An explicit granular-mechanics approach to marine sediment acoustics

Here, we theoretically and computationally study the frequency dependence of phase speed and attenuation for marine sediments from the perspective of granular mechanics. We leverage recent theoretical insights from the granular physics community as well as discrete-element method simulations, where the granular material is treated as a packing of discrete objects that interact via pairwise forces. These pairwise forces include both repulsive contact forces as well as dissipative terms, which may include losses from the fluid as well as losses from inelasticity at grain-grain contacts. We show that the structure of disordered granular packings leads to anomalous scaling laws for frequency-dependent phase speed and attenuation that do not follow from a continuum treatment. Our results demonstrate that granular packing structure, which is not explicitly considered in existing models, may play a crucial role in a complete theory of sediment acoustics. While this simple approach does not explicitly treat sound propagation or inertial effects in the interstitial fluid, it provides a starting point for future models that include these and other more complex features.

Investigation of damping coefficients for elastic collision particles utilizing the acoustic frequency sampling method

The damping coefficient serves to quantify the energy dissipation in particle collisions and constitutes a crucial parameter in discrete element simulations. Nevertheless, the factors influencing the damping coefficient remain unclear, and the damping coefficients of the majority of materials have not been precisely determined. In this investigation, the damping coefficients of eight representative particles were studied using the acoustic frequency sampling method, and the correlations between these coefficients and collision velocity, material density, and elastic modulus were analyzed. The findings indicate that damping coefficients exhibit insensitivity to velocity in strongly elastic and moderately elastic material particles. Conversely, for weakly elastic material particles, damping coefficients demonstrate an increase with rising velocity. The damping coefficient of metallic particles exhibits a linear relationship with material density and elastic modulus.

Depletion forces in dense mixtures of spheres and rods

We evaluate depletion forces in molecular dynamics simulation of a binary mixture of spheres (depleted particles) and rods (depletant particles) for a wide range of densities for both species. This evaluation was carried out using a recently proposed least squares fitting algorithm. We found that the restriction of the rods' rotational degrees of freedom, when the distance between two spheres is less than the rods length, creates a shallow, and apparently linear, attractive force ramp. For intersphere distances smaller than the rods' diameter, a much stronger attractive force is found, and a large repulsive barrier appears between these aforementioned regimes, roughly at the distance of the rods' thickness. The evaluated forces are validated via a comparison of the pairwise correlation functions obtained from molecular dynamics simulation of a mono-disperse sphere fluid, using the evaluated effective forces, against the original (full system) pairwise correlation functions. Agreement is excellent. We also record the angular pairwise correlation function, using the P2(x) Legendre polynomial, and find that for high densities of both species, a local nematic ordering starts to appear. This nematic order may be a factor in the small differences found between original and effective pairwise correlation functions at high densities of rods.

Complex Memory Formation in Frictional Granular Media

Using numerical simulations it is shown that a jammed, random pack of soft frictional grains can store an arbitrary waveform that is applied as a small time-dependent shear while the system is slowly compressed. When the system is decompressed at a later time, an approximation of the input waveform is recalled in time-reversed order as shear stresses on the system boundaries. This effect depends on friction between the grains, and is independent of some aspects of the friction model. This type of memory could potentially be observable in other types of random media that form internal contacts when compressed.

Frictional Weakening of Vibrated Granular Flows

We computationally study the frictional properties of sheared granular media subjected to harmonic vibration applied at the boundary. Such vibrations are thought to play an important role in weakening flows, yet the independent effects of amplitude, frequency, and pressure on the process have remained unclear. Based on a dimensional analysis and DEM simulations, we show that, in addition to a previously proposed criterion for peak acceleration that leads to breaking of contacts, weakening requires the absolute amplitude squared of the displacement to be sufficiently large relative to the confining pressure. The analysis provides a basis for predicting flows subjected to arbitrary external vibration and demonstrates that a previously unrecognized second process that is dependent on dissipation contributes to shear weakening under vibrations.

Segregation patterns in three-dimensional granular flows

Flow of size-bidisperse particle mixtures in a spherical tumbler rotating alternately about two perpendicular axes produces segregation patterns that track the location of nonmixing islands predicted by a dynamical systems approach. To better understand the paradoxical accumulation of large particles in regions defined by barriers to transport, we perform discrete element method (DEM) simulations to visualize the three-dimensional structure of the segregation patterns and track individual particles. Our DEM simulations and modeling results indicate that segregation pattern formation in the biaxial spherical tumbler is due to the interaction of size-driven radial segregation with the weak spanwise component of the advective surface flow. Specifically, we find that after large particles segregate to the surface, slow axial drift in the flowing layer, which is inherent to spherical tumblers, is sufficient to drive large particles across nominal transport barriers and into nonmixing islands predicted by an advective flow model in the absence of axial drift. Axial drift alters the periodic dynamics of nonmixing islands, turning them into "sinks" where large particles accumulate even in the presence of collisional diffusion. Overall, our results indicate that weak perturbation of chaotic flow has the potential to alter key dynamical system features (e.g., transport barriers), which ultimately can result in unexpected physical phenomena.

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.

Collisional regime during the discharge of a two-dimensional silo

The present work reports an investigation into the collisional dynamics of particles in the vicinity of the outlet of a two-dimensional silo using molecular dynamics simulations. Most studies on this granular system focus in the bulk of the medium. In this region, contacts are permanent or long-lived, so continuous approximations are able to yield results for velocity distributions or mass flow. Close to the exit, however, the density of the medium decreases and contacts are instantaneous. Thus, the collisional nature of the dynamics becomes significant, warranting a dedicated investigation as carried out in this work. More interesting, the vicinity of the outlet is the region where the arches that block the flow for small apertures are formed. It is found that the transition from the clogging regime (at small apertures) to the continuous flow regime is smooth in collisional variables. Furthermore, the dynamics of particles as reflected by the distributions of the velocities is as well unaffected. This result implies that there is no critical outlet size that separates both regimes, as had been proposed in the literature. Instead, the results achieved support the alternative picture in which a clog is possible for any outlet size.

Sheared granular matter and the empirical relations of seismicity

The frictional instability associated with earthquake initiation and earthquake dynamics is believed to be mainly controlled by the dynamics of fragmented rocks within the fault gauge. Principal features of the emerging seismicity (e.g., intermittent dynamics and broad time and/or energy scales) have been replicated by simple experimental setups, which involve a slowly driven slider on top of granular matter, for example. Yet these setups are often physically limited and might not allow one to determine the underlying nature of specific features and, hence, the universality and generality of the experimental observations. Here, we address this challenge by a numerical study of a spring-slider experiment based on two-dimensional discrete element method simulations, which allows us to control the properties of the granular matter and of the surface of the slider, for example. Upon quasistatic loading, stick-slip-type behavior emerges which is contrasted by a stable sliding regime at finite driving rates, in agreement with experimental observations. Across large parameter ranges for damping, interparticle friction, particle polydispersity, etc., the earthquake-like dynamics associated with the former regime results in several robust scale-free statistical features also observed in experiments. At first sight, these closely resemble the main empirical relations of tectonic seismicity at geological scales. This includes the Gutenberg-Richter distribution of event sizes, the Omori-Utsu-type decay of aftershock rates, as well as the aftershock productivity relation and broad recurrence time distributions. Yet, we show that the correlations associated with tectonic aftershocks are absent such that the origin of the Omori-Utsu relation, the aftershock productivity relation, and Båth's relation in the simulations is fundamentally different from the case of tectonic seismicity. This, we believe, is mainly due to a lack of macroscale relaxation processes that are closely tied to the generation of real aftershocks. We argue that the same is true for previous laboratory experiments.

Improvement of Contact Force Calculation Model Considering Influence of Yield Strength on Coefficient of Restitution

Aiming at the problem that the current coefficient of restitution model cannot effectively predict energy dissipation in the multi-body system collision process, a coefficient of restitution model considering the yield strength is proposed in this article. As an important parameter for energy loss and material deformation prediction during collision, the coefficient of restitution has an important influence on the accurate calculation of contact force. The current main coefficient of restitution models are compared and analyzed in this article. In view of the large difference between the results obtained by different models on the same parameter, through the use of ANSYS/LS–DYNA for dynamic simulation, the influence of different yield strengths on the coefficient of restitution is studied. Then, the article establishes a new coefficient of restitution model considering the yield strength combined with the J–G model, and verifies the effectiveness of the model in the article using experimental results. At the same time, the article compares the new coefficient of restitution model with the constant coefficient of restitution model, and further studies the effect of the coefficient of restitution on the dynamic results.

Mechanisms for recirculation cells in granular flows in rotating cylindrical rough tumblers

Friction at the endwalls of partially filled horizontal rotating tumblers induces curvature and axial drift of particle trajectories in the surface flowing layer. Here we describe the results of a detailed discrete element method study of the dry granular flow of monodisperse particles in three-dimensional cylindrical tumblers with endwalls and cylindrical wall that can be either smooth or rough. Endwall roughness induces more curved particle trajectories, while a smooth cylindrical wall enhances drift near the endwall. This drift induces recirculation cells near the endwall. The use of mixed roughness (cylindrical wall and endwalls having different roughness) shows the influence of each wall on the drift and curvature of particle trajectories as well as the modification of the free surface topography. The effects act in opposite directions and have variable magnitude along the length of the tumbler such that their sum determines both direction of net drift and the recirculation cells. Near the endwalls, the dominant effect is always the endwall effect, and the axial drift for surface particles is toward the endwalls. For long enough tumblers, a counter-rotating cell occurs adjacent to each of the endwall cells having a surface drift toward the center because the cylindrical wall effect is dominant there. These cells are not dynamically coupled with the two endwall cells. The competition between the drifts induced by the endwalls and the cylindrical wall determines the width and drift amplitude for both types of cells.

Phthalocyanine reactivity and interaction on the 6H-SiC(0001)-(3×3) surface by core-level experiments and simulations

The adsorption of phthalocyanine (H2Pc) on the 6H-SiC(0001)-(3×3) surface is investigated using X-ray photoelectron spectroscopy (XPS), near edge X-ray absorption fine structure spectroscopy (NEXAFS), and density functional theory (DFT) calculations....

Modeling of High-Density Compaction of Pharmaceutical Tablets Using Multi-Contact Discrete Element Method

The purpose of this work is to simulate the powder compaction of pharmaceutical materials at the microscopic scale in order to better understand the interplay of mechanical forces between particles, and to predict their compression profiles by controlling the microstructure. For this task, the new framework of multi-contact discrete element method (MC-DEM) was applied. In contrast to the conventional discrete element method (DEM), MC-DEM interactions between multiple contacts on the same particle are now explicitly taken into account. A new adhesive elastic-plastic multi-contact model invoking neighboring contact interaction was introduced and implemented. The uniaxial compaction of two microcrystalline cellulose grades (Avicel^® PH 200 (FMC BioPolymer, Philadelphia, PA, USA) and Pharmacel^® 102 (DFE Pharma, Nörten-Hardenberg, Germany) subjected to high confining conditions was studied. The objectives of these simulations were: (1) to investigate the micromechanical behavior; (2) to predict the macroscopic behavior; and (3) to develop a methodology for the calibration of the model parameters needed for the MC-DEM simulations. A two-stage calibration strategy was followed: first, the model parameters were directly measured at the micro-scale (particle level) and second, a meso-scale calibration was established between MC-DEM parameters and compression profiles of the pharmaceutical powders. The new MC-DEM framework could capture the main compressibility characteristics of pharmaceutical materials and could successfully provide predictions on compression profiles at high relative densities.

Colloidal Shear-Thickening Fluids Using Variable Functional Star-Shaped Particles: A Molecular Dynamics Study

Complex colloidal fluids, depending on constituent shapes and packing fractions, may have a wide range of shear-thinning and/or shear-thickening behaviors. An interesting way to transition between different types of such behavior is by infusing complex functional particles that can be manufactured using modern techniques such as 3D printing. In this paper, we perform 2D molecular dynamics simulations of such fluids with infused star-shaped functional particles, with a variable leg length and number of legs, as they are infused in a non-interacting fluid. We vary the packing fraction (ϕ) of the system, and for each different system, we apply shear at various strain rates, turning the fluid into a shear-thickened fluid and then, in jammed state, rising the apparent viscosity of the fluid and incipient stresses. We demonstrate the dependence of viscosity on the functional particles’ packing fraction and we show the role of shape and design dependence of the functional particles towards the transition to a shear-thickening fluid.

An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary environments

The angle between the sloping side of a heap of particles and the horizontal, called angle of repose, is often used to characterize the flowability of granular materials on Earth and planetary environments, such as sand, dust aerosols, and powders. In planetary research, this angle provides an excellent proxy for particle size. The smaller the particle is, the larger the effect of attractive forces between atoms and molecules on the surface of the particles relative to particle weight, the less flowable the material, and the steeper, thus, the angle of repose. We present a model that accurately predicts the angle of repose as a function of particle size, both on Earth and under extraterrestrial gravity.

The angle of repose—i.e., the angle θr between the sloping side of a heap of particles and the horizontal—provides one of the most important observables characterizing the packing and flowability of a granular material. However, this angle is determined by still poorly understood particle-scale processes, as the interactions between particles in the heap cause resistance to roll and slide under the action of gravity. A theoretical expression that predicts θr as a function of particle size and gravity would have impact in the engineering, environmental, and planetary sciences. Here we present such an expression, which we have derived from particle-based numerical simulations that account for both sliding and rolling resistance, as well as for nonbonded attractive particle–particle interactions (van der Waals). Our expression is simple and reproduces the angle of repose of experimental conical heaps as a function of particle size, as well as θr obtained from our simulations with gravity from 0.06 to 100 times that of Earth. Furthermore, we find that heaps undergo a transition from conical to irregular shape when the cohesive to gravitational force ratio exceeds a critical value, thus providing a proxy for particle-scale interactions from heap morphology.

Effects of size polydispersity on segregation of spherical particles in rotating drum

To get insight into the segregation process of a polydisperse granular materials flow, we numerically investigated the migration process of particles in a rotating drum operating in the rolling regime by means of the discrete element method. Particle migration is analyzed through the variation of the proportion of particles in different zones where the flow property is characterized. The proportion of particles in different zones of the drum shows to increase in the center of the flow radially and axially where a higher concentration of small particles is observed, while its decreases in other zones with a higher concentration of larger particles. Interestingly, we find that the migration process of particles leads to radial and axial segregation which is caused by a combination between the exerted fluctuation forces on particles and its surrounding pressure gradient.

Scaling behavior of the tensile strength of viscocohesive granular aggregates

We numerically analyze the tensile strength of a single wet agglomerate modeled as a viscocohesive aggregate impacting a flat surface by using the discrete-element simulations. The viscocohesive agglomerate composed of primary spherical particles with the inclusion of the interstitial liquid in the form of the capillary bridges characterized by the cohesive and viscous forces between particles is extracted from a cuboidal sample of granular materials by applying a spherical probe. The tensile strength is measured from the impact test of a wet agglomerate by systematically varying different values of the surface tension of the interstitial liquid, the liquid viscosity, and the impact speed. We show that the tensile stress increases immediately when the collision occurs between the agglomerate and the flat surface. The peak of the tensile stress obtained after the collision, then decreases smoothly with increasing the particle movement. The maximum tensile stress is defined to be the tensile strength of such agglomerate. It is remarkable that the normalized tensile strength of such agglomerate can be well described as a function of a dimensionless impact number that incorporates the capillary number and Stokes number (calculated from the surface tension and the viscosity of the liquid and the impact rate of the agglomerate), thus providing the confirmation for the unified representation of the liquid properties and the impact rate of wet granular media.

Virtual Experiments of Particle Mixing Process with the SPH-DEM Model

Particle mixing process is critical for the design and quality control of concrete and composite production. This paper develops an algorithm to simulate the high-shear mixing process of a granular flow containing a high proportion of solid particles mixed in a liquid. DEM is employed to simulate solid particle interactions; whereas SPH is implemented to simulate the liquid particles. The two-way coupling force between SPH and DEM particles is used to evaluate the solid-liquid interaction of a multi-phase flow. Using Darcy’s Law, this paper evaluates the coupling force as a function of local mixture porosity. After the model is verified by two benchmark case studies, i.e., a solid particle moving in a liquid and fluid flowing through a porous medium, this method is applied to a high shear mixing problem of two types of solid particles mixed in a viscous liquid by a four-bladed mixer. A homogeneity metric is introduced to characterize the mixing quality of the particulate mixture. The virtual experiments with the present algorithm show that adding more liquid or increasing liquid viscosity slows down the mixing process for a high solid load mix. Although the solid particles can be mixed well eventually, the liquid distribution is not homogeneous, especially when the viscosity of liquid is low. The present SPH-DEM model is versatile and suitable for virtual experiments of particle mixing process with different blades, solid particle densities and sizes, and liquid binders, and thus can expedite the design and development of concrete materials and particulate composites.

Avoiding chaos in granular dampers

Granular dampers are passive devices used to attenuate mechanical vibrations. The most common configuration consists in an enclosure, partiallyfilled with particles, attached to the vibrating structure that needs to be damped. The energy is dissipated due to inelastic collisions and friction between the grains and between the grains and the inner walls of the container as the structure vibrates. As a result of the collisions, the mechanical response of the system often results in chaotic motion even if the driving is harmonic. Despite the vibration attenuation achieved, this chaotic response may render the granular damper unsuitable for a range of applications. In this work, we showcase two simple modifications of the enclosure design that are able to mitigate the chaotic response of the granular damper. To this end we use Discrete Element Method simulations of: (a) a granular damper with a conical base, and (b) a granular damper with obstaclesfixed inside the enclosure. We compare results against a standardflat-base enclosure damper. The basic mechanical response of the dampers is characterized by measuring the apparent mass and the loss factor. The suppression of the chaotic response is assessed qualitatively via the phase space diagram.

Velocity scaling in the region of orifice influence in silo draining under gravity

This study utilizes computations based on a soft-particle discrete element method for investigating the scaling of velocity in the region of orifice influence situated directly above and in proximity to the outlet in a two-dimensional silo. The velocity at the exit scales with the outlet size (D), in striking agreement with the earlier studies. However, the scaling of velocity upstream of the outlet with D as the length scale does not exist. Consequently, we present a scaling with a length parameter h_{e} being the height of an equi-inertial curve, which is defined to be a curve on which the inertial number is constant, thereby consolidating the coexisting different flow regimes in a discharging silo. The velocity corresponding to an equi-inertial curve, when measured relative to the velocity at the outlet, scales very well with h_{e} for low inertial numbers belonging to the dense flow regime. However, such scaling does not hold for high inertial numbers corresponding to the rapid flow regime in the region located closer to the orifice. We tie this scaling breakdown to the velocity fluctuations in light of the similarity between the profiles of scaled relative velocity and the scaled kinetic pressure, suggesting h_{e} to be a promising candidate for unifying the kinematics of granular flow near the outlet in the silo.

Impact in granular matter: Force at the base of a container made with one movable wall

In geotechnics as well as in planetary science, it is important to find a means by which to protect a base from impacts of micrometeoroids. In the moon, for example, covering a moon base with regolith, and housing such regolith by movable bounding walls, could work as a stress-leaking shield. Using a numerical model, by performing impacts on a granular material housed in a rectangular container made with one movable sidewall, it is found that such wall mobility serves as a good means for controlling the maximum force exerted at the container's base. We show that the force exerted at the container's base decreases as the movable wall decreases in mass, and it follows a Janssen-like trend. Moreover, by making use of a dynamically defined redirecting coefficient K(X), proposed by Windows-Yule et al. [Phys. Rev. E 100, 022902 (2019)2470-004510.1103/PhysRevE.100.022902], which depends on the container's width X, we propose a model for predicting the maxima measured at the container's base. The model depends on the projectile and granulate properties, and the container's geometry.

Self-Induced Rayleigh-Taylor Instability in Segregating Dry Granular Flows

Dry-granular material flowing on rough inclines can experience a self-induced Rayleigh-Taylor (RT) instability followed by the spontaneous emergence of convection cells. For this to happen, particles are different in size and density; the larger particles are denser but still segregate toward the surface. When the flow is initially made of two layers of particles (dense particles above), a RT instability develops during the flow. When the flow is initially made of one homogeneous layer mixture, the granular segregation leads to the formation of an unstable layer of large, dense particles at the surface, that subsequently destabilizes in a RT plume pattern. The unstable density gradient has been only induced by the motion of the granular matter. This self-induced Rayleigh-Taylor instability and the two-layer RT instability are studied using two different methods: experiments and simulations. At last, contrary to the usual fluid behavior where the RT instability relaxes into two superimposed stable layers of fluid, the granular flow evolves to a pattern of alternated bands corresponding to recirculation cells analogous to Rayleigh-Bénard convection cells where segregation sustains the convective motion.

Dynamic Modeling of the Dissipative Contact and Friction Forces of a Passive Biped-Walking Robot

This work presents and discusses a general approach for the dynamic modeling and analysis of a passive biped walking robot, with a particular focus on the feet-ground contact interaction. The main purpose of this investigation is to address the supporting foot slippage and viscoelastic dissipative contact forces of the biped robot-walking model and to develop its dynamics equations for simple and double support phases. For this investigation, special attention has been given to the detection of the contact/impact between the legs of the biped and the ground. The results have been obtained with multibody system dynamics applying forward dynamics. This study aims at examining and comparing several force models dealing with different approaches in the context of multibody system dynamics. The normal contact forces developed during the dynamic walking of the robot are evaluated using several models: Hertz, Kelvin-Voight, Hunt and Crossley, Lankarani and Nikravesh, and Flores. Thanks to this comparison, it was shown that the normal force that works best for this model is the dissipative Nonlinear Flores Contact Force Model (hysteresis damping parameter - energy dissipation). Likewise, the friction contact/impact problem is solved using the Bengisu equations. The numerical results reveal that the stable periodic solutions are robust. Integrators and resolution methods are also purchased, in order to obtain the most efficient ones for this model.

Additive rheology of complex granular flows

Granular flows are omnipresent in nature and industrial processes, but their rheological properties such as apparent friction and packing fraction are still elusive when inertial, cohesive and viscous interactions occur between particles in addition to frictional and elastic forces. Here we report on extensive particle dynamics simulations of such complex flows for a model granular system composed of perfectly rigid particles. We show that, when the apparent friction and packing fraction are normalized by their cohesion-dependent quasistatic values, they are governed by a single dimensionless number that, by virtue of stress additivity, accounts for all interactions. We also find that this dimensionless parameter, as a generalized inertial number, describes the texture variables such as the bond network connectivity and anisotropy. Encompassing various stress sources, this unified framework considerably simplifies and extends the modeling scope for granular dynamics, with potential applications to powder technology and natural flows.

Granular materials are abundant in nature, but we haven’t fully understood their rheological properties as complex interactions between particles are involved. Here, Vo et al. show that granular flows can be described by a generalized dimensionless number based on stress additivity.

Evolution of wet agglomerates inside inertial shear flow of dry granular materials

We use particle dynamics simulations to investigate the evolution of a wet agglomerate inside homogeneous shear flows of dry particles. The agglomerate is modeled by introducing approximate analytical expressions of capillary and viscous forces between particles in addition to frictional contacts. During shear flow, the agglomerate may elongate, break, or be eroded by loss of its capillary bonds and primary particles. By systematically varying the shear rate and surface tension of the binding liquid, we characterize the rates of these dispersion modes. All the rates increase with increasing inertial number of the flow and decreasing cohesion index of the agglomerate. We show that the data points for each mode collapse on a master curve for a dimensionless scaling parameter that combines the inertial number and the cohesion index. The erosion rate vanishes below a cutoff value of the scaling parameter. This leads to a power-law borderline between the vanishing erosion states and erosion states in the phase space defined by the inertial number and the cohesion index.

Granular segregation induced by a moving subsurface blade

Size-driven particle segregation can occur when an object such as a blade moves through an otherwise static bed of granular material. Here we use discrete element method (DEM) simulations to study segregation resulting from a subsurface blade moving through a bed of size-bidisperse spherical particles. Segregation increases with each pass of the blade until a surface layer of mostly large particles forms above a small-particle layer adjacent to the bottom wall. The rate of segregation decreases with each pass so that the degree of segregation asymptotically approaches its maximum value, and the number of passes to reach a steady segregation state increases as the bed depth is increased or the blade height decreased. In shallow beds, the characteristic number of passes for segregation, τ, scales with the inverse of the granular inertial number, I. In deep beds with small blade heights, the effect of the blade is more localized to its immediate vicinity, resulting in many more passes of the blade to reach a steady segregation state, and a corresponding deviation from the shallow bed scaling of τ with I^{-1}.

Agglomeration of wet particles in dense granular flows

In order to get insight into the wet agglomeration process, we numerically investigate the growth of a single granule inside a dense flow of an initially homogeneous distribution of wet and dry particles. The simulations are performed by means of the discrete element method and the binding liquid is assumed to be transported by the wet particles, which interact via capillary and viscous force laws. The granule size is found to be an exponential function of time, reflecting the conservation of the amount of liquid and the decrease of the number of available wet particles inside the flow during agglomeration. We analyze this behavior in terms of the accretion and erosion rates of wet particles for a range of different values of material parameters such as mean particle size, size polydispersity, friction coefficient and liquid viscosity. In particular, we propose a phase diagram of the granule growth as a function of the mean primary particle diameter and particle size span, which separates the parametric domain in which the granule grows from the domain in which the granule does not survive.

Root growth and force chains in a granular soil

Roots provide basic functions to plants such as water and nutrient uptake and anchoring in soil. The growth and development of root systems contribute to colonizing the surrounding soil and optimizing the access to resources. It is generally known that the variability of plant root architecture results from the combination of genetic, physiological, and environmental factors, in particular soil mechanical resistance. However, this last factor has never been investigated at the soil grain scale for roots. In this paper, we are interested in the effect of the disordered texture of granular soils on the evolution of forces experienced by the root cap during its growth. We introduce a numerical model in which the root is modeled as a flexible self-elongating tube that probes a soil composed of solid particles. By means of extensive simulations, we show that the forces exerted on the root cap reflect interparticle force chains. Our simulations also show that the mean force declines exponentially with root flexibility, the highest force corresponding to the soil hardness. Furthermore, we find that this functional dependence is characterized by a single dimensionless parameter that combines granular structure and root bending stiffness. This finding will be useful to further address the biological issues of mechanosensing and thigmomorphogenesis in plant roots.

Spatiotemporal establishment of dense bacterial colonies growing on hard agar

The physical interactions of growing bacterial cells with each other and with their surroundings significantly affect the structure and dynamics of biofilms. Here a 3D agent-based model is formulated to describe the establishment of simple bacterial colonies expanding by the physical force of their growth. With a single set of parameters, the model captures key dynamical features of colony growth by non-motile, non EPS-producing E. coli cells on hard agar. The model, supported by experiment on colony growth in different types and concentrations of nutrients, suggests that radial colony expansion is not limited by nutrients as commonly believed, but by mechanical forces. Nutrient penetration instead governs vertical colony growth, through thin layers of vertically oriented cells lifting up their ancestors from the bottom. Overall, the model provides a versatile platform to investigate the influences of metabolic and environmental factors on the growth and morphology of bacterial colonies.

Rheological transition in simple shear of moderately dense assemblies of dry cohesive granules

The rheology of homogeneous cohesive granular assemblies under shear at moderate volume fractions is investigated using the discrete element method for both frictionless and frictional granules. A transition in rheology from inertial to quasistatic scaling is observed at volume fractions below the jamming point of noncohesive systems, which is a function of the granular temperature, energy dissipation, and cohesive potential. The transition is found to be the result of growing clusters, which eventually percolate the domain, and change the mode of momentum transport in the system. Differences in the behavior of the shear stress normalized by the pressure are observed when frictionless and frictional cases are compared. These differences are explained through contact anisotropy after percolation occurs. Both frictionless and frictional systems are found to be vulnerable to instabilities after full system percolation has occurred, where the former becomes thermodynamically unstable and the latter may form shear bands. Finally, implications for constitutive modeling are discussed.

Spreading of a granular droplet under horizontal vibrations

By means of three-dimensional discrete element simulations, we study the spreading of a granular droplet on a horizontally vibrated plate. Apart from a short transient with a parabolic shape, the droplet adopts a triangular profile during the spreading. The dynamics of the spreading is governed by two distinct regimes: a superdiffusive regime in the early stages driven by surface flow followed by a second one which is subdiffusive and governed by bulk flow. The plate bumpiness is found to alter only the spreading rate but plays a minor role on the shape of the granular droplet and on the scaling laws of the spreading. Importantly, we show that in the subdiffusive regime, the effective friction between the plate and the granular droplet can be interpreted in the framework of the μ(I)-rheology.

Effect of pressure on segregation in granular shear flows

The effect of confining pressure (overburden) on segregation of granular material is studied in discrete element method (DEM) simulations of horizontal planar shear flow. To mitigate changes to the shear rate due to the changing overburden, a linear with depth variation in the streamwise velocity component is imposed using a simple feedback scheme. Under these conditions, both the rate of segregation and the ultimate degree of segregation in size bidisperse and density bidisperse granular flows decrease with increasing overburden pressure and scale with the overburden pressure normalized by the lithostatic pressure of the particle bed. At overburdens greater than approximately 20 times the lithostatic pressure at the bottom of the bed, the density segregation rate is zero while the size segregation rate is small but nonzero, suggesting that different physical mechanisms drive the two types of segregation. The segregation rate scales close to linearly with the inertial number for both size bidisperse and density bidisperse mixtures under various flow conditions, leading to a proposed pressure dependence term for existing segregation velocity correlations. Surprisingly, particle stiffness has only a minor effect on segregation, although it significantly affects the packing density.

Recirculation cells for granular flow in cylindrical rotating tumblers

To better understand the velocity field and flowing layer structure, we have performed a detailed discrete element method study of the flow of monodisperse particles in a partially filled three-dimensional cylindrical rotating tumblers. Similar to what occurs near the poles in spherical and conical tumblers, recirculation cells (secondary flows) develop near the flat endwalls of a cylindrical tumbler in which particles near the surface drift axially toward the endwall, while particles deeper in the flowing layer drift axially toward the midlength of the tumbler. Another recirculation cell with the opposite sense develops next to each endwall recirculation cell, extending to the midlength of the tumbler. For a long enough tumbler, each endwall cell is about one quarter of the tumbler diameter in length. Endwall cells are insensitive to tumbler length and relatively insensitive to rotation speed (so long as the flowing layer remains flat and continuously flowing) or fill level (from 25% to 50% full). However, for shorter tumblers (0.5 to 1.0 length/diameter aspect ratio) the endwall cell size does not change much, while center cells reduce their size and eventually disappear for the shortest tumblers. For longer tumblers (length/diameter aspect ratio larger than 2), a stagnation zone appears in between the central cells. These results provide insight into the mixing of monodisperse particles in rotating cylindrical tumblers as well as the frictional effects of the tumbler endwalls.

Two-dimensional numerical simulation of chimney fluidization in a granular medium using a combination of discrete element and lattice Boltzmann methods

We present here a numerical study dedicated to the fluidization of a submerged granular medium induced by a localized fluid injection. To this end, a two-dimensional (2D) model is used, coupling the lattice Boltzmann method (LBM) with the discrete element method (DEM) for a relevant description of fluid-grains interaction. An extensive investigation has been carried out to analyze the respective influences of the different parameters of our configuration, both geometrical (bed height, grain diameter, injection width) and physical (fluid viscosity, buoyancy). Compared to previous experimental works, the same qualitative features are recovered as regards the general phenomenology including transitory phase, stationary states, and hysteretic behavior. We also present quantitative findings about transient fluidization, for which several dimensionless quantities and scaling laws are proposed, and about the influence of the injection width, from localized to homogeneous fluidization. Finally, the impact of the present 2D geometry is discussed, by comparison to the real three-dimensional (3D) experiments, as well as the crucial role of the prevailing hydrodynamic regime within the expanding cavity, quantified through a cavity Reynolds number, that can presumably explain some substantial differences observed regarding upward expansion process of the fluidized zone when the fluid viscosity is changed.

Continuum modelling of segregating tridisperse granular chute flow

Segregation and mixing of size multidisperse granular materials remain challenging problems in many industrial applications. In this paper, we apply a continuum-based model that captures the effects of segregation, diffusion and advection for size tridisperse granular flow in quasi-two-dimensional chute flow. The model uses the kinematics of the flow and other physical parameters such as the diffusion coefficient and the percolation length scale, quantities that can be determined directly from experiment, simulation or theory and that are not arbitrarily adjustable. The predictions from the model are consistent with experimentally validated discrete element method (DEM) simulations over a wide range of flow conditions and particle sizes. The degree of segregation depends on the Péclet number, Pe, defined as the ratio of the segregation rate to the diffusion rate, the relative segregation strength κ_ij between particle species i and j, and a characteristic length L, which is determined by the strength of segregation between smallest and largest particles. A parametric study of particle size, κ_ij , Pe and L demonstrates how particle segregation patterns depend on the interplay of advection, segregation and diffusion. Finally, the segregation pattern is also affected by the velocity profile and the degree of basal slip at the chute surface. The model is applicable to different flow geometries, and should be easily adapted to segregation driven by other particle properties such as density and shape.

Evidence of reverse and intermediate size segregation in dry granular flows down a rough incline

In a dry granular flow, size segregation had been shown to behave differently for a mixture containing a few large particles with a size ratio above 5 [N. Thomas, Phys. Rev. E 62, 961 (2000)1063-651X10.1103/PhysRevE.62.961]. For moderately large size ratios, large particles migrate to an intermediate depth in the bed: this is called "intermediate segregation." For the largest size ratios, large particles migrate down to the bottom of the flow: this is called "reverse segregation," in contrast with surface segregation. As the reversal and intermediate depth values depend on the fraction of particles, this numerical study mainly uses one single large tracer. Small fractions of large beads are also computed showing the link between single tracer behavior and collective segregation process. For each device (half-filled rotating tumbler and rough plane), two (2D) and three (3D) dimensional cases are distinguished. In the tumbler, the trajectories of a large tracer show that it reaches a constant depth during the flowing phase. For large size ratios, this depth is intermediate. A progressive sinking of the depth is obtained when the size ratio is increased. The largest size ratios correspond to tracers being at the bottom of the flowing layer. All 3D simulation results are in quantitative agreement with the experimental surface, intermediate, and reverse-segregation results. In the flow down a rough incline, a large tracer reaches an equilibrium depth during flow. For large size ratios, the depth is inside the bed, at an intermediate position, and for the largest size ratios, this depth is reverse, located near the bottom. Results are slightly different for a thin or a thick flow. For 3D thick flows, the reversal between surface and bottom positions occurs within a short range of size ratios: no tracer stabilizes near half-height and two reachable intermediate depth layers exist, below the surface and above the bottom reverse layer. For 3D thin flows, all intermediate depths are reachable by a tracer, depending on the size ratio. The numerical study of larger fractions of tracers (5% or 10%) shows the three segregation patterns (surface, intermediate, reverse) corresponding to the three types of equilibrium depth. The reversal is smoother than for a single tracer, and happens around the size ratio 4.5, in good agreement with experiments.