Wave phenomena in vibrofluidized dry and partially wet granular materials confined in a quasi-two-dimensional geometry are investigated with numerical simulations considering individual particles as hard spheres. Short ranged cohesive interactions arising from the formation of liquid bridges between adjacent particles are modeled by changing the velocity dependent coefficient of restitution. Such a change effectively suppresses the formation of surface waves, in agreement with previous experimental observations. The difference in pattern creation arises from the suppressed momentum transfer due to wetting and it can be quantitatively understood from an analysis of binary impacts.
The formation of kink wave fronts (KWFs) in a quasi-two-dimensional granular system is investigated numerically with a focus on the role of cohesive interactions between individual particles. The cohesive particle-particle interaction is achieved through tuning the velocity-dependent coefficient of restitution, based on an analytical model introduced recently. A comparison with experimental results indicates that the threshold for the emergence of traveling KWFs matches the regime in which the center of mass height of the granular layers fluctuates with a period that triples the vibration peri…
Shock wave formation and propagation in two-dimensional granular materials under vertical vibration are studied by digital high speed photography. The steepen density and temperature wave fronts form near the plate as granular layer collides with vibrating plate and propagate upward through the layer. The temperature front is always in the transition region between the upward and downward granular flows. The effects of driving parameters and particle number on the shock are also explored.
A three-dimensional granular system fluidized by vertical container vibrations was studied using pulsed field gradient (PFG) NMR coupled with one-dimensional magnetic resonance imaging (MRI). The system consisted of mustard seeds vibrated vertically at 50 Hz, and the number of layers N_ell <= 4 was sufficiently low to achieve a nearly time-independent granular fluid. Using NMR, the vertical profiles of density and granular temperature were directly measured, along with the distributions of vertical and horizontal grain velocities. The velocity distributions showed modest deviations from Maxwel…
The spontaneous symmetry breaking taking place in the direction perpendicular to the energy flux in a dilute vibrofluidized granular system is investigated, using both a hydrodynamic description and simulation methods. The latter include molecular dynamics and direct Monte Carlo simulation of the Boltzmann equation. A marginal stability analysis of the hydrodynamic equations, carried out in the WKB approximation, is shown to be in good agreement with the simulation results. The shape of the hydrodynamic profiles beyond the bifurcation is discussed.
Modeling collective motion in non-conservative systems, such as granular materials, is difficult since a general microscopic-to-macroscopic approach is not available: there is no Hamiltonian, no known stationary densities in phase space, not a known small set of relevant variables. Phenomenological coarse-grained models are a good alternative, provided that one has identified a few slow observables and collected a sufficient amount of data for their dynamics. Here we study the case of a vibrofluidized dense granular material. The experimental study of a tracer, dispersed into the media, showed…
Nuclear magnetic resonance (NMR) experiments are described for two granular-flow systems, the vibrofluidized bed and the gas-fluidized bed. Using pulsed field gradient, magnetic resonance imaging, and hyperpolarized gas NMR, detailed information is obtained for the density and motions of both grains and interstitial gas. For the vibrofluidized bed, the granular temperature profile is measured and compared with a first-principles formulation of granular hydrodynamics. For the gas-fluidized bed, dynamic correlations in the grain density are used to measure the bubble velocity and hyperpolarized …
Experiments are conducted in a two-dimensional mono-layer vibrofluidized bed of glass beads, with a goal to understand the transition scenario and the underlying microstructure and dynamics in different patterned-states. At small shaking accelerations ($Γ=Aω^2/g <1$), the particles remain attached with the base of the vibrating container -- this is known as the solid bed (SB). With increasing $Γ$ (at large enough shaking amplitude $A/d$) and/or with increasing $A/d$ (at large enough $Γ$), the sequence of transitions/bifurcations unfolds as follows: SB to BB ("bouncing bed") to LS ("Leidenfrost…
Motivated by recent experiments we have carried out an Event Driven computer simulation of a diluted binary mixture of granular particles vertically vibrated in the presence of gravity. The simulations not only confirm that the kinetic energies of the two species are not equally distributed, as predicted by various theoretical models, but also seem to reproduce rather well the density and temperature profiles measured experimentally. Rotational degrees of freedom do not seem to play any important qualitative role. Instead, simulation shows the onset of a clustering instability along the horizo…
We examine the steady state properties of binary systems of driven inelastic hard spheres. The spheres, which move under the influence of gravity, are contained in a vertical cylinder with a vibrating base. We computed the trajectories of the spheres using an event-driven molecular dynamics algorithm. In the first part of the study, we chose simulation parameters that match those of experiments performed by Wildman and Parker. Various properties computed from the simulation including the density profile, granular temperature and circulation pattern are in good qualitative agreement with the ex…
The failure of 2D numerical cohesive granular steps collapsing under gravity are simulated for a large range of cohesion. Focussing on the cumulative displacement of the grains, and defining a displacement threshold, we establish a sensible criterion for capturing the failure characteristics. We are able to locate the failure in time and to identify the different stages of the destabilisation. We find that the onset of the failure is delayed by increasing cohesion, but its duration becomes shorter. Defining a narrow displacement interval, a well-defined shear band revealing the failure comes o…
An experimental apparatus measuring free-surface deformation of a centrifuged granular pile is developed. By horizontally rotating a quasi two-dimensional granular pile whose apex is located at the vertical rotation axis, the resultant force of gravity and centrifuge yields the deformation of the granular pile. In this setup, centrifugal force depends on distance from the rotation axis whilst gravitational force is constant everywhere. Therefore, free-surface deformation by various centrifuge degrees can be systematically examined using this apparatus. In the system, a small unit consisting of…
We present experimental study of vibrofluidized granular materials by high speed photography. Statistical results present the averaged dynamic behaviors of granular materials in one cycle, including the variations of height, velocity and mechanical energy of the center of mass. Furthermore, time-space distribution of granular temperature which corresponds to the random kinetic energy shows that a temperature peak forms in the compression period and propagates upward with a steepened front. The Mach number in the steepened front is found to be greater than unity, indicating a shock propagating …
Molecular dynamical (MD) simulations are performed to simulate two dimensional vibrofluidized granular materials in this work. Statistics on simulation results indicate that there exist shocks propagating upward in each vibrating cycle. Under certain driving parameters surface waves similar to Faraday instability in normal fluid coexist with internal waves. Relationship between the two kinds of waves is explored. Moreover simulation results indicate that periodically structured bottom can change the dispersion relationship and amplitude of surface waves.
In this paper, we consider the effect of cohesion on the stability of a granular heap. We first briefly review literature results on the cohesion force between two rough granular beads and specifically consider the dependence of the adhesion force on the normal load. We then compute the dependence of the maximum angle of stability of the heap as a function of the cohesion. We point out that the dependence of the cohesive forces on the external normal load between grains is a key point in determining the localization of the failure plane. While for a constant cohesive force, slip occurs deep in…
Density-wave fronts in a vibrofluidized wet granular layer undergoing a gas-liquid-like transition are investigated experimentally. The threshold of the instability is governed by the amplitude of the vertical vibrations. Fronts, which are curved into a spiral shape, propagate coherently along the circular rim of the container with leading edges. They are stable beyond a critical distance from the container center. Based on an analysis of the emerging time and length scales, we propose a model for the pattern formation by considering the competition between the time scale for the condensation …
It is widely recognized in particle technology that adhesive powders show a wide range of different bulk behavior due to the peculiarity of the particle interaction. We use Discrete Element simulations to investigate the effect of contact cohesion on the steady state of dense powders in a slowly sheared split-bottom Couette cell, which imposes a wide stable shear band. The intensity of cohesive forces can be quantified by the {\em granular Bond number} ($Bo$), namely the ratio between maximum attractive force and average force due to external compression. We find that the shear banding phenome…
We study the transition of a granular packing from liquid to solid bonding in the course of drying. The particles are initially wetted by a liquid brine and the cohesion of the packing is ensured by capillary forces, but the crystallization of the solute transforms the liquid bonds into partially cemented bonds. This transition is evidenced experimentally by measuring the compressive strength of the samples at regular intervals of times. Our experimental data reveal three regimes: 1) Up to a critical degree of saturation, no solid bonds are formed and the cohesion remains practically constant;…
Liquid has a significant effect on the flow of wet granular assemblies. We explore the effects of liquid induced cohesion on the flow characteristics of wet granular materials. We propose a cohesion-scaling approach that enables invariant flow characteristics for different particles sizes in rotating drums. The strength of capillary forces between the particles is significantly reduced by making the glass beads hydrophobic via chemical silanization. Main results of rotating drum experiments are that liquid-induced cohesion decreases both the width of the flowing region and the velocity of the …
The spontaneous clustering of a vibrofluidized granular gas is employed to generate directed transport in two different compartmentalized systems: a "granular fountain" in which the transport takes the form of convection rolls, and a "granular ratchet" with a spontaneous particle current perpendicular to the direction of energy input. In both instances, transport is not due to any system-intrinsic anisotropy, but arises as a spontaneous collective symmetry breaking effect of many interacting granular particles. The experimental and numerical results are quantitatively accounted for within a fl…
Pattern formation of a thin layer of vertically agitated wet granular matter is investigated experimentally. Due to the strong cohesion arising from the capillary bridges formed between adjacent particles, agitated wet granular matter exhibits a different scenario compared with cohesionless dry particles. Rotating spirals with three arms, which correspond to the kinks between regions with different colliding phases with the vibrating plate, have been found to be the dominating pattern. From both top view snapshots and laser profilometry methods, the rotation frequency of the spiral arms is cha…
Wet granular materials in a quasi-static steady state shear flow have been studied with discrete particle simulations. Macroscopic quantities, consistent with the conservation laws of continuum theory, are obtained by time averaging and spatial coarse-graining. Initial studies involve understanding the effect of liquid content and liquid properties like the surface tension on the macroscopic quantities. Two parameters of the liquid bridge contact model have been studied as the constitutive parameters that define the structure of this model (i) the rupture distance of the liquid bridge model, w…
Granular media take on great importance in industry and geophysics, posing a severe challenge to materials science. Their response properties elude known soft rheological models, even when the yield-stress discontinuity is blurred by vibro-fluidization. Here we propose a broad rheological scenario where average stress sums up a frictional contribution, generalizing conventional $μ(I)$-rheology, and a kinetic collisional term dominating at fast fluidization. Our conjecture fairly describes a wide series of experiments in a vibrofluidized vane setup, whose phenomenology includes velocity weakeni…
When dealing with unsaturated wet granular materials, a fundamental question is: what is the effect of capillary cohesion on the bulk flow and yield behavior? We inwestigate the dense flow rheology of unsaturated granular materials through experiments and discrete element simulations of homogeneous, simple annular shear flows of frictional, cohesive, spherical particles.
Simulation results are presented on the collapse of granular columns composed of rod-like particles. Columns can be stable and free-standing if either the friction coefficient is large enough, or the rods long enough. Destabilizing gravitational forces are counteracted by increased frictional forces between the rods. Different to columns made of spherical particles this is possible, because rod contacts can slide along the rod axes to generate the necessary "frictional cohesion".
Rheometric measurements on assemblies of wet polystyrene bead assemblies, in steady uniform quasistatic shear flow, for varying liquid content within the small saturation (pendular) range of isolated liquid bridges, are supplemented with a systematic study by discrete numerical simulations. Numerical results and experimental ones agree quantitatively is the intergranular friction coefficient is set to 0.09, suitable for the dry material. Shear resistance and solid fraction are recorded as functions of the reduced pressure p, comparing normal stress to capillary bridge tensile strength. The Moh…
We study the rheology of dry and wet granular materials in the steady quasistatic regime using the Discrete Element Method (DEM) in a split-bottom ring shear cell with focus on the macroscopic friction. The aim of our study is to understand the local rheology of bulk flow at various positions in the shear band, where the system is in critical state. The general(ized) rheology has four dimensionless control parameters that relate the time scales of five significant phenomena, namely, the time scales related to confining pressure $t_p$, shear rate $t_{\dotγ}$, particle stiffness $t_k$, gravity $…
Origin of geometric cohesion in non-convex granular materials: interplay between interdigitation and rotational constraints enhancing frictional stability
Université de Montpellier, CNRS（蒙彼利埃大学）；Departamento de Ingeniería Civil y Ambiental, Facultad de Ingeniería, Universidad de los Andes（安第斯大学）；LMGC, Univ Montpellier, IMT Mines Ales, CNRS（蒙彼利埃大学）；Department of Civil, Geological, and Mining Engineering, Polytechnique Montréal（蒙特利尔高等学院）
Cohesion-induced hysteresis and breakdown of marginal stability in jammed granular materials
Institute of Science and Engineering, Shimane University（岛根大学理工学研究科）；Department of Applied Physics, Tokyo University of Science（东京理科大学应用物理系）；Graduate School of Arts and Sciences, The University of Tokyo（东京大学大学院人文社会系研究科）
Discrete Element Methods (DEM) are a useful tool to model the fracture of cohesive granular materials. For this kind of application, simple particle shapes (discs in 2D, spheres in 3D) are usually employed. However, dealing with more general particle shapes allows to account for the natural heterogeneity of grains inside real materials. We present a discrete model allowing to mimic cohesion between contacting or non-contacting particles whatever their shape in 2D and 3D. The cohesive interactions are made of cohesion points placed on interacting particles, with the aim of representing a cohesi…
Most studies on granular physics have focused on dry granular media, with no liquids between the grains. However, in geology and many real world applications (e.g., food processing, pharmaceuticals, ceramics, civil engineering, constructions, and many industrial applications), liquid is present between the grains. This produces inter-grain cohesion and drastically modifies the mechanical properties of the granular media (e.g., the surface angle can be larger than 90 degrees). Here we present a review of the mechanical properties of wet granular media, with particular emphasis on the effect of …
In this work we derive an analytic expression for the Kolmogorov-Sinai entropy of dilute wet granular matter, valid for any spatial dimension. The grains are modelled as hard spheres and the influence of the wetting liquid is described according to the Capillary Model, in which dissipation is due to the hysteretic cohesion force of capillary bridges. The Kolmogorov-Sinai entropy is expanded in a series with respect to density. We find a rapid increase of the leading term when liquid is added. This demonstrates the sensitivity of the granular dynamics to humidity, and shows that the liquid sign…
We study the geometrically induced cohesion of ensembles of granular "u-particles" which mechanically entangle through particle interpenetration. We vary the length-to-width ratio $l/w$ of the u-particles and form them into free-standing vertical columns. In laboratory experiment we monitor the response of the columns to sinusoidal vibration (frequency $f$, peak acceleration $Γ$). Column collapse occurs in a characteristic time, $τ$, which follows the relation $τ= f^{-1} \exp(Δ/ Γ)$. $Δ$ resembles an activation energy and is maximal at intermediate $l/w$. Simulation reveals that optimal streng…
We investigate the conditions leading to large drag force fluctuations in granular materials. The study is based on a set of experimental drag tests, which involve pulling a plate vertically through a cohesionless granular material. In agreement with previous observations, drag force exhibits significant and sudden drops -up to 60%- when the plate is pulled out at low velocities. We further find that this instability vanishes at higher pullout velocities and near the surface. We empirically characterise the frequency and amplitude of these fluctuations and find that these properties are not co…
Tunable mechanical properties and air-based lubrication in an acoustically levitated granular material
James Franck Institute, University of Chicago（詹姆斯·弗兰克研究所，芝加哥大学）；Department of Physics, University of Chicago（芝加哥大学物理系）；Department of Physics, Drexel University（德雷塞尔大学物理系）；Department of Chemistry, Stanford University（斯坦福大学化学系）；Department of Radiology, Stanford University（斯坦福大学放射学系）；Department of Chemical Engineering, Stanford University（斯坦福大学化学工程系）
Experiments on a thin layer of cohesive wet granular matter under vertical vibrations reveal kink separated domains that collide with the container at different phases. Due to the strong cohesion arising from the formation of liquid bridges between adjacent particles, the domains move collectively upon vibrations. Depending on the periodicity of this collective motion, the kink fronts may propagate, couple with each other and form rotating spiral patterns in the case of period tripling, or stay as standing wave patterns in the case of period doubling. Moreover, both patterns may coexist with g…
Multi-phase flows encountered in nature or in industry, exhibit non trivial rheological properties, that can be understood better thanks to model materials and appropriate rheometers. Here, we use model unsaturated granular materials: assemblies of frictional spherical particles bonded by a small quantity of a wetting liquid, over a rough inclined plane. Our results show steady uniform flows for a wide range of parameters (the inclination angle and the mass flow-rate). A theoretical model, based on the Mohr-Coulomb yield criterion extended to inertial flows: $τ$ = $τ$c + $μ$(I)P, in which $τ$c…
The shear strength of cohesionless granular materials is generally attributed to the compactness or anisotropy of their microstructure. An open issue is how such compact or anisotropic microstructures, and thus the shear strength, depend on the particle properties. We first recall the role of fabric and force anisotropies with respect to the critical-state shear stress. Then, a model of accessible geometrical states in terms of particle connectivity and contact anisotropy is presented. This model incorporates in a simple way the fact that, due to steric exclusions, the highest levels of connec…
Liquid may give strong cohesion properties to a granular medium, and confer a solid-like behavior. We study the erosion of a fixed circular aggregate of wet granular matter subjected to a flow of dry grains inside a half-filled rotating drum. During the rotation, the dry grains flow around the fixed obstacle. We show that its diameter decreases linearly with time for low liquid content, as wet grains are pulled-out of the aggregate. This erosion phenomenon is governed by the properties of the liquids. The erosion rate decreases exponentially with the surface tension while it depends on the vis…
Wet granular aggregates are common precursors of construction materials, food, and health care products. The physical mechanisms involved in the mixing of dry grains with a wet substrate are not well understood and difficult to control. Here, we study experimentally the accretion of dry grains on a wet granular substrate by measuring the growth dynamics of the wet aggregate. We show that this aggregate is fully saturated and its cohesion is ensured by the capillary depression at the air-liquid interface. The growth dynamics is controlled by the liquid fraction at the surface of the aggregate a…
We performed experimental studies of the effect of humidity on the dynamics of electrostatically-driven granular materials. Both conducting and dielectric particles undergo a phase transition from an immobile state (granular solid) to a fluidized state (granular gas) with increasing applied field. Spontaneous precipitation of solid clusters from the gas phase occurs as the external driving is decreased. The clustering dynamics in conducting particles is primarily controlled by screening of the electric field but is aided by cohesion due to humidity. It is shown that humidity effects dominate t…
The rheology of 2D steady surface flow of cohesionless cylinders in a rotating drum is investigated through {\em Non Smooth Contact Dynamics} simulations. Profile of volume fraction, translational and angular velocity, rms velocity, strain rate and stress tensor were measured at the midpoint along the length of the surface flowing layer where the flow is generally considered as steady and homogeneous. Analysis of these data and their inter-relations suggest the local inertial number - defined as the ratio between local inertial forces and local confinement forces - to be the relevant dimension…
The rheology of cohesive granular materials, under a constant pressure condition, is studied using molecular dynamics simulations. Depending on the shear rate, pressure, and interparticle cohesiveness, the system exhibits four distinctive phases: uniform shear, oscillation, shear-banding, and clustering. The friction coefficient is found to increase with the inertial number, irrespective of the cohesiveness. The friction coefficient becomes larger for strong cohesion. This trend is explained by the anisotropies of the coordination number and angular distribution of the interparticle forces. In…
We discuss the difference between cohesive and non-cohesive granular media in the context of a recent report of "dry quicksand." Weak low density states with properties like dry quicksand are readily formed in common household powders. In contrast, such states cannot be formed in cohesionless granular media such as ordinary sand.
