Initial Packing Fraction Research Articles

Polydispersity effect on dry and immersed granular collapses: an experimental study

The column collapse experiment is a simplified version of natural and industrial granular flows. In this set-up, a column built with grains collapses and spreads over a horizontal plane. Granular flows are often studied with a monodisperse distribution; however, this is not the case in natural granular flows where a variety of grain sizes, known as polydispersity, is a common feature. In this work, we study the effect of polydispersity, and of the inherent changes that polydispersity causes in the initial packing fraction, in dry and immersed columns. We show that dry columns are not significantly affected by polydispersity, reaching similar distances at similar times. In contrast, immersed columns are strongly affected by the polydispersity and packing fraction, and the collapse sequence is linked to changes of the basal pore fluid pressure $P$ . At the collapse initiation, negative changes of $P$ beneath the column produce a temporary increase of the column strength. The negative change of $P$ lasts longer in polydisperse columns than in monodisperse columns, delaying the collapse sequence. Conversely, during the column spreading, positive changes of $P$ lead to a decrease of the shear strength. For polydisperse collapses, the excess of $P$ lasts longer, allowing the material to reach farther distances, compared with the collapses of monodisperse materials. Finally, we show that a mobility model that scales the final runout with the collapse kinetic energy remains true for different polydispersity levels in a three-dimensional configuration, capturing the scaling between the micro to macro controlling features.

Effects of salinity on the flow of dense colloidal suspensions.

We experimentally study the effects of salt concentration on the flowing dynamics of dense suspensions of micrometer-sized silica particles in microfluidic drums. In pure water, the particles are fully sedimented under their own weight, but do not touch each other due to their negative surface charges, which results in a "frictionless" dense colloidal suspension. When the pile is inclined above a critical angle θc ∼ 5° a fast avalanche occurs, similar to what is expected for classical athermal granular media. When inclined below this angle, the pile slowly creeps until it reaches flatness. Adding ions in solution screens the repulsive forces between particles, and the flowing properties of the suspension are modified. We observe significant changes in the fast avalanche regime: a time delay appears before the onset of the avalanche and increases with the salt concentration, the whole dynamics becomes slower, and the critical angle θc increases from ∼5° to ∼20°. In contrast, the slow creep regime does not seem to be heavily modified. These behaviors can be explained by considering an increase in both the initial packing fraction of the suspension Φ0, and the effective friction between the particles μp. These observations are confirmed by confocal microscopy measurements to estimate the initial packing fraction of the suspensions, and AFM measurements to quantify the particles surface roughness and the repulsion forces, as a function of the ionic strength of the suspensions.

Numerical study on critical flow velocity of ice slurry in the pipe of ice source heat pump system

The traditional evaporator of water source heat pump system is easy to freeze when the water source temperature is too low in winter. A novel ice source heat pump system is proposed, which can use low temperature surface water to supply heat to buildings. One of the key problems for safe transportation is velocity range of ice slurry in ice outlet pipeline. In order to study the critical flow velocity of ice slurry in the pipe, an Euler model of horizontal straight pipe and 90° elbow pipe were established by Fluent software. The influence of five factors on the critical flow velocity of two kinds of pipes, including initial ice packing fraction, ice particle size, pipe diameter, length of straight pipe and radius curvature of elbow was studied. It found that the initial ice content should be controlled from 10% to 15%. The inlet flow rate was 20% higher than the critical flow rate under the most unfavorable condition. Ice particle size was less than 0.2 mm. The total length of ice discharge pipeline was less than 50 m. Curvature radius of the bend should be met the minimum requirements of the specification of the pipe used.

Roles of packing fraction, microscopic friction, and projectile spin in cratering by impact.

From small seeds falling from trees to asteroids colliding with planets and moons, the impact of projectiles onto granular targets occurs in nature at different scales. In this paper, we investigate open questions in the mechanics of granular cratering, in particular, the forces acting on the projectile and the roles of granular packing, grain-grain friction, and projectile spin. For that, we carried out discrete element method computations of the impact of solid projectiles on a cohesionless granular medium, where we varied the projectile and grain properties (diameter, density, friction, and packing fraction) for different available energies (within relatively small values). We found that a denser region forms below the projectile, pushing it back and causing its rebound by the end of its motion, and that solid friction affects considerably the crater morphology. Besides, we show that the penetration length increases with the initial spin of the projectile, and that differences in initial packing fractions can engender the diversity of scaling laws found in the literature. Finally, we propose an ad hoc scaling that collapsed our data for the penetration length and can perhaps unify existing correlations. Our results provide new insights into the formation of craters in granular matter.

Micromechanical simulations of the collapse of a submerged granular column

In this work, we present a numerical study of a granular collapse in a viscous fluid adopting a DEM-PFV (Pore Finite Volume) coupled model. We analyze the time evolution of the collapse and the final morphology of the deposit (triangular or trapezoidal) as a function of the initial solid fraction and column aspect ratio. Finally, we discuss the role of the initial packing fraction of the granular material on the time evolution of the pore pressure. The numerical results are consistent with experimental observation [3] showing the capability of the DEM-PFV coupled model to simulate saturated granular media from triggering to flowing and stopping conditions.

Modeling of elastic properties and conductivity of partially sintered ceramics with duplex microstructure and different grain size ratio

The elastic constants and conductivity of partially sintered single-phase and two-phase ceramics (exemplified by alumina ceramics and alumina-zirconia composites, respectively) with different grain size ratio (from 1:1 to 1:4) are investigated by numerical modeling. The relative elastic moduli of partially sintered two-phase ceramics are shown to be relatively similar to those of single-phase ceramics, whereas the relative conductivity is significantly lower, because of the higher phase contrast. The more the grain size ratio deviates from unity, the higher is the initial packing fraction, and the lower are the relative elastic moduli and conductivity of the partially sintered ceramics. The porosity dependence of the Poisson ratio shows a decreasing trend which is only very weakly affected by the grain size ratio. Correlations between relative Young’s modulus and relative conductivity lie between upper and lower cross-property bounds. For single-phase materials the correlation lies below, for two-phase materials above, the Pabst-Gregorová cross-property relation.

Compaction mechanics of a polydisperse crushable spherical granular assembly using discrete element method

The macroscopic behaviour of an assembly of polydisperse spherical particles is studied using a numerical model based on discrete element method (DEM), which accounts for the microscopic interactions between individual particles and their damage. DEM models particle–particle interactions enabling to understand the influence of microscopic particle–particle interactions on the macroscopic response. The method is used to stimulate the mechanical response of a polydisperse particle assembly under uniaxial compressive load. The influence of damage rate and the initial packing fraction on the macroscopic stress–strain response is investigated. The analysis shows that the initial nonlinear elastic behaviour is influenced by the initial packing factor, whereas the critical stress is influenced by both initial packing fraction and damage rate. It is also observed that critical stress occurs when the assembly reaches a particular damage state. Furthermore, the failure behaviour of different sized particles within a polydisperse assembly is also investigated. The experimental data from the literature show that the crush strength of the particle of given size is observed to vary over a range. Such variation of crush strengths for a given particle size is also implemented in the present work.

Compaction Dynamics during Progenitor Cell Self-Assembly Reveal Granular Mechanics

Summary We study the self-assembly dynamics of human progenitor cells in agarose microwells that are used for production of chondrogenic organoids. Using image analysis on time-lapse microscopy, we estimate the aggregate area in function of time for a large number of aggregates. In control conditions, the aggregate radius follows an exponential relaxation that is consistent with the dewetting dynamics of a liquid film. Upon introducing Y-27632 Rho kinase inhibitor, the compatibility with the liquid model is lost, and slowed-down relaxation dynamics are observed. We demonstrate that these aggregates behave as granular piles undergoing compaction, with density relaxation that follows a stretched exponential. Using simulations with an individual cell-based model, we construct a phase diagram of cell aggregates that suggests that the aggregate in presence of Rho kinase inhibitor approaches glass transition.

Influence of particle size on vertical plate penetration into dense cohesionless granular materials (large-scale DEM simulation using real particle size)

The influence of the particle size on the vertical plate penetration into dense cohesionless granular materials was numerically investigated. Simulations were performed in quasi-two-dimensional conditions by changing the mean particle diameters d50 but maintaining the plate thickness B from B/d50 = 63–2.6. The initial bulk packing fraction was kept high, irrespective of the particle size. In the smallest particle size case (B/d50 = 63), the size ratio reached almost the same level as that in the laboratory experiments using natural sand particles. The results demonstrated that the mean penetration resistance force acting on the plate tip surface increases with a decrease of B/d50, while the tangential force acting on the side surfaces does not change with B/d50. Tip resistances increase linearly with the penetration depth, while the tangential resistances increase with the square of the depth regardless of B/d50. The behavior of the resistance fluctuations changes qualitatively between B/d50 = 31 and 21. For all cases, we confirmed the formation of a wedge-shaped flow with a high forward velocity in front of the plate tip. The wedge flow width was larger than the plate thickness by almost a mean particle diameter, and was responsible for the increase in the mean resistance depending on the particle size. For the large B/d50 cases only, the resistance exhibited quasi-periodic fluctuations, which was attributable to the intermittent nucleation and disappearance of the shear bands. Moreover, we investigated the dependence of B/d50 on the band evolutions by analyzing the band thickness.Graphic abstractThe influence of the particle size on the vertical plate penetration into dense cohesionless granular materials was numerically investigated using DEM. Simulations were performed in quasi-two-dimensional conditions by changing the median particle diameters d50 but maintaining the plate thickness B. The initial bulk packing fraction was kept high, irrespective of the particle size. Upper and lower figures show the result of small (B/d50 = 63) and large particle size case (B/d50 = 21), respectively. In the small particle size case (B/d50 = 63), the size ratio reached almost the same level as that in the laboratory and the dynamics of 35.5 million particles was considered. Right and left figures illustrate instantaneous shear strain rate and local packing fraction distributions, respectively. Large qualitative change in the granular behaviors as well as penetration resistance was observed between B/d50 = 31 and 21. The intermittent nucleation and disappearance of the shear bands were clearly observed only for large B/d50 cases.

Jamming by shear in a dilating granular system

Jamming can occur in frictional granular materials undergoing shear at a fixed packing fraction, $$\phi $$, within a range below the isotropic jamming point, with the amount of strain required to induce jamming, $$\gamma $$, increasing with decreasing $$\phi $$. We are interested in how the shear jamming process is affected when the system dilates as it is sheared. We conduct experiments to shear a 2D granular system while continuously increasing the system volume. Below a certain dilation rate, the system is still able to jam for $$\phi $$ smaller than the initial $$\phi _0$$. We measure $$\gamma $$ for different dilation rates and initial packing fractions by monitoring the coordination number of non-rattlers and the system pressure. We find that $$\gamma $$ is the same as the $$\gamma $$ required to jam a system with fixed packing fraction $$\phi $$ via pure shear.

Packing-dependent granular friction exerted on a rod withdrawn from a granular layer: the role of shear jamming

Resistance force acting on a rod vertically withdrawn from a granular layer is studied by experiments and numerical simulations. The initial packing fraction of the granular layer is controlled to evaluate the packing dependence of the resistance force. In both experiments and numerical simulations, the frictional resistance force in the steady slipping regime increases as the initial packing fraction is increased. According to the numerical results, the principal reason for the increase of frictional resistance is the increase of normal force acting on the rod. This large normal force stems from the effective solidification of the granular layer which is caused by the shearing induced by the withdrawn rod. Based on this shear-induced solidification, the experimental data are analyzed using a simple ‘cylindrical shear-jammed zone’ model. Then, the critical divergence of the size of solidified (shear-jammed) zone is observed by increasing the initial packing fraction towards the jamming packing fraction.

Activity-induced mixing and phase transitions of self-propelled swimmers.

We study the mixing of active swimmers. Two different types of swimmers (modeled as particles) are placed initially in two boxes with an interconnection between them. The mixing of swimmers happens as they move with their own self-propelled forces. The self-propelled force is constant and the direction of the exerted thrust is governed by the neighboring swimmers. Overall mixing of the swimmers depends on the magnitude of the exerted thrust, the initial packing fraction, and the activity level. Different nonequilibrium states are also identified depending on the exerted thrust and the initial packing fraction of the swimmers.

Models and simulations of surfactant-driven fracture in particle rafts

A continuum-based model for the surfactant-driven fracture of closely-packed particle rafts is extended to examine the influence of micro-scale density variability. The model treats the particle monolayer as an elastic sheet endowed with a critical fracture energy that can be reduced through interaction with a flowing surfactant. In addition to the displacement of the monolayer, the model employs a surfactant damage field that serves as both an indicator function for the surfactant concentration as well as the damage to the monolayer. Spatial variability in the particle packing is incorporated in the model through a continuum mapping approach. The formulation gives rise to a coupled system of nonlinear partial differential equations with an irreversibility constraint. The evolution equations are recast in variational form and discretized with an adaptive finite element method. Simulations are provided to demonstrate convergence of the model, illustrate the sensitivity of the fracture process to variations in the initial packing fraction field, and make comparisons with experimental observations. The results indicate that crack bifurcations can occur in regions with spatially uniform packing as well as spatially variable packing, suggesting that both the macro-scale mechanics and the random aspects of the packing contribute to these instabilities. The model is also used to predict the response of these systems to multiple injection sources and obstacles in the domains. Finally, the model is extended to non-planar surfaces as a means to study systems in which confinement and jamming can only occur due to multiple injection sites.

Discrete element analysis of buffering capacity of non-spherical granular materials based on super-quadric method

Granular system commonly encountered in industry or nature is comprised of non-spherical grains. Comparing with spherical particles, high discretization and interlocking among non-spherical particles can effectively dissipate the system energy and improve the buffer capacity. The superquadric element based on continuous function envelop can form the geometric shape of irregular particles accurately, and then contact collision action between particles can be calculated easily. In this paper, we provide a comprehensive introduction to particle-particle and particle-boundary contact collision. In addition, considering different shapes and surface curvatures under various contact patterns between super-quadric particles, the linear contact force model cannot be applied to the accurate calculation of the contact force, and a corresponding non-linear viscoelastic force model is developed. In this model, the equivalent radius of curvature at a local contact point is adopted to calculate the normal contact force, and the tangential contact force is simplified based on the contact model of spherical elements. To examine the validity of the algorithm and this model, we compare the discrete element analytical results with the analytical results for a single cylinder impacting a flat wall and the previous experimental results for spherical granular material under impact load, and this method is verified by good agreement between the simulated results and the previous experimental results. According to the aforementioned method, we study the buffer capacity of non-spherical particles under impact load by the discrete element method, and the influences of granular thickness and particle shapes on the buffer capacity are discussed. The results show that a critical thickness Hc is obtained for different particle shapes. The buffer capacity is improved with increasing the granular thickness when H Hc, but is independent of the granular thickness and particle shapes when H Hc. Moreover, the impact peak and initial packing fraction increase significantly with increasing the blockiness. Rectangular particles account for the highest packing fraction, and the packing fraction of cylindrical particles is higher than the packing fraction of spherical particles. Therefore, Rectangular particles are more likely to form dense face-face contacts and ordered packing structures with high packing fraction. These denser packings prevent the particles from their relatively moving, and thus reducing the buffering capacity of the particles. Furthermore, the impact peak and initial packing fraction decrease with increasing or reducing the aspect ratio of cylindrical particles and the aspect ratio of rectangular particles. The aspect ratio of particle can be used to adjust the dense packing structure and reduce the stability of the system. It means that the particles have more effective buffer capacity for the non-spherical particle system.

Unifying Impacts in Granular Matter from Quicksand to Cornstarch.

A sharp transition between liquefaction and transient solidification is observed during impact on a granular suspension depending on the initial packing fraction. We demonstrate, via high-speed pressure measurements and a two-phase modeling, that this transition is controlled by a coupling between the granular pile dilatancy and the interstitial fluid pressure generated by the impact. Our results provide a generic mechanism for explaining the wide variety of impact responses in particulate media, from dry quicksand in powders to impact hardening in shear-thickening suspensions like cornstarch.

Numerical study on influences of bed resettling, breeding zone orientation, and purge gas on temperatures in solid breeders

We apply coupled computational fluid dynamics and discrete element method (CFD-DEM) modeling tools with new numerical implementations of pebble fragmentation to study the combined effects of granular crushing and ensemble restructuring, granular fragment size, and initial packing for different breeder volume configurations. In typical solid breeder modules, heat removal from beds relies on maintaining pebble–pebble and pebble–wall contact integrity. However, contact is disrupted when an ensemble responds to individually crushed pebbles. Furthermore, restructuring of metastable packings after crushing events are, in part, dependent on gravity forces acting upon the pebbles. We investigate two representative pebble bed configurations under constant volumetric heat sources; modeling heat removed from beds via inter-particle conduction, purge gas convection, and contact between pebble beds and containers. In one configuration, heat is removed from at walls oriented parallel to the gravity vector (no gap formation possible); in the second, heat is removed at walls perpendicular to gravity, allowing for the possibility of gap formation between bed and wall. Judging beds on increase in maximum temperatures as a function of crushed pebble amount, we find that both pebble bed configurations to have advantageous features that manifest at different stages of pebble crushing. However, all configurations benefit from achieving high initial packing fractions.

Compaction of granular material inside confined geometries

In both nature and the laboratory, loosely packed granular materials are often compacted inside confined geometries. Here, we explore such behaviour in a quasi-two dimensional geometry, where parallel rigid walls provide the confinement. We use the discrete element method to investigate the stress distribution developed within the granular packing as a result of compaction due to the displacement of a rigid piston. We observe that the stress within the packing increases exponentially with the length of accumulated grains, and show an extension to current analytic models which fits the measured stress. The micromechanical behaviour is studied for a range of system parameters, and the limitations of existing analytic models are described. In particular, we show the smallest sized systems which can be treated using existing models. Additionally, the effects of increasing piston rate, and variations of the initial packing fraction, are described.

Effect of volume fraction on granular avalanche dynamics.

We study the evolution and failure of a granular slope as a function of prepared volume fraction, ϕ(0). We rotated an initially horizontal layer of granular material (0.3-mm-diam glass spheres) to a 45° angle while we monitor the motion of grains from the side and top with high-speed video cameras. The dynamics of grain motion during the tilt process depended sensitively on ϕ(0)∈[0.58-0.63] and differed above or below the granular critical state, ϕ(c), defined as the onset of dilation as a function of increasing volume fraction. For ϕ(0)-ϕ(c)<0, slopes experienced short, rapid, precursor compaction events prior to the onset of a sustained avalanche. Precursor compaction events began at an initial angle θ(0)=7.7±1.4° and occurred intermittently prior to the onset of an avalanche. Avalanches occurred at the maximal slope angle θ(m)=28.5±1.0°. Granular material at ϕ(0)-ϕ(c)>0 did not experience precursor compaction prior to avalanche flow, and instead experienced a single dilational motion at θ(0)=32.1±1.5° prior to the onset of an avalanche at θ(m)=35.9±0.7°. Both θ(0) and θ(m) increased with ϕ(0) and approached the same value in the limit of random close packing. The angle at which avalanching grains came to rest, θ(R)=22±2°, was independent of ϕ(0). From side-view high-speed video, we measured the velocity field of intermittent and avalanching flow. We found that flow direction, depth, and duration were affected by ϕ(0), with ϕ(0)-ϕ(c)<0 precursor flow extending deeper into the granular bed and occurring more rapidly than precursor flow at ϕ(0)-ϕ(c)>0. Our study elucidates how initial conditions-including volume fraction-are important determinants of granular slope stability and the onset of avalanches.

Granular flow through an aperture: influence of the packing fraction.

For the last 50 years, the flow of a granular material through an aperture has been intensely studied in gravity-driven vertical systems (e.g., silos and hoppers). Nevertheless, in many industrial applications, grains are horizontally transported at constant velocity, lying on conveyor belts or floating on the surface of flowing liquids. Unlike fluid flows, that are controlled by the pressure, granular flow is not sensitive to the local pressure but rather to the local velocity of the grains at the outlet. We can also expect the flow rate to depend on the local density of the grains. Indeed, vertical systems are packed in dense configurations by gravity, but, in contrast, in horizontal systems the density can take a large range of values, potentially very small, which may significantly alter the flow rate. In the present article, we study, for different initial packing fractions, the discharge through an orifice of monodisperse grains driven at constant velocity by a horizontal conveyor belt. We report how, during the discharge, the packing fraction is modified by the presence of the outlet, and we analyze how changes in the packing fraction induce variations in the flow rate. We observe that variations of packing fraction do not affect the velocity of the grains at the outlet, and, therefore, we establish that flow-rate variations are directly related to changes in the packing fraction.

Predicting the settlement of coarse granular materials under vertical loading.

Granular materials are widely used in industrial processes despite their complex and poorly understood mechanical behaviour both in static and dynamic regimes. A prototypical example is the settlement and compaction of a granular bed under vibrational loading. The elementary mechanisms of this process are still unclear and there is presently no established theory or methodology to predict the settlement and its statistical variability. By means of a parametric study, carried out on a full-scale track, and a critical analysis of density relaxation laws, we introduce a novel settlement model in coarse granular materials under cyclic loading. Our extensive experimental data indicate that the settlement process is governed by three independent parameters strongly correlated with the vibration intensity and initial packing fraction. We show that the mean settlement is well predicted by the model with its parameter values extracted from experimental data.