Motion Of Individual Grains Research Articles

Morphodynamics of Barchan‐Barchan Interactions Investigated at the Grain Scale

AbstractCorridors of size‐selected crescent‐shaped dunes, known as barchans, are commonly found in water, air, and other planetary environments. The growth of barchans results from the interplay between a fluid flow and a granular bed, but their size regulation involves intricate exchanges between different barchans within a field. One size‐regulating mechanism is the binary interaction between nearby dunes, when two dunes exchange mass via the near flow field or by direct contact (collision). In a recent Letter (Assis & Franklin, 2020, https://doi.org/10.1029/2020GL089464), we identified five different patterns arising from binary interactions of subaqueous barchans and proposed classification maps. In this paper, we further inquire into binary exchanges by investigating the motion of individual grains while barchans interact with each other. The experiments were conducted in a water channel where the evolution of pairs of barchans in both aligned and off‐centered configurations was recorded by conventional and high‐speed cameras. Based on image processing, we obtained the morphology of dunes and motion of grains for all interaction patterns. We present the trajectories of individual grains, from which we show the origin and destination of moving grains, and their typical lengths and velocities. We also show that grains from the impacting dune spread with a diffusion‐like component over the target barchan, and we propose a diffusion length. Our results provide new insights into the size‐regulating mechanisms of barchans and barchanoid forms found on Earth and other planets.

Dynamics of undeforming regions in the lead up to failure: jumping scales from lab to field

Knowledge transfer from micromechanics of granular media failure to geohazard forecasting and mitigation has been slow. But in the face of a rapidly expanding data infrastructure on the motion of individual grains for laboratory samples – and ground motion data at the field scale – opportunities to accelerate this knowledge transfer are emerging. In particular, such data assets coupled with data-driven approaches enable ‘new eyes’ to re-examine granular failure. To this end, effective strategies that can jump scales from bench to field are urgently needed. Here we demonstrate one strategy that focusses on the study of deformation patterns in the precursory failure regime using kinematic data. Unlike previous studies which focus on regions of high strains, here we probe the development and evolution of near-undeforming regions through the lens of explosive percolation. We find a common dynamical signature in which undeforming regions, which are initially transient in the precursory failure regime, become persistent from the time of imminent failure. We demonstrate the robustness of these findings for data on individual grain motions in a classical laboratory test and ground motion in two real landslides at vastly different scales.

Linking shape and rotation of grains during triaxial compression of sand

Particle shape has a strong effect on the mechanical response of coarse soils. This has been usually observed examining specimen-scale or engineering-scale responses, which are the sum of many microscale interactions. In this work we observe the effects of particle shape directly at the microscale level. X-ray tomography (μ-CT) of two sand specimens is exploited to measure three-dimensional particle shape descriptors but also to track individual particle motions during triaxial compression. A discrete digital volume correlation algorithm is employed to track the motion of individual grains (around 50,000 for each sand specimen) during the test and measure, with good precision, their cumulated displacements and rotations. The specimens examined failed in a clearly localised shear mode. Advantage is taken of this to obtain data relevant for very different kinematical regimes: one uniform and more constrained and the other close to critical state. A direct comparison between the shape and kinematic databases shows to what degree particle shape descriptors are related to observed kinematics. It appears that true sphericity is a good predictor of upper bound rotational restraint.

Three-dimensional phase field sintering simulations accounting for the rigid-body motion of individual grains

Sintering is a widely used powder processing technique in industrial applications. During sintering, atoms migrate to decrease the energy of the system via two main mechanisms: coarsening and densification, both of which lead to significant morphological variation of the sintered microstructure. When simulating sintering dynamics, the phase-field method has been broadly utilized because of its convenience in tracking morphology evolution. When a large number of grains is involved, it is common to use the same order parameter to describe multiple grains that are not in direct contact with one another (in order to reduce the computational memory demands). However, with this treatment it is difficult to handle the rigid-body motion of individual grains during densification. In this work, an implementation scheme is introduced to overcome the challenge of calculating individual particle motion based on existing equations. It uses a grouping algorithm and sets a cutoff radius on each grain for calculating the particle velocity during densification. This method allows for the incorporation of the densification mechanism, which has been commonly ignored in previous work, into phase-field sintering models in three-dimensional simulations with a large number of particles/grains. Moreover, through combination with the smoothed boundary method, material properties of sintered microstructures, such as the effective diffusivity and Young’s modulus, can be calculated during the sintering processes.

Influence of accounting for translational motion of grains on grain growth kinetics and size distribution

The thermodynamic dissipation-based approach, being one of the approved effective methods for treatment of grain growth, is refined by accounting for dissipation due to translational motion of individual grains during grain growth. The present model introduces an interaction function correlating the velocity of translational motion and the rate of growth for individual grains. The comparison of results of simulations based on the present model with existing phase-field simulations indicates that about 1/4 to 1/3 of the driving force is dissipated by translational motion of grains lowering the grain growth kinetics and changing of the steady state grain radii distribution function.

Determining the onset of hydrodynamic erosion in turbulent flow

We revisit the longstanding question of the onset of sediment transport driven by a turbulent fluid flow via laboratory measurements. We use particle tracking velocimetry to quantify the fluid flow as well as the motion of individual grains. As we increase the flow speed above the transition to sediment transport, we observe that an increasing fraction of grains are transported downstream, although the average downstream velocity of the transported grains remains roughly constant. However, we find that the fraction of mobilized grains does not vanish sharply at a critical flow rate. Additionally, the distribution of the fluctuating velocities of non-transported grains becomes broader with heavier tails, meaning that unambiguously separating mobile and static grains is not possible. As an alternative approach, we quantify the statistics of grain velocities by using a mixture model consisting of two forms for the grain velocities: a decaying-exponential tail, which represents grains transported downstream, and a peaked distribution centered at zero velocity, which represents grains that fluctuate due to the turbulent flow but remain in place. Our results suggest that more sophisticated statistical measures may be required to quantify grain motion near the onset of sediment transport, particularly in the presence of turbulence.

Understanding heavy mineral enrichment using a three‐dimensional numerical model

AbstractLayered deposits of relatively light and heavy minerals can be found in many aquatic environments. Quantification of the physical processes which lead to the fine‐scale layering of these deposits is often limited with flumes or in situ field experiments. Therefore, the following research questions were addressed: (i) how can selective grain entrainment be numerically simulated and quantified; (ii) how does a mixed bed turn into a fully layered bed; and (iii) is there any relation between heavy mineral content and bed stability? Herein, a three‐dimensional numerical model was used as an alternative measure to study the fine‐scale process of density segregation during transport. The three‐dimensional model simulates particle transport in water by combining a turbulence‐resolving large eddy simulation with a discrete element model prescribing the motion of individual grains. The granular bed of 0·004 m in height consisted of 200 000 spherical particles (D50 = 500 μm). Five suites of experiments were designed in which the concentration ratio of heavy (5000 kg m−3) to light particles (i.e. 2560 kg m−3) was increased from 6%, 15%, 35%, 60% to 80%. All beds were tested for 10 sec at a predefined flow speed of 0·3 m sec−1. Analysis of the particle behaviour in the interior of the beds showed that the lighter particles segregated from the heavy particles with increasing time. The latter accumulated at the bottom of the domain, forming a layer, whereas the lighter particles were transported over the layer forming sweeps. Particles below the heavy particle layer indicated that the layer was able to armour the particles below. Consequentially, enrichment of heavy minerals in a layer is controlled by the segregation of a heavy mineral fraction from the light counterpart, which enhances current understanding of heavy mineral placer formation.

Multiscale properties of dense granular materials

Purpose – Granular materials possess multiscale structures, i.e. micro-scales involving atoms and molecules in a solid particle, meso-scales involving individual particles and their correlated structure, and macroscopic assembly. Strong and abundant dissipations are exhibited due to mesoscopic unsteady motion of individual grains, and evolution of underlying structures (e.g. force chains, vortex, etc.), which defines the key differences between granular materials and ordinary objects. The purpose of this paper is to introduce the major studies have been conducted in recent two decades. Design/methodology/approach – The main properties at individual scale are introduced, including the coordination number, pair-correlation function, force and mean stress distribution functions, and the dynamic correlation function. The relationship between meso- and macro-scales is analyzed, such as between contact force and stress, the elastic modulus, and bulk friction in granular flows. At macroscales, conventional engineering models (i.e. elasto-plastic and hypo-plastic ones) are introduced. In particular, the so-called granular hydrodynamics theory, derived from thermodynamics principles, is explained. Findings – On the basis of recent study the authors conducted, the multiscales (both spatial and temporal) in granular materials are first explained, and a multiscale framework is presented for the mechanics of granular materials. Originality/value – It would provide a paramount view on the multiscale studies of granular materials.

Numerical simulation of turbulence and sediment transport of medium sand

A model of sand transport in water is produced by combining a turbulence-resolving large eddy simulation (LES) with a discrete element model (DEM) prescribing the motion of individual grains of medium sand. The momentum effect of each particle on the fluid is calculated at the LES cell containing the particle, and the fluid velocity and pressure, interpolated to each particle center, is used to derive fluid force on each particle in the DEM. Eleven numerical experiments are conducted of an initially flat bed of particles. The experiments span a range of motion, from essentially no motion to vigorous suspension. Hydraulic roughness is found to increase abruptly at the transition from bed load to suspended load transport. Suspended sediment extracts momentum from the flow and decreases the rate of shear. Whereas, slightly higher in the flow, vertical drag by suspended grains damps turbulence and increases the rate of shear. Vertical sediment diffusivity and effective particle settling velocity are much smaller than is commonly assumed in suspended sediment models. The bed load experiments suggest that saltation by itself is a poor model of bed load sand transport. In contrast to expectations from saltation models, the peak bed load flux occurs at essentially the same level as the bed, and grains move slowly in frequent contact with other grains. Higher- and faster-moving bed load grains that can be considered to be in saltation represent a smaller portion of the total flux. Entrainment of bed load grains occurs in response to fluid penetration of the bed by high-vorticity turbulence structures embedded within broader high speed fluid regions referred to as a sweeps or high-speed wedges.

On the initiation of cyclic oxidation-induced rumpling of platinum-modified nickel aluminide coatings

The evolution of the surface roughness of an initially flat platinum-modified nickel aluminide (NiPtAl) coating on a single crystal superalloy with cyclic oxidation has been measured by optical profilometry and correlated with the aluminide microstructure. The roughness evolution is dominated by the relative motion of individual grains on thermal cycling, with the larger sized grains moving up and the smaller grains moving down with respect to the average surface. Detailed crystallographic analysis indicates that the grains in the coating are randomly distributed and have no crystallographic relationship with the underlying single crystal superalloy. Furthermore, there is a correlation between the number of sides a grain has and the propensity for its center to move relative to the average surface plane: grains with six or more sides bow up, whereas the surfaces of those grains with fewer than six sides bow down. It is proposed that rumpling initiates due to the vertical displacement of the smaller grains having fewer than six sides. Once initiated, rumpling proceeds driven by the strain energy in the thermally grown oxide.

Erosion of a granular bed driven by laminar fluid flow

Motivated by examples of erosive incision of channels in sand, we investigate the motion of individual grains in a granular bed driven by a laminar fluid to give us new insights into the relationship between hydrodynamic stress and surface granular flow. A closed cell of rectangular cross-section is partially filled with glass beads and a constant fluid fluxQflows through the cell. The refractive indices of the fluid and the glass beads are matched and the cell is illuminated with a laser sheet, allowing us to image individual beads. The bed erodes to a rest heighthrwhich depends onQ. The Shields threshold criterion assumes that the non-dimensional ratio θ of the viscous stress on the bed to the hydrostatic pressure difference across a grain is sufficient to predict the granular flux. Furthermore, the Shields criterion states that the granular flux is non-zero only for θ > θc. We find that the Shields criterion describes the observed relationshiphr∝Q1/2when the bed height is offset by approximately half a grain diameter. Introducing this offset in the estimation of θ yields a collapse of the measured Einstein numberq* to a power-law function of θ − θcwith exponent 1.75 ± 0.25. The dynamics of the bed height relaxation are described well by the power-law relationship between the granular flux and the bed stress.

Convection in a vibrated granular layer

When a granular layer is submitted to an oscillating acceleration with a peak value larger than gravity, a large scale motion develops. This movement is in some ways similar to the one displayed by a liquid heated from below, and it is called granular convection. Different conditions beside the parameters of the forcing can affect it, such as the presence of an interstitial gas or the roughness of the walls. We have carried out an experiment to study the convective movement of a granular layer with a temporal resolution high enough to describe the motion of individual grains within one oscillating period. We also present experimental results concerning the friction that the lateral walls exert on the grains and its relevance on granular convection.

Characterization of granular flow of wet solids in a bladed mixer

AbstractIn this study, we measure instantaneous, average, and fluctuating velocity fields at exposed surfaces for dry and wet grains in a vertical cylindrical mixer, agitated by four pitched blades. When the material is dry, the free surface of the granular bed deforms, rising where the blades are present, and falling between blade passes. Although average velocities are predominantly azimuthal, instantaneous velocities tracked in time reveal three‐dimensional particle circulations, including significant periods of particle motion in the opposite direction to that of the blades, indicative of bed penetration. When moisture is added to the solid particles, the flow dynamics change from a regime dominated by the motion of individual grains to a regime controlled by the motion of small clumps that form as a result of the cohesive forces. This transition is characterized by a reduced particle–particle collision frequency and exhibits a sharp decrease in the granular temperature at the free surface. This transition is also characterized by an increase in bed porosity, which is attributed to increased cohesiveness arising from liquid bridges. A Fourier transform analysis conducted on the tangential component of the velocities (dominant flow) shows that a group of high frequencies exceeding the blade rotation frequency become significant with added moisture. These are characteristics of the large number of wet agglomerates flowing between successive blade passes. © 2006 American Institute of Chemical Engineers AIChE J, 2006

DEM Applications to Aeolian Sediment Transport and Impact Process in Saltation

Keywords A discrete element model (DEM) is developed for investigation of the dynamic behavior of sand grains, in which the motion of individual grains is considered. The DEM has been used for simulating 9000 grains' motion blown by wind, resulting in ripples and saltating paths. Exchange between saltation and creep along the surface is also calculated, which is helpful for revealing the intrinsic mechanism of ripple formation. A critical event in the trajectory of sand grain saltating in the air is its interaction with the surface. As another application of DEM, the numerical experiment of a sand bed impacted by a single grain traveling at 8 ms−1 and 11.5° is performed to quantitatively evaluate the splash process. A normalized Maxwellian distribution function f(ν y ) = a · ν c y · exp(−b· ν d y ) is proposed for the vertical velocity distribution of splashed grains, where the parameters a, b, c, and d can be regressed from the vertical velocity component of saltating grains. Generally, the vertical velocity of saltating grains fits the Maxwellian function well, with the correlation coefficients larger than 0.8. The result also shows that the restitution and surface friction coefficients of grains have negligible influence on the Maxwellian function. Therefore, the DEM can simulate sand movement and offer more detailed information as to what happens inside the flow, which could be applied in a wider suitable range in comparison with previous models.

Numerical simulation of aeolian sediment transport

A discrete element model (DEM) is developed for aeolian sediment transport in the scope of investigation of the dynamic behavior of grains, in which the motion of individual grain is considered while velocity distribution of wind is given according to bed forms. The above model has been used for simulating the phenomenon of 4000 grains blown by wind, resulting in ripples and saltating paths, which shows good agreements with experimental observations. The result is helpful for revealing the intrinsic mechanism of sand flow.

Distinct element simulation of grain alignment in mushy-state forging of magnets

A method for simulating the motion of grains in mushy-state forming of magnets is proposed on the basis of the distinct element method. The grains of the magnet are modelled to be a lot of elliptical elements, and the effect of the liquid phase on the motion of the grains is treated as viscous resistance to the movement. The motion of individual grains is obtained by solving the equations of motion for a time increment under the action of the elastic repulsive, frictional and viscous forces. Macroscopic plastic deformation of a metallic capsule containing the magnet is calculated by the viscoplastic finite element method, and the obtained motion of the interface between the capsule and magnet is used as a boundary condition in the distinct element simulation. The motion of grains in mushy-state plane-strain upsetting of a rare earth magnet contained in a steel capsule is chosen as an example of the simulation. The degree of grain alignment due to the upsetting increases as the reduction in height increases. The calculated degree of grain alignment agrees well with that for a model experiment using acrylic resin grains and a plasticine capsule.

Simulation of Grain Alignment in Mushy-State Forming of Magnets by Distinct Element Method.

A method for simulating the motion of grains in mushy-state forming of magnets is proposed on the basis of the distinct element method. The grains of the magnet are modelled to be a lot of elliptical elements, and the effect of the liquid phase on the motion of the grains is treated as viscous resistance to the movement. The motion of individual grains is obtained by solving the equations of motion for a mail time step under the action of elastic repulsive, frictional and viscous forces. Plastic deformation of a metallic capsule containing the magnet is calculated by the viscoplastic finite element method, and the obtained motion of the interface between the capsule and the magnet is used as a boundary condition in the distinct element simulation. Mushy-state plane-strain upsetting of a rare earth magnet contained in a steel capsule is chosen as an example of the simulation. The calculated degree of grain alignment is in good agreement with that obtained by a model experiment using acrylic grains, a plasticine capsule and Vaseline.

The Influence of Piezoelectric Grain Resonance on the Dielectric Spectra of LiNbO3 Ceramics

It has often been suggested that the higher frequency dispersion (f∼107∼108 Hz) evident in the dielectric response of high‐permittivity ferroelectric ceramics might be associated with piezoelectrically driven resonant mechanical motion of individual grains. The hypothesis certainly appears reasonable, but so far no direct verification appears to have been attempted. Our discovery that the individual crystallite resonances are well preserved in poled LiNbO3 bicrystals suggested that we explore the dispersion of LiNbO3 ceramics. In both conventionally sintered and uniaxially hot‐pressed ceramics, the dielectric dispersion around 108 Hz has obvious resonant character. Using a modified ECAP computer program demonstrated that both the real and imaginary components of the impedance can be quantitatively described using the equivalent circuit models for the coupled individual grain resonances.