Dense Random Packing Research Articles

Structure of pressure-induced amorphous form ofSnI4at high pressure

The structure of pressure-induced amorphous form of ${\text{SnI}}_{4}$ has been studied by synchrotron x-ray diffraction measurements using diamond-anvil cell. The structure factor, the reduced radial distribution function, and the density were obtained between 25 and 55 GPa. Comparison of measured structure factor with that calculated for a randomly oriented dimerized molecules model shows no similarity between them. Experimentally obtained radial distribution function provides clear evidence for the absence of both distances between tin and iodine atoms and between iodine atoms within the ${\text{SnI}}_{4}$ tetrahedral molecule. Characteristic features of the structure factor for amorphous ${\text{SnI}}_{4}$ show a marked resemblance to those for elemental metallic glasses which are successfully reproduced by a model of dense random packing of equal-sized spheres. Indeed, various quantities such as positions of peaks in measured structure factors and in experimental radial distribution functions, the coordination number are in precise agreement with those derived from the dense random-packing model. We conclude that the structure of the high-pressure amorphous form of ${\text{SnI}}_{4}$ is the relatively rigid packing of tetrahedra composed of iodine and substitutional tin atoms.

Infinite-Acting Physically Representative Networks for Capillarity-Controlled Displacements

Summary Drainage/imbibition simulations are traditionally performed on finite regular lattices. If physically representative networks are used instead, the spatial correlation of pore space features inherent in granular materials is automatically accounted for. However, even these networks are obtained from finite samples, and conditions must be specified on the boundaries. Making the conditions correspond to physically realistic situations is difficult, especially for simulations of phase trapping. This paper presents a method of constructing infinite-acting model rocks, in which a well-defined criterion for phase trapping is possible that is independent of boundary conditions. The foundation of the model is computergenerated dense random periodic packings of spheres. We illustrate the method with simulations of drainage and irreducible wetting-phase saturations. To eliminate possible confounding effects from grains being arranged differently, we compare simulations in infinite-acting networks with simulations in the finite network taken from the unit cell of the periodic packing. Wetting-phase connectivity is assessed globally and accounts for all phase morphologies, including pendular rings. The drainage endpoint for a finite network was highly sensitive to the number and location of the exit pores; while using the infinite-acting network, we removed this latter sensitivity. Comparison with experiments showed that a strict criterion of wetting-phase connectivity (pores connected only by throats filled with wetting phase) cannot account for typical values of Sw,irr and that connectivity must persist via pendular rings. Typical laboratory experiments and simulations in finite networks yield drainage curves that approach irreducible wetting phase saturation Sw,irr gradually, with large changes in capillary pressure inducing only small changes in saturation. Simulations in infinite-acting networks do not exhibit this behavior. We argue that these simulations are more representative of behavior in the field and that typical laboratory measurements underestimate the value of Sw,irr.

Quantitative Mechanism for Permeability Reduction by Small Water Saturation in Tight-Gas Sandstones

Summary In tight-gas sandstone, the productivity of a well is sometimes quite different from that of a nearby well. Several mechanisms for this observation have been advanced. Of interest in this paper is the possibility that a small change in water saturation can change the gas-phase permeability significantly in rocks with small porosity and very small permeability. We quantify the effect of small saturations of the wetting phase on nonwetting-phase relative permeability by modeling the geometry of the wetting phase. We also show how a porosity-reducing process relevant in tight-gas sandstones magnifies this effect. The basis for these observations is a model of the grain-scale geometry of low-porosity sandstones. The model is built from a dense random packing of spheres modified geometrically to simulate quartz-overgrowth cementation. To compute phase geometry and permeability, we use a physically representative network model extracted from the model rock. At small saturations (at or near the drainage endpoint), the wetting phase exists largely in the form of pendular rings held at grain contacts. Pore throats correspond to the constriction between groups of three grains, each pair of which can be in contact. Thus, the existence of these pendular rings decreases the void area available for flowing nonwetting phase. Because the hydraulic conductance of the throat varies with the square of the void area, the effect on permeability is disproportionate to the volume occupied by the rings. Convention holds that connate water has little effect on oil or gas permeability because it occupies the smaller pores. Comparing predictions for unconsolidated model rocks with those for cemented model rocks allows one to reconcile this view with the sensitivity reported in the field and the laboratory.

The structure of random packings of freely jointed chains of tangent hard spheres

We analyze the structure of dense random packings of freely jointed chains of tangent hard spheres as a function of concentration (packing density) with particular emphasis placed on the behavior in the vicinity of their maximally random jammed (MRJ) state. Representative configurations over the whole density range are generated through extensive off-lattice Monte Carlo simulations on systems of average chain lengths ranging from N=12 to 1000 hard spheres. Several measures of order are used to quantitatively describe either local structure (sphere arrangements and bonded geometry) or global behavior (chain conformations and statistics). In addition, the employed measures are used to elucidate the effect of connectivity on structure, by comparing monatomic and chain assemblies of hard spheres at the MRJ state.

Random Loose Packing in Granular Matter

We introduce and simulate a two-dimensional Edwards-style model of granular matter at vanishing pressure. The model incorporates some of the effects of gravity and friction, and exhibits a random loose packing density whose standard deviation vanishes with increasing system size, a phenomenon that should be verifiable for real granular matter.

Surface area and pore volume of a system of particles as a function of their size and packing

Size-dependent properties of colloidal and nanoscale systems could be evaluated in only two limiting approximations: supposing particles to be free or employing random dense packing models and their quantitative versions. However, real colloidal and nanoscale systems are formed by neither free nor densely packed particles, and the methods enabling one to calculate their properties at intermediate densities remain unknown. In this paper, simple relations between the particle radius R, surface area A s , pore volume V p , and packing fraction ρ are constructed in terms of the gapped gapless packing model. Calculations using recent data on A s and V p reveal that the particle radii predicted by the model are in good agreement with experimental measurements, and the ρ values evaluated for the first time depend on the pre-history of the system studied. Finally, conclusions are drawn that any dispersed solid of the specific surface area exceeding 30 m 2/g must be constituted of nano-sized particles, and that assemblages of nano-sized particles of R > 2.6 nm are inevitably mesoporous.

Local organization and atomic clustering in multicomponent amorphous steels

The characteristics of atom packing in multicomponent metallic alloys with distinct short- and mediumrange order SMRO are notoriously difficult to provide as the local structure is made up of multiple overlapping pair correlations. In the case of binary glasses, several cluster models have been proposed that can describe the SMRO well going beyond models of dense random packing of hard spheres. By combining the pair density function analysis of neutron-diffraction data and modeling using ab initio computational techniques, the tendency for local atomic clustering is investigated and properties of multicomponent bulk Fe78x-yTMxREyC22zBz amorphous alloys transition metal TM and rare earth RE are studied going beyond simple binary systems. The results are relevant to most bulk metallic glass forming alloys with more than one kind of solute ion.

Icosahedral and dense random cluster packing in metallic glass structures

It has recently been shown that metallic glass structures can be idealized as inter-penetrating solute-centered atomic clusters that are packed with essentially periodic symmetry. The present work applies the same methodology to explore whether experimental observations can be matched by inter-connected solute-centered clusters that are organized in space via dense random cluster packing, Bergman icosahedral cluster packing or Mackay icosahedral cluster packing. Idealized partial pair distribution functions are developed where the symmetry of the solute positions in the structure is derived from the cluster-packing symmetry and the solute concentration, which establishes occupation of inter-cluster sites, especially β structural sites enclosed by an octahedron of solute-centered clusters. While each of the three models matches major features of the measured solute–solute partial pair distribution functions, the arrangement of clusters with Mackay icosahedral ordering provides the best fit. However, this model is not able to match an essential feature in solute-lean glasses and does not provide the same overall agreement as does periodic cluster packing for solute-rich glasses. Strong similarities between the structure factors in the Mackay icosahedral and periodic cluster-packing models, along with expected deviations from the idealized solute positions studied here, are likely to hinder an unambiguous distinction between these two models.

Rotating bearings in regular and irregular granular shear packings

For 2D regular dense packings of solid mono-size non-sliding disks there is a mechanism for bearing formation under shear that can be explained theoretically. There is, however, no easy way to extend this model to include random dense packings which would better describe natural packings. A numerical model that simulates shear deformation for both near-regular and irregular packings is used to demonstrate that rotating bearings appear roughly with the same density in random and regular packings. The main difference appears in the size distribution of the rotating clusters near the jamming threshold. The size distribution is well described by a scaling form with a large-size cut-off that seems to grow without bounds for regular packings at the jamming threshold, while it remains finite for irregular packings. At packing densities above the jamming transition there can be no shear, unless the disks are allowed to break. Breaking of disks induces a large number of small local bearings. Clusters of rotating particles may contribute to e.g. pre-rupture yielding in landslides, snow avalanches and to the formation of aseismic gaps in tectonic fault zones.

金属ガラス粉末のホットプレス緻密化制御

The equations for the densification control by viscous flow in the hot pressing of metallic glass powders are derived and a criterion for the full densification thereof and an approach for the porosity control are proposed. The kinetic equations are derived on the basis of Arzt's hot pressing theory; in which the densification is modeled by the contraction of the Bolonoi cell of the random dense packing of spherical particles. The constitutive equation for the viscous flow is obtained from the hitherto proposed creep rate equation setting the rate exponent to be unity. The hypothetical constraint for the deformation due to the three grain edges formed in the later stage of densification is taken into account as a modification of the pressure term in the kinetic equations. The relative density is expressed as functions of hot pressing time and the ratio of the viscosity and the pressure. It is shown that the time required for full densification of metallic glass powders depends only on the viscosity/pressure ratio. The criterion for the full densification is expressed as a straight line on the time-viscosity/pressure ratio plane, which divides the area into full-dense and porous areas. The porosity control of the metallic glass powder compacts is also demonstrated as another practical application of the present theory. The results are discussed on the basis of the reported data.

3D statistical analysis of a copper powder sintering observed in situ by synchrotron microtomography

Sintering of a copper spherical powder was observed in situ by X-ray microtomography at the European Synchrotron Radiation Facility. Morphological tools have been developed to obtain three-dimensional (3D) quantitative microstructural characteristics of the particle packing. The average microstructural changes (neck size, coordination number, pore size distribution) and the macroscopic densification are in agreement with the predictions of the mean field sintering models, which assume a uniform shrinkage of the powder compact. The present 3D results confirm that the effect of the inherent heterogeneity of a random dense particle packing on the average microstructural changes during sintering is limited.

Predictive model for permeability reduction by small wetting phase saturations

Laboratory experiments show that the rate of decrease in gas phase permeability as a function of water saturation can be large at small saturations. Drying out the water saturation during gas injection has been observed to reduce absolute permeability. This paper proposes a quantitative grain‐scale explanation for these observations. We also show why the effect is magnified in rocks having lower porosity. To compute phase geometry and permeability, we use a physically representative network model. The network is extracted from a model rock, built from a dense random packing of spheres modified geometrically to simulate rock‐forming processes. At small saturations the wetting phase exists largely in the form of pendular rings held at grain contacts. The rings decrease the void area available for flowing nonwetting phase. Because the hydraulic conductance of the throat varies with the square of the void area (other factors being equal), the effect on permeability is disproportionate to the volume occupied by the rings. The same approach quantifies the reduction in permeability by salt precipitation during drying.

Investigating magnetorheological properties of a mixture of two types of carbonyl iron powders suspended in an ionic liquid

In this work, properties of a magnetorheological (MR) fluid, prepared by dispersing a mixture of two types of carbonyl iron powders (CIPs) of different sizes, in an ionic liquid ( N, N-diethyl- N-methyl- N-(2-methoxyethyl) ammonium tetrafluoroborate) that is stable from 9 °C to ca. 300 °C, have been investigated. At first, the random packing density of the mixture was computed as function of mixing ratio of CIP, in order to find out the tendency of the variation. Next, several mixtures, all having the same weight, were prepared at various mixing ratios and dispersed in the ionic liquid, in order to experimentally find the most suitable mixing ratio of CIP. Then, the magnetic clusters of the synthesized MR fluids were observed by using a digital microscope equipped with two permanent magnets, whereas the MR properties were investigated by using a rotation viscometer equipped with a solenoid coil. The experimental results pointed out that the MR fluid with 60 wt% fraction of large particles exhibited the highest MR response.

Mechanism for Permeability Reduction by Small Water Saturation in Tight Gas Sandstones

This article, written by Assistant Technology Editor Karen Bybee, contains highlights of paper SPE 107950, "Quantitative Mechanism for Permeability Reduction by Small Water Saturation in Tight Gas Sandstones," by Siyavash Motealleh, SPE, and Steven L. Bryant, SPE, University of Texas at Austin, prepared for the 2007 SPE Rocky Mountain Oil & Gas Technology Symposium, Denver, 16–18 April. The full-length paper examines the possibility that a small change in water saturation can change the gas-phase permeability significantly in rocks with low porosity and very low permeability. The model of the grain-scale geometry of low-porosity sandstones is built from a dense random packing of spheres modified geometrically to simulate quartz over growth cementation. Introduction In tight gas sandstone, the productivity of one well sometimes is quite different from that of a nearby well. Wells also can be very sensitive to small amounts of water. Although the effect of water saturation on the effective permeability to gas has been the subject of numerous experiments, a fully mechanistic explanation has not been offered as to why the effect appears larger in tight gas reservoirs. The full-length paper explores the possibility that the grain-scale geometry of tight sandstone is responsible. Small wetting saturation is mainly irreducible wetting phase that exists in two forms. One is volumes of water held in the smallest pores. The other is pendular rings held at grain contacts or liquid bridges held between two grains separated by a gap. The former forces gas to flow around the filled pores, decreasing the average connectivity of the gas phase. The latter reduces the area open to gas (the nonwetting phase) as it passes through a pore throat. It is possible to quantify the effects of these topological and geometrical changes on gas-phase permeability. Method Pore-Space Model. The geometry of pore space in porous media is very complex, and a large number of pores must be modeled to obtain reasonable predictions of macroscopic behavior. Direct simulation of flow within pore space is now possible, but physically representative network models of pore space provide an inexpensive alternative. Delaunay tessellation of the sphere centers subdivides pore space and grain space simultaneously. The tessellation yields tetrahedra. Each face of a tetrahedron corresponds to a pore throat. The geometry of the throats is the primary control on permeability. Each edge of the tetrahedron corresponds to a grain/grain contact (if the spheres touch) or a gap between grains (if the spheres do not touch). The contacts/gaps can support pendular rings/liquid bridges of the wetting phase, depending on capillary pressure. The geometry of these rings/bridges and the geometry of the throats provide the link between small water saturations and effective permeability to the gas phase. This rock model can be modified geometrically to simulate various rock-forming processes. Many modes of porosity reduction occur in tight gas sandstone. Only isopachous quartz cementation is considered in the full-length paper. The simplest model of this process treats the quartz cement as a coating of uniform thickness on all sediment grains.

Observation of a shape-dependent density maximum in random packings and glasses ofcolloidal silica ellipsoids

We have measured the random packing density of monodisperse colloidal silica ellipsoidswith a well-defined shape, gradually deviating from a sphere shape up to prolates withaspect ratios of about 5, to find for a colloidal system the first experimental observationfor the density maximum (at an aspect ratio near 1.6) previously found onlyin computer simulations of granular packings. Confocal microscopy of ellipsoidpackings, prepared by rapidly quenching ellipsoid fluids via ultra-centrifugation,demonstrates the absence of orientational order and yields pair correlation functionsvery much like those for random sphere packings. The density maximum, about12% above the Bernal random sphere packing density, also manifests itself as a maximum in thehydrodynamic friction that resists the swelling osmotic pressure of the ellipsoid packings.The existence of the density maximum is also predicted to strongly effect the dynamics ofcolloidal non-sphere glasses: slightly perturbing the sphere shape in a sphere glass willcause it to melt.

Density, Thermal Stability and Mechanical Properties of Zr-Ti-Al-Cu-Ni Bulk Amorphous Alloys with High Al Plus Ti Concentrations

Bulk amorphous Zr 70-x-y Ti x Al y Cu 20 Ni 10 alloys with a thickness of 2.5 mm were formed in a wide composition range of 0 to 10 at%Ti and 7.5 to 15 at%Al by a squeeze casting process. The bulk amorphous alloys containing 0 to 5%Ti and 12.5 to 15%Al exhibit good combined properties of high tensile fracture strength above 1850 MPa, high specific strength of 28.4 × 10 5 N.m/kg and high T g / T m above 0.60 which have not been obtained for the Zr-based amorphous alloys reported hitherto. These bulk amorphous alloys have small difference in density of 0.3 to 0.6% between ascast amorphous and crystallized states. The high dense random packing fraction in the multicomponent amorphous structure seems to cause the high glass-forming ability and the high thermal stability of the supercooled liquid region by the decrease in atomic mobility. Furthermore, the crystallized phases change from NiZr 2 +CuZr+Zr 3 Al in the range of 5 to 15%Al and 0 to 2.5%Ti to NiZr+CuZr 2 +Zr 3 Al in the range of 5 to 15%Al and 2.5 to 7.5%Ti. The melting temperatures (T m ) of these crystallized compounds increase in the order of ZrNi > Zr 2 Ni > Zr 2 Cu > ZrCu and hence the crystallized structure of the 5%Ti-containing alloys is composed of ZrNi and Zr 2 Cu with higher T m . The change in the amorphous structure leading to the precipitation of the compounds with higher T m may be the reason for the higher mechanical strength in the higher Al and Ti contents.

Structure of eutectic alloys of Au with Si and Ge

Au–Si and Au–Ge alloy systems have a deep eutectic point in the Au-rich concentration region where the melting point falls down to 633 K. In order to investigate the liquid structure in relation to the glass-forming tendency of these alloys, high-energy X-ray diffraction measurements have been carried out at the eutectic composition and at compositions with excess amounts of Au or IVb element. The nearest neighbor correlations in the eutectic liquids are intense and sharp in the pair distribution function and exhibit a rather small temperature dependence in comparison with those alloys of other than the eutectic composition. Structural models for these liquid alloys are proposed with the aid of reverse Monte Carlo simulation. The reproduced atomic arrangements around the eutectic region exhibit a substitutional-type structure where the dense random packing of Au atoms is preserved and Si or Ge atoms occupy the Au-sites at random.

Short- and Intermediate-Range Order in Liquid Bi–BiBr3 Mixtures: Importance of Voids

The neutron diffraction (ND) measurements and the detailed structural modeling by reverse Monte Calro (RMC) simulation have been performed for l-BiBr 3 and l-45 and 55 mol % Bi mixtures. The partial structure factor S i j ( Q ), partial radial distribution function g i j ( r ), and snapshot produced from RMC configurations have been examined. The structure of l-BiBr 3 is dominated by the network of trigonal pyramidal units. The l-mixtures consist of the –Br–Bi–Br– chain fragments terminated by Br. A Voronoi–Delaunay analysis has been applied to characterize the voids within network or chain. We find that the voids are surrounded by six pyramids in l-BiBr 3 and by chains in l-mixture. The packing density is 0.59 for l-BiBr 3 and 0.45 for l-45 mol % Bi mixture which is substantially low compared with that of dense random packing. The void–void structure factor S ' V–V ( Q ) involving void centers have the pre-peak at ∼1.2 A -1 which is in common with the pre-peak in experimentally observed S ( Q ). It is co...

Using ultra-short pulses to determine particle size and density distributions

We analyze the time dependent response of strongly scattering media (SSM) to ultra-short pulses of light. A random walk technique is used to model the optical scattering of ultra-short pulses of light propagating through media with random shapes and various packing densities. The pulse spreading was found to be strongly dependent on the average particle size, particle size distribution, and the packing fraction. We also show that the intensity as a function of time-delay can be used to analyze the particle size distribution and packing fraction of an optically thick sample independently of the presence of absorption features. Finally, we propose an all new way to measure the shape of ultra-short pulses that have propagated through a SSM.

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.