Packing Of Grains Research Articles

Goddard rattler-jamming mechanism for quantifying pressure dependence of elastic moduli of grain packs

An analysis is presented to show how it is possible for unconsolidated granular packings to obey overall non-Hertzian pressure dependence due to the imperfect and random spatial arrangements of the grains in these packs. With imperfect arrangement, some gaps that remain between grains can be closed by strains applied to the grain packing. As these gaps are closed, former rattler grains become jammed and new stress-bearing contacts are created that increase the elastic stiffness of the packing. By allowing for such a mechanism, detailed analytical expressions are obtained for increases in bulk modulus of a random packing of grains with increasing stress and strain. Only isotropic stress and strain are considered in this analysis. The model is shown to give a favorable fit to laboratory data on variations in bulk modulus due to variations in applied pressure for bead packs.

Migration of air channels: An instability of air flow in mobile saturated porous media

A set of two-dimensional laboratory visualization experiments reveals a previously unrecognized gas-flow instability in a porous medium saturated with a glycerine–water solution. The medium is a non-fixed vertically placed packing of grains of crushed fused silica glass. The interaction of the injected air flow and the medium structure leads to mobilization of the medium and an instability, which causes the air channel to migrate. This instability is dominated by a dimensionless number α , which can be interpreted as a normalization of a critical velocity with a dipole velocity for saturated conditions. The channel migration appears as a sequence of previous channels collapsing and new channels opening. The channel migration comes to a stop after some time, leaving one thin and stable channel. The process is studied by calculating the cumulated lateral movement distance of a channel and the lateral width of the area affected by the migration, both scaled by α with an empirical power of 0.25. Another dimensionless number f is defined to qualify the migration under different grain size, height of bed, and air flow rate.

Low temperature perovskite phase formation in PCT 90/10 system by modified chemical route

Perovskite phase development study of PCT 90/10 system was carried out. Modified chemical technique was used for synthesis. Single perovskite phase with a polycrystalline tetragonal structure was obtained in PCT 90/10 ceramic system at 600 °C processing temperature. Dense packing of grains with average grain size ∼1 μm was observed in PCT 90/10 ceramic samples. Curie transition temperature ( T c) of PCT 90/10 ceramic samples was found to be ∼180 °C with diffuse phase transition.

Sound waves in 3D periodic granular materials

The sound propagation mechanisms inside dense granular matter, even for periodical structures, are challenging the attempts to describe it because of the discrete nature of the material. Phenomena like dissipation, scattering, and dispersion are hard to predict based on the material state and/or properties and vice-versa. We propose here a simulation method using dynamic discrete elements in order to get more insight in this problem. The small perturbation created on one side of a dense, static regular packing of grains is examined during its propagation and when it arrives at the opposite side. Both longitudinal and shear perturbation are studied and an interesting wave-acceleration is observed [1]. Moreover the rotational degree of freedom permits to observe the role of rotations in the wave propagation. The control of the inter-particle forces like, contact potential, cohesion and friction make possible to observe the effect of these micro-parameters on the macro-behavior (at the wave scale). Long term goal is to predict the large-scale macroscopic material behavior from the microscopic structure and material parameters. [1] O. Mouraille, W A Mulder and S. Luding: Sound wave acceleration in granular materials, J. Stat. Mech. (2006) P07023.

Density inversion in rapid granular flows: the supported regime

This paper presents numerical findings on rapid 2D and 3D granular flows on a bumpy base. In the supported regime studied here, a strongly sheared, dilute and agitated layer spontaneously appears at the base of the flow and supports a compact packing of grains moving as a whole. In this regime, the flow behaves like a sliding block on the bumpy base. In particular, for flows on a horizontal base, the average velocity decreases linearly in time and the average kinetic energy decreases linearly with the travelled distance, those features being characteristic of solid-like friction. This allows us to define and measure an effective friction coefficient, which is independent of the mass and velocity of the flow. This coefficient only loosely depends on the value of the micromechanical friction coefficient whereas the infuence of the bumpiness of the base is strong. We give evidence that this dilute and agitated layer does not result in significantly less friction. Finally, we show that a steady regime of supported flows can exist on inclines whose angle is carefully chosen.

Spatial dispersion of aggregate in concrete a computer simulation study

Experimental research revealed that the spatial dispersion of aggregate grains exerts pronounced influences on the mechanical and durability properties of concrete. Therefore, insight into this phenomenon is of paramount importance. Experimental approaches do not provide direct access to three-dimensional spacing information in concrete, however. Contrarily, simulation approaches are mostly deficient in generating packing systems of aggregate grains with sufficient density. This paper therefore employs a dynamic simulation system (with the acronym SPACE), allowing the generation of dense random packing of grains, representative for concrete aggregates. This paper studies by means of SPACE packing structures of aggregates with a Fuller type of size distribution, generally accepted as a suitable approximation for actual aggregate systems. Mean free spacing , mean nearest neighbour distance (NND) between grain centres , and the probability density function of D3 are used to characterize the spatial dispersion of aggregate grains in model concretes. Influences on these spacing parameters are studied of volume fraction and the size range of aggregate grains. The values of these descriptors are estimated by means of stereological tools, whereupon the calculation results are compared with measurements. The simulation results indicate that the size range of aggregate grains has a more pronounced influence on the spacing parameters than exerted by the volume fraction of aggregate. At relatively high volume density of aggregates, as met in the present cases, theoretical and experimental values are found quite similar. The mean free spacing is known to be independent of the actual dispersion characteristics (Underwood 1968); it is a structural parameter governed by material composition. Moreover, scatter of the mean free spacing among the serial sections of the model concrete in the simulation study is relatively small, demonstrating the sample size to be representative for composition homogeneity of aggregate grains. The distribution of observed in this study is markedly skew, indicating a concentration of relatively small values of . The estimate of the size of the representative volume element (RVE) for configuration homogeneity based on NND exceeds by one order of magnitude the estimate for structure-insensitive properties. This is in accordance with predictions of Brown (1965) for composition and configuration homogeneity (corresponding to structure-insensitive and structure-sensitive properties) of conglomerates.

Numerical study of the stress response of two-dimensional dense granular packings

We investigate the Green function of two-dimensional dense random packings of grains in order to discriminate between the different theories of stress transmission in granular materials. Our computer simulations allow for a detailed quantitative investigation of the dynamics which is difficult to obtain experimentally. We show that both hyperbolic and parabolic models of stress transmission fail to predict the correct stress distribution in the studied region of the parameters space. We demonstrate that the compressional and shear components of the stress compare very well with the predictions of isotropic elasticity for a wide range of pressures and porosities and for both frictional and frictionless packings. However, the states used in this study do not include the critical isostatic point for frictional particles, so that our results do not preclude the fact that corrections to elasticity may appear at the critical point of jamming, or for other sample preparation protocols, as discussed in the main text. We show that the agreement holds in the bulk of the packings as well as at the boundaries and we validate the linear dependence of the stress profile width with depth.

Performance of time‐stepping schemes for discrete models in fracture dynamic analysis

AbstractIn this work we present a critical evaluation of different time integration schemes within the setting of non‐linear dynamic analysis of brittle fracture problem represented by a discrete model. The discrete model of this kind consists of Voronoi cells representing the grains of a heterogeneous structure, which are interconnected by cohesive forces modelled by beam‐like links capable of taking properly into account both brittle dynamic fracture and large displacement of a still connected pack of grains that might split from the structure. The brittle behaviour of cohesive links requires that the dynamic analysis of such a model be treated with care, and the best possible integration scheme be selected. Four different schemes are explored and compared in application to a dynamic traction test, including Newmark explicit and implicit schemes, HHT‐α scheme and energy‐decaying scheme. Copyright © 2005 John Wiley & Sons, Ltd.

Application of modern radiative transfer tools to model laboratory quartz emissivity

Planetary remote sensing of regolith surfaces requires use of theoretical models for interpretation of constituent grain physical properties. In this work, we review and critically evaluate past efforts to strengthen numerical radiative transfer (RT) models with comparison to a trusted set of nadir incidence laboratory quartz emissivity spectra. By first establishing a baseline statistical metric to rate successful model‐laboratory emissivity spectral fits, we assess the efficacy of hybrid computational solutions (Mie theory + numerically exact RT algorithm) to calculate theoretical emissivity values for micron‐sized α‐quartz particles in the thermal infrared (2000–200 cm−1) wave number range. We show that Mie theory, a widely used but poor approximation to irregular grain shape, fails to produce the single scattering albedo and asymmetry parameter needed to arrive at the desired laboratory emissivity values. Through simple numerical experiments, we show that corrections to single scattering albedo and asymmetry parameter values generated via Mie theory become more necessary with increasing grain size. We directly compare the performance of diffraction subtraction and static structure factor corrections to the single scattering albedo, asymmetry parameter, and emissivity for dense packing of grains. Through these sensitivity studies, we provide evidence that, assuming RT methods work well given sufficiently well‐quantified inputs, assumptions about the scatterer itself constitute the most crucial aspect of modeling emissivity values.

Electro‐osmotic coupling in compact clays

Electro‐osmotic coefficients are determined experimentally and compared to numerical data. The numerical model assumes random packings of grains of various shapes; the prediction corresponds to a modified analytical solution. A special set up was designed to measure all relevant properties independently as functions of the porosity and electrolyte concentration. Two model clays and a compact natural clay were used. Good agreement was found between experimental and numerical results, indicating that the electro‐osmotic coefficient can be predicted from conductivity and permeability.

Regular packing of grains as a model of snow structure

AbstractThis paper presents a model of snow structure (model of regular grain packing) that is based on experimental determination of various geometrical characteristics of fine-, medium- and large-grained granular snow. Data analysis supports the possibility of approximating the ice-matrix configuration as a regular lattice of nearly spherical ice grains connected by rigid ice bonds. The model was successfully used for relating microstructural parameters of snow to snow density, compaction behavior and evolution of mechanical properties.

Physical properties and textural parameters of calcarenitic rocks: qualitative and quantitative evaluations

Petrophysical and mechanical properties of sedimentary rocks are influenced by size, shape, and packing of grains, porosity, cement and matrix content, all controlled strongly by depositional fabric and postdepositional processes. This paper presents a study on the textural characteristics of soft and porous calcarenites and the main methods to determine petrophysical data. The examined calcarenites, sampled from three quarry districts located in Apulia (southeastern Italy), are fine-grained and coarse-grained grainstones (“A” and “D”) and medium-grained packstones (“B”) belonging to a plio-pleistocenic formation (Calcarenite di Gravina) outcropping in the whole region. The study involved, particularly, textural analysis on thin sections using optical petrographic microscopy and evaluation of total and effective porosity by means of standard geotechnical laboratory tests, mercury intrusion porosimetry and image analysis. Grain size frequency distribution was also carried out by traditional sieve and sedimentation analysis on disaggregated materials and image analysis. Computer analysis of digital images was performed on photomicrographs applying the methods of quantitative stereology to pore size and grain size distributions. A comparison between results showed that each technique used has its limitations linked to the textural characteristics, primarily geometry and topology of the pore network, granulometry, grain shape and packing of calcarenites.

Transport Properties of Compact Clays: I. Conductivity and Permeability

Conductivity and permeability of model and natural clays have been studied experimentally. Local properties such as porosity and zeta potentials were measured as functions of the electrolyte solutions. Whenever possible, experimental data were compared to numerical data obtained for random packings of grains of arbitrary shape, and a good agreement was found between them.

Geometrical and transport properties of random packings of spheres and aspherical particles

Random packings of grains of arbitrary shape are built with an algorithm that is mostly applied to spheres, ellipsoids, cylinders, and parallelepipeds. A systematic account of the main geometrical properties such as the porosity, the reduced specific area, etc. is given. The conductivity, the permeability, and the dispersion are also systematically determined and they are shown not to depend upon their mode of construction.

The spatial distribution of grains and crystals in rocks

Characterisation and analysis of the spatial distribution pattern (SDP) of grains or crystals in rocks is potentially a powerful technique which can be used to constrain the processes which operate in the formation of rocks. A method to quantify the SDP of grains in thin section is presented. The distance betwen the centre of a grain and the centre of its nearest neighbour is calculated for all the grains in the sample area to produce a distribution of distances that characterises the spatial pattern of grains in the rock. This distribution is then normalised to a random distribution of points with the same population density to give a descriptive value, R. Values of R for rock samples are plotted against porosity (modal abundance of other phases in igneous and metamorphic rocks) to characterise the SDP. The SDP of randomly packed distributions of equal size spheres varies systematically with porosity, producing a line on a porosity versus R plot, termed the random sphere distribution line (RSDL). Rocks which plot above the RSDL have an ordered SDP and those that plot below, a clustered SDP. The effects of variation in grain packing order, grain sorting, compaction and random crystallisation (overgrowth) on determined R values were investigated using a combination of 3-D sphere models and 2-D texture models. The maximum possible value of R is 2.148, corresponding to a perfect section through hexagonal/cubic close packing of grains. The minimum value of R is dependent on the proportion of grains in the sample volume and may be as low as 1.2, for a sample volume with 30% grains which are clustered. Variations in size sorting can cause R to vary by approximately 0.25. Mechanical compaction of a loose framework of grains results in a higher packing order and an increase in R. Continued compaction creates a fabric in the texture and R decreases as cluster patterns are developed perpendicular to the principal stress. The overgrowth of grains in a touching framework alters the location of the geometric grain centre as the crystal shape changes, leading to an increase in R as porosity decreases. Results reveal that grain sorting, compaction and grain overgrowth produce different R versus porosity relationships which can be identified in, and therefore used to constrain, the relative importance of these processes in rock samples.

Anomalous density dependence of static friction in sand

We measured experimentally the static friction force ${\mathit{F}}_{\mathit{s}}$ on the surface of a glass rod immersed in dry sand. We observed that ${\mathit{F}}_{\mathit{s}}$ is extremely sensitive to the closeness of packing of grains. A linear increase of the grain density yields to an exponentially increasing friction force. We also report on the periodicity of ${\mathit{F}}_{\mathit{s}}$ during gradual pulling out of the rod. Our observations demonstrate the central role of grain bridges and arches in the macroscopic properties of granular packings. \textcopyright{} 1996 The American Physical Society.

Mechanical behaviour of brittle cement grains

Before attempting a modelling approach to the crushing mechanisms of “cement clinker” it was necessary to characterize the mechanical behaviour of this material up to breakage. The diametrical compressive test was chosen, as it is the closest to the typical loading within a packing of grains and a very convenient experimental approach for the analysis of mechanical behaviour law up to fragmentation of brittle granular material. The modellization of the grain as a hard brittle core surrounded by a thin crumbly skin leads us to associate the contact setting with the crumbly skin behaviour and the breakage with the brittle core behaviour. This analysis allowed us to define scaling laws for the skin thickness and breakage load. The breakage force increases as a power law of the grain diameter with an exponent of 1.5 and it is shown that the mean prefactor K0 is an intrinsic characteristic parameter proportional to the tenacity of the material.

Capillary Pressures in Stratigraphic Traps

Capillary pressures between oil and water in rock pores are responsible for trapping oil, and the height of oil column, zo, in a reservoir may be calculated from the Hobson equation modified as follows: [EQUATION] where ^ggr is the interfacial tension between oil and water, rt is the radius of pore throats in the barrier rock, rp is the radius of pores in the reservoir rock, g is acceleration of gravity, and ^rgrw and ^rgro are the densities of water and oil, respectively, under subsurface conditions. To apply the equation, pore sizes must be estimated from mean effective grain sizes of the reservoir and barrier rocks. Effective grain size, De, in centimeters can be approximated from core analysis data by means of an empirical permeability equation from which [EQUATION] where n is porosity in percent and k is permeability in milli-darcys. Then pore and throat sizes may be estimated as functions of mean effective grain size as based on theoretical packings of grains. The oil-column equation assumes hydrostatic conditions, and additional column, ^Dgrzo, may be trapped if hydrodynamic flow occurs down the dip from barrier to reservoir facies, or [EQUATION] where dh/dx is the potentiometric gradient and xo is the width of the oil accumulation. Calculations of oil columns in stratigraphic fields show that the equations give values which are in fair to good agreement with observed oil columns; that porous and permeable, very fine-grained sandstones and siltstones are commonly effective barriers to oil migration; and that the recognition of such barriers can be important in exploration for stratigraphic traps.

The Final Distribution of Retained Liquid in an Ideal Uniform Soil

If liquid, initially saturating the pores of a soil, is allowed to drain from that soil, no such complete drainage as occurs in a simple capillary tube is observed; large quantities of liquid are retained. The quantity of liquid held by the soil immediately after drainage gradually alters; it decreases to a stationary value and the liquid so held finally arranges itself in a stable distribution. Whatever be the distribution, the bounding liquid surfaces are capillary ones and subject to the laws of thermodynamics and capillarity; the Kelvin relation, in general determines the curvatures. The problem is considered for an ideal soil, that is an assemblage of spheres, of a single size, packed at random. There are in the ideal soil three types of distribution. First, there is a pendular region where the liquid is retained in the form of single rings of liquid wrapped around the axis of each pair of adjacent grains in contact. Second, there is a funicular region, which may be considered to arise by coalescence of the rings; we have two or more grain contacts imbedded in a single liquid mass, that is, webs of liquid enmeshing two or more grain contacts and which may involve many grains of the packing. There is, finally, a saturation region in which all pores are completely filled. The limits of each of these zones are determined. The funicular zone is a zone of hysteresis and all values between a normal minimum and complete saturation are usually possible. To calculate the normal minimum distribution the actual packing is replaced by an average packing of grains in hexagonal array and equally spaced to give the required porosity. The funicular distribution is now in the form of single rings wrapped around the axis of each pair of grains of the packing. The volume of each type of ring is determined in terms of (σ/ρghr), where σ is the surface tension of the liquid and ρ its density, r the grain radius, and h the height of the ring above a free liquid reference plane. The average volume of each type of ring is obtained for all rings confined between two given planes. From the average ring volume and the number of such in each cc of packed space, the total retention in each zone above saturation is found. The distribution, that is, the liquid retained in any lamina at a height h above the free liquid, is also given. The results are compared with the data of King.