dynamics leads to a slow compaction along with a non-trivial patterning of the system, with high density regions forming which shelter long-lived low-density valleys. Further, as a result of these large density fluctuations, the shear band which was initially equally likely to be found anywhere on the lattice, gets progressively trapped for longer and longer periods of time. This state is however meta-stable, and the system continues to evolve slowly in a manner reminiscent of glassy dynamics. Several quantities have been studied numerically which support this picture and elucidate the unusual system-size effects at play.Comment: 11 pages, 15 figures revtex, submitted to PRE, See also: cond-mat/020921