Granular Packing Research Articles

Mathematical Models and Experiments on the Acoustic Properties of Granular Packing Structures (Measurement of Tortuosity in Hexagonal Close-Packed and Face-Centered Cubic Lattices).

In this study, the sound absorption characteristics of hexagonal close-packed and face-centered cubic lattices were estimated by theoretical analysis. Propagation constants and characteristic impedances were obtained by dividing each structure into elements perpendicular to the incident direction of sound waves and by approximating each element to a clearance between two parallel planes. Consequently, the propagation constant and the characteristic impedance were treated as a one-dimensional transfer matrix in the propagation of sound waves, and the normal incident sound absorption coefficient was calculated by the transfer matrix method. The theoretical value of the sound absorption coefficient was derived by using the effective density applied to the measured tortuosity. As a result, the theoretical value was becoming closer to the measured value. Therefore, the measured tortuosity is reasonable.

Investigation of Flow Characteristics of Landslide Materials Through Pore Space Topology and Complex Network Analysis

AbstractUnlike embankments, earth dams, and other man‐made structures, most landslide dams are formed by rapid accumulation of rock or debris rather than mechanical compaction; thus, they are loose and pose a great risk of seepage failure. Landslide materials usually have complex pore structures with randomly distributed pores of various sizes, making the flow and transport processes very complex. Aiming at these challenges, we systematically investigated the influences of pore structure on the micro‐and macro‐scale flow characteristics of landslide materials. First, landslide materials are simplified as spherical granular packings with wide grain size distributions. Then, we use the Finite‐difference method Stokes solver to simulate the fluid flow through granular packings and calculate their permeability. We characterize the pore structure using different topological measures, including these borrowed from complex network theory. Among these measures, tortuosity and global efficiency show clear relations with permeability. The pore network modeling indicates that pore size heterogeneity and pore connectivity significantly influence the flow characteristics. The correlation between pore‐scale velocity and throat diameters follows a power‐law scaling with an exponent close to two, suggesting that the Hagen–Poiseuille law would still be valid in complex porous media. The permeability and porosity, throat radius, and tortuosity of pore structure can be related by the equation proposed by Nishiyama and Yokoyama (2017, https://doi.org/10.1002/2016JB013793). The complex network analysis reveals that the assortative network is more permeable than the disassortative network. Furthermore, pores with larger closeness centrality have higher flow efficiency, resulting in higher macroscopic permeability.

Hyperuniform jammed sphere packings have anomalous material properties.

A spatial distribution is hyperuniform if it has local density fluctuations that vanish in the limit of long length scales. Hyperuniformity is a well known property of both crystals and quasicrystals. Of recent interest, however, is disordered hyperuniformity: the presence of hyperuniform scaling without long-range configurational order. Jammed granular packings have been proposed as an example of disordered hyperuniformity, but recent numerical investigation has revealed that many jammed systems instead exhibit a complex set of distinct behaviors at long, emergent length scales. We use the Voronoi tessellation as a tool to define a set of rescaling transformations that can impose hyperuniformity on an arbitrary weighted point process, and show that these transformations can be used in simulations to iteratively generate hyperuniform, mechanically stable packings of athermal soft spheres. These hyperuniform jammed packings display atypical mechanical properties, particularly in the low-frequency phononic excitations, which exhibit an isolated band of highly collective modes and a band gap around zero frequency.

History-dependent deformation of a rotated granular pile governed by granular friction

• Deformation of a rotated granular heap was experimentally measured and modeled by a simple force-balance model. • Hysteresis of the deformation was observed. • Empirical relations between granular friction, centrifugal loading, and packing fraction were obtained. We experimentally examined the history dependence of the rotation-induced granular deformation. As an initial state, we prepared a quasi-two-dimensional granular pile whose apex is at the rotational axis and its initial inclination is at the angle of repose. The rotation rate was increased from 0 to 620 (rpm) and then decreased back to 0. During the rotation, deformation of the rotated granular pile was captured by a camera. From the acquired image data, granular friction coefficient μ was measured as a function of the ratio between centrifugal force and gravity, Γ . To systematically evaluate the variation of μ both in the increasing (spinning up) and decreasing (spinning down) rotation-rate regimes, surface profiles of the deformed granular piles were fitted to a model considering the force balance among gravity, friction, and centrifugal force at the surface. We found that μ value grows in the increasing Γ regime. However, when Γ was reduced, μ cannot recover its initial value. A part of the history-dependent behaviors of the rotated granular pile can be understood by the force balance model.

Granular packing in complex flow geometries

We examine the packing fraction and stress ratio in different granular flow geometries. In isochoric systems, we find that the packing fraction response versus inertial number is qualitatively similar to the more well established stress ratio response. As a result, the packing fraction is well-characterized as a local function of stress across a range of geometries and flow conditions. In a non-isochoric system, specifically a hopper, we find the response is more complex. By examining the flow onset in shear cell and chute systems, we attribute the different response in the hopper to the differing time scales for the development of stress versus packing in dense, low shear flow regions.

Unified penetration depth of low-velocity intruders into granular packings.

Penetration of intruders into granular packings is well described by separately considering the dry or wet case of granular environments in previous experiments and simulations; however, the unified description of such penetration depth in these two granular media remains elusive due to lacking clear explanations about its origins. Based on three-dimensional discrete element method simulations, we introduce a power-law fitting form of the final penetration depth of a spherical intruder with low velocity vertically penetrating into dry and wet granular packings, excellently expressed on a master curve as a power-law function of a dimensionless impact number that is defined as the square root of the ratio between the inertial stress of the intruder and the linear combination of the mean gravitational stress and the cohesive stress exerted on each grain in the packings, as a remarkable extension of the inertial number in dry granular flows. This scaling robustly provides physical insights inherent in the unified description of the material properties of granular packings and the impactor penetration conditions on the final penetration depth in the impact tests, providing evidence of impact properties in different disciplines and applications in science and engineering.

A Process-Based Pore Network Model Construction for Granular Packings Under Large Plastic Deformations

We propose a process-based method for constructing a pore network model of granular packings under large deformations. The method uses the radical Voronoi tessellation and constructive solid geometry operations on meshes of deformed particles, to construct a three-dimensional solid of the pore network and estimate its geometric characteristics, CTS-model parameters and flow transport properties, and it uses the particle mechanics approach to model consolidation of powders under large deformations. This process-based method thus explicitly simulates not only a packing of grains but also its corresponding consolidation process, which in this work is restricted to powder die compaction up to a relative density close to one (i.e., to die filling, compaction to low porosity, unloading and ejection). The efficacy of the proposed method is borne out by studying granular packings with the same composition, namely a 50–50 binary mixture of two monodisperse systems comprised by elasto-plastic spheres with bonding strength, but with microstructures which are topologically different, namely a random packing, a bilayer and core-shell structures. These simulations reveal that topological differences affect the formation and evolution of the pore space statistical signature during consolidation and, therefore, showcase that process-based approaches for constructing PNM are of paramount relevance to understanding architectured granular material systems.

Experimentally Measuring Rolling and Sliding in Three-Dimensional Dense Granular Packings.

We experimentally measure a three-dimensional (3D) granular system's reversibility under cyclic compression. We image the grains using a refractive-index-matched fluid, then analyze the images using the artificial intelligence of variational autoencoders. These techniques allow us to track all the grains' translations and 3D rotations with accuracy sufficient to infer sliding and rolling displacements. Our observations reveal unique roles played by 3D rotational motions in granular flows. We find that rotations and contact-point motion dominate the dynamics in the bulk, far from the perturbation's source. Furthermore, we determine that 3D rotations are irreversible under cyclic compression. Consequently, contact-point sliding, which is dissipative, accumulates throughout the cycle. Using numerical simulations whose accuracy our experiment supports, we discover that much of the dissipation occurs in the bulk, where grains rotate more than they translate. Our observations suggest that the analysis of 3D rotations is needed for understanding granular materials' unique and powerful ability to absorb and dissipate energy.

The comparison between two methods of membrane cleaning to control membrane fouling in a hybrid membrane photobioreactor (HMPBR)

In this study, the effect of two membrane cleaning methods, such as aeration and addition of granular particles in a hybrid membrane photobioreactor (HMPBR) including Spirulina sp. with the concentration of 1.5 g·L−1 was investigated. Three different spargers [i.e., different diameters of orifice (do ): 0.5, 1, and 1.5 mm] and granular particles (i.e., three packing ratios of 0.5, 1, and 1.5%) were used. The results showed that with the increase in granular packing ratio, Rc /Rt decreased significantly. The best result was achieved by combining aeration with an orifice diameter of 1.5 mm and a granular packing ratio of 1.5%, which led to the lowest Rc /Rt value (0.38), while Rc /Rt value with a do of 1.5 mm was 0.68 without particles. In contrast, the ratio of pore blocking resistance to total resistance (Rp /Rt ) increased by 4.2% under the combined application of 1.5 mm of orifice diameter and 1.5% of granular packing ratio. The results from protein concentrations in the cake layer showed that as the do became larger, cake protein concentration decreased by 40%, whereas increasing the granular packing ratio from 0.5 to 1.5% increased protein concentration by 60% in the cake layer.

Wet mono-sized granular packing: effects of initial clusters and filling strategy

Cohesive particles have been demonstrated to affect packing structures that sometimes inhibit applications while helpful in others. Therefore, accurately tailoring the cohesive granular packing, e.g., wet particles, is very rewarding nowadays. We adopt the discrete element method (DEM) and present a packing strategy by falling different size clusters containing mono-sized particles with varying cohesion to tailor the packing structure. We demonstrate the strategy's effectiveness by comparing the result with previous experiments, and we found the larger cluster tends to form a looser packing. We evidence that a dimensionless number, l⁎, evaluating the competing importance between kinetic energy and capillary potential, can precisely describe the cohesion effect. We combine l⁎ with several key indices, e.g., packing fraction, granular temperature, coordination number and force network distribution, to describe packing formation. Meantime, we found the different characterisation of cohesion effect throughout packing stages, which can shed light on the understanding of wet granular packing.

Creep Control in Soft Particle Packings.

Granular packings display a wealth of mechanical features that are of widespread significance. One of these features is creep: the slow deformation under applied stress. Creep is common for many other amorphous materials such as many metals and polymers. The slow motion of creep is challenging to understand, probe, and control. We probe the creep properties of packings of soft spheres with a sinking ball viscometer. We find that in our granular packings, creep persists up to large strains and has a power law form, with diffusive dynamics. The creep amplitude is exponentially dependent on both applied stress and the concentration of hydrogel, suggesting that a competition between driving and confinement determines the dynamics. Our results provide insights into the mechanical properties of soft solids and the scaling laws provide a clear benchmark for new theory that explains creep, and provide the tantalizing prospect that creep can be controlled by a boundary stress.

Added-mass force in dry granular matter.

From two-dimensional (2D) numerical simulations of the motion of a circular intruder into a dry granular packing, we provide evidence for a specific force term in the case of unsteady motion in addition to the force corresponding to a steady motion. We show that this additional term is proportional to the acceleration of the intruder relative to the grains as the added-mass force known for simple fluids. This force term corresponds to a variation in the kinetic energy of the surrounding flow and is characterized by a coefficient C_{AM} which is intrinsically linked to the nature of the granular media. An analytical calculation of the added-mass coefficient C_{AM} is developed based on the specific velocity field known for 2D granular flow around a cylinder. The theoretical value is shown to depend on the grain-cylinder size ratio, in good agreement with the measurements from our unsteady simulations.

Collective Drifts in Vibrated Granular Packings: The Interplay of Friction and Structure.

We simulate vertically shaken dense granular packings with horizontal periodic boundary conditions. A coordinated translating motion of the whole medium emerges when the horizontal symmetry is broken by disorder or defects in the packing and the shaking is weak enough to conserve the structure. We argue that such a drift originates in the interplay between structural symmetry breaking and frictional forces transmitted by the vibrating plate. A nonlinear ratchet model with stick slips reproduces many faces of the phenomenon. The collective motion discussed here underlies phenomena observed recently with vibrofluidized granular materials, such as persistent rotations and anomalous diffusion.

A Numerical Characterisation of Unconfined Strength of Weakly Consolidated Granular Packs and Its Effect on Fluid-Driven Fracture Behaviour

Soft or weakly consolidated sand refers to porous materials composed of particles (or grains) weakly held together to form a solid but that can be easily broken when subjected to stress. These materials do not behave as conventional brittle, linear elastic materials and the transition between these two regimes cannot usually be described using poro-elastic models. Furthermore, conventional geotechnical sampling techniques often result in the destruction of the cementation and recovery of sufficient intact core is, therefore, difficult. This paper studies a numerical model that allows us to introduce weak consolidation in granular packs. The model, based on the LIGGGHTS open source project, simply adds an attractive contribution to particles in contact. This simple model allows us to reproduce key elements of the behaviour of the stress observed in compacted sands and clay, as well as in poorly consolidated sandstones. The paper finishes by inspecting the effect of different consolidation levels in fluid-driven fracture behaviour. Numerical results are compared qualitatively against experimental results on bio-cemented sandstones.

Particle impact on a cohesive granular media.

We investigate numerically the impact process of a particle of diameter d and velocity V_{i} onto a cohesive granular packing made of similar particles via two-dimensional discrete element method simulations. The cohesion is ensured by liquid bridges between neighboring particles and described by short range attraction force based on capillary modeling. The outcome of the impact is analyzed through the production of ejected particles from the packing, referred to as the splash process. We quantify this production as a function of the impact velocity for various capillary strength Γ and liquid content Ω. The numerical data indicate that the splash process is modified when the dimensionless cohesion number Co=6Γ/ρ_{p}gd^{2} (where ρ_{p} is the particle density, d its diameter, and g the gravitational acceleration) exceeds a critical value of the order of the unity. Above this value, we highlight that the ejection process is triggered above a threshold impact Froude number, Fr=V_{i}/sqrt[gd], which depends both on Γ and Ω and scales as Γ^{β}Ω^{δ}, where the values of the exponents are found close to 1/2 and 1/6, respectively, and can be derived from rational physical arguments. Importantly, we show that, above the threshold, the number of splashed particles follows a linear law with the impact Froude number as in the cohesionless case.

Experimental study of a pilot unit of a ground regenerator for greenhouses

The object of research: the process of heat exchange in a packing in the form of a dense layer of crushed stone as part of a thermal regenerator designed to utilize the low-grade heat of the air in a greenhouse.
 Investigated problem: increasing the efficiency of air heat accumulation in the greenhouse during the daytime by a regenerative heat exchanger with a granular packing. Conducting experimental tests of regenerator models with a packing in the form of a dense layer of granular material under natural conditions is necessary to improve the design and optimize technological parameters.
 The main scientific results: the analysis of temperature curves of air changes at the inlet and outlet of the regenerator installed in the mock-up greenhouse with a volume of 0.25 m3, and the packing material was carried out. During the heating period of the nozzle, the accumulated heat was Q=8•104 J, which can be used when the temperature in the greenhouse decreases. During the pause, the loss from the heat exchange channel to the environment is 48,000 J. The duration of the period was 358 min, while the average heat flux corresponded to 2.2 W. Heat losses during the pause period are significant due to its duration, however, the average heat transfer coefficient has a low value of k=2.3 W/m2K, so strengthening the insulation of the heat exchange channel is irrational.
 The area of practical use of the results of the study: greenhouses, allowing the possibility of installing additional heat exchange equipment.
 Innovative technological product: the innovativeness of the technical solution is determined by the possibility of using the heat of the air in the greenhouse and the implementation of contact heat exchange between the air flow and the packing particles. The design of the regenerator, the simplicity of its manufacture and operation, as well as the efficiency of air heat accumulation in the greenhouse during the daytime, allow to recommend it for use in greenhouse farms.
 The scope of the innovative technological product: regenerative heat exchangers with a dense layer of granular material for the utilization of low-grade air flows generated in food production enterprises, ventilation systems and greenhouses

The weakening of inter-particle friction and its effect on mechanical behaviors of granular soils

This paper describes a numerical study examining the effect of weakening of inter-particle friction on granular soil responses. A bi-linear friction weakening model is proposed to describe the reduction of inter-particle friction with the increase of contact normal force. Through a series of drained triaxial loading tests from 3D DEM simulations, it is observed that the influence of friction weakening is quite limited on macro-mechanical behaviors for granular packing under a low confining stress. With the increase of confining stress, the influence of friction weakening gradually becomes significant. Samples embedded with friction weakening model exhibit relative lower peak strength and less dilatancy, compared with samples with constant inter-particle friction. From micromechanical perspective, samples embedded with friction weakening model has lower particle friction, which in turn lead to higher contact sliding ratio and lower tangential contact force for the packing. Higher sliding ratio implies more particle movement and less dilatancy of the packing. The lower tangential contact force at the microscale matches well with the lower peak strength at the macroscale. At critical state, the strength for samples with different friction models is concisely explained by analyzing the critical void ratio and tangential contact force distribution.

Compaction of bi-dispersed granular packing: analogy with chemical thermodynamics

Compaction of bi-dispersed granular packing: analogy with chemical thermodynamics

Structural evolution of granular cubes packing during shear-induced ordering

Packings of granular particles may transform into ordered structures under external agitation, which is a special type of out-of-equilibrium self-assembly. Here, evolution of the internal packing structures of granular cubes under cyclic rotating shearing has been analyzed using magnetic resonance imaging techniques. Various order parameters, different types of contacts and clusters composed of face-contacting cubes, as well as the free volume regions in which each cube can move freely have been analyzed systematically to quantify the ordering process and the underlying mechanism of this granular self-assembly. The compaction process is featured by a first rapid formation of orientationally ordered local structures with faceted contacts, followed by further densification driven by free-volume maximization with an almost saturated degree of order. The ordered structures are strongly anisotropic with contacting ordered layers in the vertical direction while remaining liquid-like in the horizontal directions. Therefore, the constraint of mechanical stability for granular packings and the thermodynamic principle of entropy maximization are both effective in this system, which we propose can be reconciled by considering different depths of supercooling associated with various degrees of freedom.

ABOUT STRESS TRANSMISSION THROUGH DISORDERED MEDIA CONFINED IN SILO GEOMETRY

Granular materials are found everywhere around us. A fundamental understanding of the behaviour of these materials is bound to have profound economic benefits. To understand the macroscopic behaviour of granular media and its relationship with the microscopic properties are major objectives of granular mechanics. However, presently macroscopic equations are empiric because of the complexities at the microscopic level. Granular media exhibit properties that are different from those of solids, liquids and gas and much of their behavior has not been fully understood. In this paper a brief survey of Physics of confined granular media has been presented. This is accomplished by reviewing the experimental and theoretical work done to determine the properties of static granular media and concerning theories presented to explain the properties. The apparent mass measurement at the bottom of a granular pile confined in a vertical tube decreases for denser granular packing. The denser granular packing comprising of two different diameters of granules augment the apparent mass instead. This anomalous behavior occurs when small granules are stacked on the large ones. In the case of anomalous increase, a percolation effect is found and correlated with the augment of apparent mass at the bottom of granular column