Pore-scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings

We propose a method for effectively upscaling incompressible viscous flow in large random polydispersed sphere packings: the emphasis of this method is on the determination of the forces applied on the solid particles by the fluid. Pore bodies and their connections are defined locally through a regular Delaunay triangulation of the packings. Viscous flow equations are upscaled at the pore level, and approximated with a finite volume numerical scheme. We compare numerical simulations of the proposed method to detailed finite element (FEM) simulations of the Stokes equations for assemblies of 8 to 200 spheres. A good agreement is found both in terms of forces exerted on the solid particles and effective permeability coefficients

Stress-dependent electrical transport and its universal scaling in granular materials

We experimentally and numerically examine stress-dependent electrical transport in granular materials to elucidate the origins of their universal dielectric response. The ac responses of granular systems under varied compressive loadings consistently exhibit a transition from a resistive plateau at low frequencies to a state of nearly constant loss at high frequencies. By using characteristic frequencies corresponding to the onset of conductance dispersion and measured direct-current resistance as scaling parameters to normalize the measured impedance, results of the spectra under different stress states collapse onto a single master curve, revealing well-defined stress-independent universality. In order to model this electrical transport, a contact network is constructed on the basis of prescribed packing structures, which is then used to establish a resistor-capacitor network by considering interactions between individual particles. In this model the frequency-dependent network response meaningfully reproduces the experimentally observed master curve exhibited by granular materials under various normal stress levels indicating this universal scaling behaviour is found to be governed by i) interfacial properties between grains and ii) the network configuration. The findings suggest the necessity of considering contact morphologies and packing structures in modelling electrical responses using network-based approaches.Comment: 12 pages, 4 figure

The effects of packing structure on the effective thermal conductivity of granular media: A grain scale investigation

Structural characteristics are considered to be the dominant factors in determining the effective properties of granular media, particularly in the scope of transport phenomena. Towards improved heat management, thermal transport in granular media requires an improved fundamental understanding. In this study, the effects of packing structure on heat transfer in granular media are evaluated at macro- and grain-scales. At the grain-scale, a gas-solid coupling heat transfer model is adapted into a discrete-element-method to simulate this transport phenomenon. The numerical framework is validated by experimental data obtained using a plane source technique, and the Smoluschowski effect of the gas phase is found to be captured by this extension. By considering packings of spherical SiO2 grains with an interstitial helium phase, vibration induced ordering in granular media is studied, using the simulation methods developed here, to investigate how disorder-to-order transitions of packing structure enhance effective thermal conductivity. Grain-scale thermal transport is shown to be influenced by the local neighbourhood configuration of individual grains. The formation of an ordered packing structure enhances both global and local thermal transport. This study provides a structure approach to explain transport phenomena, which can be applied in properties modification for granular media.Comment: 11 figures, 29 page

Charging changes contact composition in binary sphere packings

Equal volume mixtures of small and large polytetrafluorethylene (PTFE) spheres are shaken in an atmosphere of controlled humidity which allows to also control their tribo-charging. We find that the contact numbers are charge-dependent: as the charge density of the beads increases, the number of same-type contacts decreases and the number of opposite-type contacts increases. This change is not caused by a global segregation of the sample. Hence, tribo-charging can be a way to tune the local composition of a granular material.Comment: 7 Pages, 5 Figure

Packing Characteristics of Different Shaped Proppants for use with Hydrofracing - A Numerical Investigation using 3D FEMDEM

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Acoustical properties of double porosity granular materials

Granular materials have been conventionally used for acoustic treatment due to their sound absorptive and sound insulating properties. An emerging field is the study of the acoustical properties of multiscale porous materials. An example of these is a granular material in which the particles are porous. In this paper, analytical and hybrid analytical-numerical models describing the acoustical properties of these materials are introduced. Image processing techniques have been employed to estimate characteristic dimensions of the materials. The model predictions are compared with measurements on expanded perlite and activated carbon showing satisfactory agreement. It is concluded that a double porosity granular material exhibits greater low-frequency sound absorption at reduced weight compared to a solid-grain granular material with similar mesoscopic characteristics

Hydro-micromechanical modeling of wave propagation in saturated granular media

Biot's theory predicts the wave velocities of a saturated poroelastic granular medium from the elastic properties, density and geometry of its dry solid matrix and the pore fluid, neglecting the interaction between constituent particles and local flow. However, when the frequencies become high and the wavelengths comparable with particle size, the details of the microstructure start to play an important role. Here, a novel hydro-micromechanical numerical model is proposed by coupling the lattice Boltzmann method (LBM) with the discrete element method (DEM. The model allows to investigate the details of the particle-fluid interaction during propagation of elastic waves While the DEM is tracking the translational and rotational motion of each solid particle, the LBM can resolve the pore-scale hydrodynamics. Solid and fluid phases are two-way coupled through momentum exchange. The coupling scheme is benchmarked with the terminal velocity of a single sphere settling in a fluid. To mimic a pressure wave entering a saturated granular medium, an oscillating pressure boundary condition on the fluid is implemented and benchmarked with one-dimensional wave equations. Using a face centered cubic structure, the effects of input waveforms and frequencies on the dispersion relations are investigated. Finally, the wave velocities at various effective confining pressures predicted by the numerical model are compared with with Biot's analytical solution, and a very good agreement is found. In addition to the pressure and shear waves, slow compressional waves are observed in the simulations, as predicted by Biot's theory.Comment: Manuscript submitted to International Journal for Numerical and Analytical Methods in Geomechanic

Minkowski Tensors of Anisotropic Spatial Structure

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors. Minkowski tensors are generalisations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations, and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The article further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic method more readily accessible for future application in the physical sciences