Column Of Grains Research Articles

Rescaling invariance and anomalous energy transport in a small vertical column of grains.

It is well known that energy dissipation and finite size can deeply affect the dynamics of granular matter, often making usual hydrodynamic approaches problematic. Here we report on the experimental investigation of a small model system, made of ten beads constrained into a 1D geometry by a narrow vertical pipe and shaken at the base by a piston excited by a periodic wave. Recording the beads motion with a high frame rate camera allows to investigate in detail the microscopic dynamics and test hydrodynamic and kinetic models. Varying the energy, we explore different regimes from fully fluidized to the edge of condensation, observing good hydrodynamic behavior down to the edge of fluidization, despite the small system size. Density and temperature fields for different system energies can be collapsed by suitable space and time rescaling, and the expected constitutive equationholds very well when the particle diameter is considered. At the same time, the balance between dissipated and fed energy is not well described by commonly adopted dependence due to the up-down symmetry breaking. Our observations, supported by the measured particle velocity distributions, show a different phenomenological temperature dependence, which yields equationsolutions in agreement with experimental results.

Modeling ozone deposition on bulk grains and ozone deposition in columns of wheat grains

To better understand ozone deposition on bulk grains to control bacterium and insects, we investigated time-dependent deposition of ozone at various depths in columns of grains. We proposed a model of ozone deposition on bulk grains based on a material balance for ozone. The model included porosity, pore shape factor and velocity of ozone gas for bulk grains. The model was applied to determine the time-dependent deposition velocities of ozone at various depths in columns of wheat grains. Ozone deposition on wheat grains had two distinct phases. Phase 1 was characterized by high deposition velocities and then rapid decrease. In phase 2, the deposition velocities were kept constant with the time at various depths in the column. The saturation time based on the deposition model was 87.1h and the relative error was 2.4% for grade 4 hard red winter wheat with a moisture content of 10.3% at 22.0 °C. The surface reaction probability was the order of magnitude of 1 × 10−6 in the saturation state. This deposition model can be applied to optimize the ozone treatment for various kinds of grains.

Emergence of structure in columns of grains and elastic loops.

It is possible to build free-standing, load-bearing structures using only rocks and loops of elastic material. We investigate how these structures emerge, and find that the necessary maximum loop spacing (the critical spacing) is a function of the frictional properties of the grains and the elasticity of the confining material. We derive a model to understand both of these relationships, which depends on a simplification of the behavior of the grains at the edge of a structure. We find that higher friction leads to larger stable grain-grain and grain-loop contact angles resulting in a simple function for the frictional critical spacing, which depends linearly on friction to first order. On the other hand, a higher bending rigidity enables the loops to better contain the hydrostatic pressure of the grains, which we understand using a hydroelastic scale. These findings will illuminate the stabilization of dirt by plant roots, and potentially enable the construction of simple adhesion-less structures using only granular material and fiber.

Experimental investigation of tsunami waves generated by granular collapse into water

Abstract

A numerical and experimental study of sand-rubber mixtures subjected to oedometric compression

The stockpiling of waste tires at landfill sites has become a nuisance for the society. One of the alternatives could be converting the recycled rubber into powdered form and mixing it with soil to use it as the backfill of the retaining structures. This paper is based on the study of such sand-rubber mixtures. In this work, Discrete Element (DEM) simulations were employed to study the mechanical response of sand-rubber mixtures with respect to a column of grains enclosed within a rigid cylindrical confinement, and subjected to an oedometric compression by the fixed velocity displacement of one of the horizontal walls. Further, experimental analysis was also carried out by using a uniaxial load cell to load the sand-rubber mixtures under compression. Different initial packings of sand-rubber mixture were prepared by varying: (a) the packing volume fraction and (b) the volume fraction of rubber. The mechanical response at small strains was studied for these sand-rubber packings. The mixture behavior was observed to be more sand-dominant or rubber-dominant depending on the rubber fraction and the mixture quality. Moreover, variation in the initial volume fraction of the packing also caused a difference in the load bearing of the packings for a given strain and a given rubber fraction.

Estimating Passive Stress Acting on a Grain Entrapment Victim's Chest.

Grain entrapments remain a major concern in the grain industry, with 1,100 incidents documented since the 1970s. One particular concern is the ability of a victim to breathe while entrapped in grain. Anecdotal reports suggest that victims struggle to breathe when entrapped in grain to a depth that covers their chests, yet some evidence indicates that victims should be able to breathe normally as long as their airways are not blocked regardless of depth. The hypothesis for this discrepancy is that previously published experiments measured an active stress state in the grain, while a person breathing also experiences a passive stress state during inhalation. The passive stress is significantly larger than the active stress. The objective of this study was to measure the passive stress when pushing against grain, such as during inhalation, and compare it to active stress state measurements. An MTS Criterion testing machine, which is a force deformation testing device, was used to push a block horizontally against a column of grain and record the force and displacement during the movement. The measured passive stress was calculated from the force and displacement values and ranged from 9.4 to 11.0 kPa at a depth of 20 to 30 cm. These values are three to four times larger than previously published measurements of stresses at similar depths. This result indicates that the discrepancy between experimental results and anecdotal reports is most likely due to the type of stress state experienced in grain entrapment. Findings imply that the pressures on the victim's chest during entrapment are sufficient to cause breathing difficulties or crush/positional asphyxiation in some cases. A full-scale study is recommended.

Stress profile in a two-dimensional silo: Effects induced by friction mobilization.

The effects of friction mobilization on the stress profile within a two-dimensional silo are investigated via simulations of discrete elements. Friction mobilization is driven by cyclic vertical displacement of the sidewalls. Two regimes have been observed for small filling height, with stress profiles identified as saturated (Janssen's profile) and exponentially growing. The transition between these regimes is denoted by an almost linear stress profile, similar to that of a hydrostatic system, with a significantly greater characteristic height compared to the height of the column of grains. For tall columns, the process of friction inversion is more complex. A partial inversion of friction mobilization is observed when the motion is reversed from upward to downward, which results in two coexisting zones of opposite mobilization. These zones are separated by a wide compaction front with a gradual upward progression sustained by the displacement of the walls. Conversely, if the motion is reversed, the two opposing friction mobilization zones retract, the transition zone becomes smooth, and the system rapidly transforms from two coexisting mobilization states to a Janssen-like regime. In both regimes, the general characteristics from the resulting stress profiles are depicted by generalizing Janssen's equation to include partial mobilization through the varying effective friction coefficient along the silo walls.

English

The crambe has emerged as an option for the production of biodiesel, constituting itself as an alternative for off-season grain in Brazil. To obtain the best performance in the post-harvest product processing, knowledge of physical characteristics of the grains to as well as of the design of machines and structure storage is necessary. After pre-cleaning, the crambe (Crambe abyssinica Hochst) with a water content of 8% (wb) was placed into a silo prototype, provided a fan and plenum, and subjected to five airflow densities that were pre-determined in a total of four repetitions for each tested airflow. The static pressure was measured through the column in five layers. The results show that there is a significant effect of air flow on the static air pressure in the crambe column, which increased linearly with depth. The experimental data fitted with good accuracy the models of Hunter and Shedd, thus enabling their use for the crambe column as well. The objectives of this study were to evaluate the variation of static pressure along a column of grains of crambe that were subjected to five airflow densities and check the fit of this variation following mathematical models suggested by Sheed and Hunter. Key words: Crambe abyssinica, resistance to airflow, Sheed, Hunter.

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution.

Recent advances in high-resolution measurements means it is now possible to identify and track the local "fabric" or contact topology of individual grains in a deforming sand throughout loading history. These provide compelling impetus to the development of methods for inferring changes in the contact forces and energies at multiple spatiotemporal scales, using information on grain contacts alone. Here we develop a surrogate measure of the fluctuating kinetic energy based on changes in the local contact topology of individual grains. We demonstrate the method for dense granular materials under quasistatic biaxial shear. In these systems, the initially stable and solidlike response eventually gives way to liquidlike behavior and global failure. This crossover in mechanical behavior, akin to a phase transition, is marked by bursts of kinetic energy and frictional dissipation. Mechanisms underlying this release of energy include the buckling of major load-bearing structures known as force chains. These columns of grains represent major repositories for stored strain energy. Stored energy initially accumulates at all of the contacts along the force chain, but is released collectively when the chain overloads and buckles. The exact quantification of the buildup and release of energy in force chains, and the manner in which force chain buckling propagates in the sample (i.e., diffuse and systemwide versus localized into shear bands), requires detailed knowledge of contact forces. To date, however, the forces at grain contacts continue to elude measurement in natural granular materials like sand. Here, using data from computer simulations, we show that a proxy for the fluctuating kinetic energy in dense granular materials can be suitably constructed solely from the evolving properties of the grain's local contact topology. Our approach directly relates the evolution of fabric to energy flux and makes possible research into the propagation of failure from measurements of grain contacts in real granular materials.

Study of the accumulation of grains in a two dimensional vibrated U-tube without interstitial fluid

We present an experimental and computational study using Molecular Dynamics simulations of the development of an accumulation of grains in one side of a two dimensional U-tube under vertical vibrations. Studying the evolution of the height difference between the columns of grains in the branches of the tube, we found that it reaches a saturation value after vibrating for some time. We obtain that this saturation value is the same if the simulation or experiment start with the arms leveled or with a large initial height difference. We explore computationally the effect of the width of the tube, the density of the grains and the coefficient of restitution between the grains and the wall on the value of the saturation. We obtain a value of the width of the tube for which the saturation value reaches a maximum, and show that the transport of grains between arms is favored for low grain densities and high grain-wall restitution coefficient.

Experimental study of a vertical column of grains submitted to a series of impulses

We report physical phenomena occurring in a vertical Newton's cradle system. A dozen of metallic spheres are placed in a vertical tube. Therefore, the gravity induces a non-uniform pre-compression of the beads and a restoring force. An electromagnetic hammer hits the bottom bead at frequencies tuned between 1 and 14Hz. The motion of the beads are recorded using a high-speed camera. For low frequencies, the pulses travel through the pile and expel a few beads from the surface. Then, after a few bounces of these beads, the system relaxes to the chain of contacting grains. When the frequency is increased, the number of fluidized beads increases. In the fluidized part of the pile, adjacent beads are bouncing in opposition of phase. This phase locking of the top beads is observed even when the bottom beads experience chaotic motions. While the mechanical energy increases monotically with the bead vertical position, heterogeneous patterns in the kinetic energy distribution are found when the system becomes fluidized.

Spectral Properties of Zero Temperature Dynamics in a Model of a Compacting Granular Column

The compacting of a column of grains has been studied using a one-dimensional Ising model with long range directed interactions in which down and up spins represent orientations of the grain having or not having an associated void. When the column is not shaken (zero 'temperature') the motion becomes highly constrained and under most circumstances we find that the generator of the stochastic dynamics assumes an unusual form: many eigenvalues become degenerate, but the associated multi-dimensional invariant spaces have but a single eigenvector. There is no spectral expansion and a Jordan form must be used. Many properties of the dynamics are established here analytically; some are not. General issues associated with the Jordan form are also taken up.

Effect of friction on the granular U-tube instability

Abstract When a granular material (like fine sand) fills a U shaped tube and is vibrated vertically, the column of grains in one branch of the tube grows while the other one empties. The height difference of the level of grains in each branch shows an exponential growth dependence with time for low frequencies of oscillation (∼10 Hz). A complete explanation of this phenomenon is still a matter of discussion. The exponential growth rate of the height difference is affected by parameters such as the amplitude and frequency of oscillation, properties of the granular material and the geometry of the U tube. This work presents an experimental study on the effect of friction between the tube walls and the granular medium, on the exponential growth rate. The internal walls of the tube were covered with sand paper of different average grain sizes (28.5 μm, 46.25 μm and 201 μm). As granular materials we used glass spheres with diameter between 180 and 300 μm. We found that increasing wall roughness lowers the exponential growth rate, and also restricts the range of amplitudes over which the effect occurs. We also compare our results with the predictions of a simple model for the instability, and show that it works only for cases with low wall roughness.

The effects of grain shape and frustration in a granular column near jamming

We investigate the full phase diagram of a column of grains near jamming, as a function of varying levels of frustration. Frustration is modelled by the effect of two opposing fields on a grain, due respectively to grains above and below it. The resulting four dynamical regimes (ballistic, logarithmic, activated and glassy) are characterised by means of the jamming time of zero-temperature dynamics, and of the statistics of attractors reached by the latter. Shape effects are most pronounced in the cases of strong and weak frustration, and essentially disappear around a mean-field point.

Experimental study on the vertical motion of grains in a vibrated U-tube

Weinvestigateexperimentallythebehaviorofthe exponential growth rate of a column of grains, in a partially filled vertically shaken U-tube. For the set of frequencies used we identify three qualitatively different behaviors for the exponential growth rate γ as a function of the dimen- sionless acceleration Γ : (1) an interval of zero growth for low Γ with a smooth change to nonzero growth, analogous to a continuous phase transition; (2) a sigmoidal region for γ at intermediate values of the dimensionless acceleration Γ ; and(3)anabruptchangefromhighvaluesof γ tozerogrowth at high values of Γ , similar to a first order phase transition. We obtain that our experimental data is well described by a Boltzmann Sigmoidal funtion, for the change of the expo- nential growth rate with the dimensionless acceleration of the vertical vibrations.

Heterogeneities in granular dynamics

The absence of Brownian motion in granular media is a source of much complexity, including the prevalence of heterogeneity, whether static or dynamic, within a given system. Such strong heterogeneities can exist as a function of depth in a box of grains; this is the system we study here. First, we present results from three-dimensional, cooperative and stochastic Monte Carlo shaking simulations of spheres on heterogeneous density fluctuations. Next, we juxtapose these with results obtained from a theoretical model of a column of grains under gravity; frustration via competing local fields is included in our model, whereas the effect of gravity is to slow down the dynamics of successively deeper layers. The combined conclusions suggest that the dynamics of a real granular column can be divided into different phases-ballistic, logarithmic, activated, and glassy-as a function of depth. The nature of the ground states and their retrieval (under zero-temperature dynamics) is analyzed; the glassy phase shows clear evidence of its intrinsic ("crystalline") states, which lie below a band of approximately degenerate ground states. In the other three phases, by contrast, the system jams into a state chosen randomly from this upper band of metastable states.

Raining into shallow water as a description of the collapse of a column of grains

A modified shallow-water model is presented for the collapse of tall columns of grains. The flow is divided in two parts. Depth-averaged shallow-water equations are applied to a thin horizontally spreading layer which is subjected to Coulombic friction. The falling mass of grains is gradually added to the zone of the initial column during the free-fall time of the column. This ‘rain’ is assumed to have no horizontal momentum. The results obtained here are in agreement with both planar and axisymmetric experiments over a range of aspect ratio (axisymmetric). The flow dynamics compares well with discrete simulations which have been successfully compared with experiments.

Ground-state structure and dynamics in a toy model for granular compaction

We report on a toy model for the glassy compaction dynamics of granular systems, introduced and investigated in collaboration with Anita Mehta and Peter Stadler. A stochastic dynamics is defined on a column of grains. Grains are anisotropic and possess a discrete orientational degree of freedom. Gravity induces long-range directional interactions down the column. The key control parameter of the model, ε , is a representation of granular shape. Rational and irrational values of ε correspond to very different kinds of behavior, both in statics (structure of ground states) and in low-temperature dynamics (retrieval of ground states).

A three-phase mixture theory for particle size segregation in shallow granular free-surface flows

Particle-size segregation within granular materials is of great technological significance yet it is still very poorly understood. There are several causes of segregation, but this paper focuses on kinetic sieving which is the dominant mechanism in dense gravity-driven shallow free-surface flows, or, granular avalanches. The segregation model is derived from a three-phase mixture theory composed of large particles, small particles and a passive interstitial fluid. Steady-state solutions are constructed for a normally graded inflow in a steady uniform flow field. This problem is of fundamental interest, because it shows how an unstably stratified layer readjusts into a stable configuration. Expansion fans and concentration shocks are generated and sufficiently far downstream inversely graded segregated layers form, with the larger particles overlying the finer ones. This a good approximation for segregation in flows with weak diffusive remixing. The distance for complete segregation to occur is shown to increase with rising fluid density and tends to infinity as its density approaches that of the grains. If the particles are buoyant then the initial configuration is stable. An exact time-dependent two-dimensional solution is constructed for plug flow, which exploits the uncoupling of material columns of grains in the absence of shear. This yields insight into the nature of more complex numerical solutions for strong shear, which are computed with a high-resolution shock-capturing numerical scheme.

PERMEABILITY OF CORN, SOYBEANS, AND SOFT RED AND WHITE WINTER WHEAT AS AFFECTED BY BULK DENSITY

Darcys law is a function of viscosity, permeability, and velocity and can be used to predict the airflow resistancein granular materials at low air velocities. Permeability also governs the magnitude of natural convection currents duringperiods of non-aerated grain storage. The permeability of corn, soybeans, soft white winter wheat, and soft red winter wheatwere measured as a function of bulk density and moisture content. Air was passed through a column of grain and the flowrate and pressure drop measured. Bulk density and kernel density were also measured to determine the porosity of grain inthe test column. Two filling methods were used to change the bulk density of grain by approximately 50 kg/m3, an increaseof 7%. This resulted in a reduction in porosity of approximately 4 percentage points. However, permeability decreased by amaximum of 45%. Wheat had the lowest permeability (between 1.15 10-8 and 7.29 10-9 m2 or highest resistancecoefficient between 1591 and 2510 Pa.s/m2, respectively, depending on bulk density and moisture content), while corn andsoybeans were similar (permeability varied between 1.30 10-8 and 3.03 10-8 m2 or resistance coefficient between 1,408and 604 Pa.s/m2, respectively). Experiments were conducted up to an air velocity of 0.0052 m/s that resulted in a Reynoldsnumber of 2.5, which was slightly above the maximum air velocity expected during non-aerated grain storage. Nevertheless,Darcys law would be appropriate for predicting natural convection currents during non-aerated storage.