Both the shape of individual particles and their surface properties contribute to the strength of a granular material under shear. Here we show the degree to which these two aspects can be intertwined. In experiments on assemblies of 3D printed, convex lens-shaped particles, we measure the stress-strain response under repeated compressive loading and find that the aggregate's shear strength falls rapidly when compared to other particle shapes. We probe the granular material at mm-scales with X-ray computed tomography and $μ$m-scales with high-resolution surface metrology to look for the cause of the degradation. We find that wear due to accumulated deformation smooths out the lens surfaces in a controlled and systematic manner that correlates with a significant loss of shear strength observed for the assembly as a whole. The sensitivity of lenses to changes in surface properties contrasts with results for assemblies of 3D printed tetrahedra and spheres, which under the same load cycling are found to exhibit only minor degradation in strength. This case study provides insight into the relationship between particle shape, surface wear, and the overall material response, and suggests new strategies when designing a granular material with desired evolution of properties under repeated deformation.
An impact of particles' roughness on the self-diffusion coefficient in granular gases is investigated. For a simplified collision model where the normal and tangential restitution coefficients are assumed to be constant we develop an analytical theory for the diffusion coefficient, which takes into account non-Maxwellain form of the velocity-angular velocity distribution function. We perform molecular dynamics simulations for a gas in a homogeneous cooling state and study the dependence of the self-diffusion coefficient on restitution coefficients. Our theoretical results are in a good agreeme…
Combining X-ray tomography with simultaneous shear force measurement, we investigate shear-induced granular avalanches using spherical particles with different surface roughness. We find that systems consisting of particles with large surface roughness display quasi-periodic avalanches interrupted by crackling-like small ones. In contrast, systems consisting of particles with small roughness display no detectable avalanches. The stress drop of quasi-periodic avalanche shows a linear relation with the correlation length of particle non-affine displacement, suggesting that roughness enhances int…
From event-driven simulations of a gravity-driven channel flow of inelastic hard-disks, we show that the velocity distribution function remains close to a Gaussian for a wide range densities (even when the Knudsen number is of order one) if the walls are smooth and the particle collisions are nearly elastic. For dense flows, a transition from a Gaussian to a power-law distribution for the high velocity tails occurs with increasing dissipation in the center of the channel, irrespective of wall-roughness. For a rough wall, the near-wall distribution functions are distinctly different from those …
A method of modifying the roughness of soda-lime glass spheres is presented, with the purpose of tuning inter-particle friction. The effect of chemical etching on the surface topography and the bulk frictional properties of grains is systematically investigated. The surface roughness of the grains is measured using white light interferometry and characterised by the lateral and vertical roughness length scales. The underwater angle of repose is measured to characterise the bulk frictional behaviour. We observe that the co-efficient of friction depends on the vertical roughness length scale. We…
Recent studies have pointed out the importance of the basal friction on the dynamics of granular flows. We present experimental results on the influence of the roughness of the inclined plane on the dynamics of a monodisperse dry granular flow. We found experimentally that it exists a maximum of the friction for a given relative roughness. This maximum is shown to be independent of the angle of the slope. This behavior is observed for four planes with different bump sizes (given by the size of the beads glued on the plane) from 200 microns to 2 mm. The relative roughness corresponding to the m…
Base roughness plays an important role to the dynamics of granular flows but is yet poorly understood due to the difficulty of its quantification. For a bumpy base made by spheres, at least two factors should be considered to characterize its geometric roughness, namely the size ratio of base- to flow-particles and the packing of base particles. In this paper, we propose a definition of base roughness, Ra, which is a function of both the size ratio and the packing arrangement of base particles. The function is generalized for random and regular packing of multi-layered spheres, where the range…
Boundary shape, particularly roughness, strongly controls the amount of wall slip in dense granular flows. In this paper, we aim to quantify and understand which aspects of a dense granular flow are controlled by the boundary condition, and to incorporate these observations into a cooperative nonlocal model characterizing slow granular flows. To examine the influence of boundary properties, we perform experiments on a quasi-2D annular shear cell with a rotating inner wall and a fixed outer wall; the later is selected from among 6 walls with various roughness, local concavity, and compliance. W…
We discuss the advantages and results of using a mixing-length, compressible model to account for shear banding behaviour in granular flow. We formulate a general approach based on two function of the solid fraction to be determined. Studying the vertical chute flow, we show that shear band thickness is always independent from flowrate in the quasistatic limit, for Coulomb wall boundary conditions. The effect of bin width is addressed using the functions developed by Pouliquen and coworkers, predicting a linear dependence of shear band thickness by channel width, while literature reports contr…
We investigate the effective friction encountered by a mass sliding on a granular layer as a function of bed thickness and boundary roughness conditions. The observed friction has minima for a small number of layers before it increases and saturates to a value which depends on the roughness of the sliding surface. We use an index-matched interstitial liquid to probe the internal motion of the grains with fluorescence imaging in a regime where the liquid has no significant effect on the measured friction. The shear profiles obtained as a function of depth show decrease in slip near the sliding …
A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is carried out to identify the conditions for stability of a granular gas of rough hard spheres. The description is based on the results for the transport coefficients derived from the Boltzmann equation for inelastic rough hard spheres [Phys. Rev. E 90, 022205 (2014)], which take into account the complete nonlinear dependence of the transport coefficients and the cooling rate on the coefficients of normal and tangential restitution. As expected, linear stability analysis shows that a doubly…
Two-dimensional Particle Tracking Velocimetry (PTV) is a promising technique to study the behaviour of granular flows. The aim is to experimentally determine the free surface width and position of the shear band from the velocity profile to validate simulations in a split-bottom shear cell geometry. The position and velocities of scattered tracer particles are tracked as they move with the bulk flow by analyzing images. We then use a new technique to extract the continuum velocity field, applying coarse-graining with the postprocessing toolbox MercuryCG on the discrete experimental PTV data. F…
Size bidisperse granular materials in a spherical tumbler segregate into two different patterns of three bands with either small particles at the equator and large particles at the poles or vice versa, depending upon the fill level in the tumbler. Here we use discrete element method (DEM) simulations with supporting qualitative experiments to explore the effect of the tumbler wall roughness on the segregation pattern, modeling the tumbler walls as either a closely packed monolayer of fixed particles resulting in a rough wall, or as a geometrically smooth wall. Even though the tumbler wall is i…
A simple model for a granular ratchet corresponding to a single grain bouncing off a vertically vibrating sawtooth-like base is studied. Depending on the vibration strength, the sawtooth roughness and the restitution coefficient, horizontal transport in both the preferred and unfavoured directions is observed. A phase diagram indicating the regions in parameter space where each of the three possible regimes (no current, normal current, and current reversal) occurs is presented.
Predicting the force exerted on an object as it penetrates a granular medium is of interest in engineering, locomotive, and geotechnical applications. Current models of granular drag, however, vary widely in applicability and parameterization, and the physical origin of the granular resistive force itself is a subject of debate. Here we perform constant speed penetration experiments, combined with calibrated, large-scale molecular dynamics simulations, at velocities up to 2 m/s to test the effect of impact velocity on the depth dependent `hydrostatic' drag force. We discover that the evolution…
A polydisperse granular gas made of inelastic and rough hard disks is considered. Focus is laid on the kinetic-theory derivation of the partial energy production rates and the total cooling rate as functions of the partial densities and temperatures (both translational and rotational) and of the parameters of the mixture (masses, diameters, moments of inertia, and mutual coefficients of normal and tangential restitution). The results are applied to the homogeneous cooling state of the system and the associated nonequipartition of energy among the different components and degrees of freedom. It…
Using particle trajectory data obtained from x-ray tomography, we determine two kinds of effective temperatures in a cyclically sheared granular system. The first one is obtained from the fluctuation-dissipation theorem which relates the diffusion and mobility of lighter tracer particles immersed in the system. The second is the Edwards compactivity defined via the packing volume fluctuations. We find robust excellent agreement between these two temperatures, independent of the type of the tracers, cyclic shear amplitudes, and particle surface roughness. We further elucidate that in granular s…
Magic Sand, a hydrophobic toy granular material, is widely used in popular science instructions because of its non-intuitive mechanical properties. A detailed study of the failure of an underwater column of magic sand shows that these properties can be traced to a single phenomenon: the system self-generates a cohesive skin that encapsulates the material inside. The skin, consists of pinned air-water-grain interfaces, shows multi-scale mechanical properties: they range from contact-line dynamics in the intra-grain roughness scale, plastic flow at the grain scale, all the way to the sample-scal…
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 threedimensional 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 r…
We show that a freshly sedimented granular bed settles and creeps forward over extended periods of time under an applied hydrodynamic shear stress, which is below the critical value for bedload transport. The rearrangements are found to last over a time scale which is millions of times the sedimentation time scale of a grain in the fluid. Compaction occurs uniformly throughout the bed, but creep is observed to decay exponentially with depth, and decreases over time. The granular volume fraction in the bed is found to increase logarithmically, saturating at the random close packing value $ϕ_{rc…
The Discrete Particle Method (DPM) is used to model granular flows down an inclined chute. We observe three major regimes: static piles, steady uniform flows and accelerating flows. For flows over a smooth base, other (quasi-steady) regimes are observed where the flow is either highly energetic and strongly layered in depth for small inclinations, or non-uniform and oscillating for larger inclinations. For steady uniform flows, depth profiles of density, velocity and stress have been obtained using an improved coarse-graining method, which allows accurate statistics even at the base of the flo…
We performed computer simulations based on a two-dimensional Distinct Element Method to study granular systems of magnetized spherical particles. We measured the angle of repose and the surface roughness of particle piles, and we studied the effect of magnetization on avalanching. We report linear dependence of both angle of repose and surface roughness on the ratio $f$ of the magnetic dipole interaction and the gravitational force (\emph{interparticle force ratio}). There is a difference in avalanche formation at small and at large interparticle force ratios. The transition is at $f_c \approx…
Dense suspensions of colloidal or granular particles can display pronounced non-Newtonian behaviour, such as discontinuous shear thickening (DST) and shear jamming (SJ). The essential contribution of particle surface roughness and adhesive forces confirms that stress-activated contacts can play a key role in these phenomena. By employing a system of microparticles coated by responsive polymers that allow friction, adhesion, and surface roughness to be selectively and independently tuned as a function of temperature, we offer a way to disentangle these contributions. We find that DST occurs at …
The flow of dense suspensions, glasses, and granular materials is heavily influenced by frictional interactions between constituent particles. However, neither hydrodynamics nor friction has successfully explained the full range of flow phenomena in concentrated suspensions. Particles with asperities represent a case in point. Lubrication hydrodynamics fail to completely capture two key rheological properties - namely, that the viscosity increases drastically and the first normal stress difference can switch signs as volume fraction increases. Yet, simulations that account for interparticle fr…
A rigid-plastic Cosserat model for slow frictional flow of granular materials, proposed by us in an earlier paper, has been used to analyze plane and cylindrical Couette flow. In this model, the hydrodynamic fields of a classical continuum are supplemented by the couple stress and the intrinsic angular velocity fields. The balance of angular momentum, which is satisfied implicitly in a classical continuum, must be enforced in a Cosserat continuum. As a result, the stress tensor could be asymmetric, and the angular velocity of a material point may differ from half the local vorticity. An import…
Numerical simulations of two-dimensional granular flows under uniform shear and external body torque were performed in order to extract the constitutive equations for the system. The outcome of the numerical simulations is analyzed on the basis of the micropolar fluid model. Uniform mean shear field and mean spin field, which is not subordinate to the vorticity field, are realized in the simulations. The estimates of stresses based on kinetic theory by Lun [Lun, J. Fluid Mech., 1991, 233, 539] are in good agreement with the simulation results for a low area fraction $ν=0.1$ but the agreement b…
In a granular gas of rough particles the spin of a grain is correlated with its linear velocity. We develop an analytical theory to account for these correlations and compare its predictions to numerical simulations, using Direct Simulation Monte Carlo as well as Molecular Dynamics. The system is shown to relax from an arbitrary initial state to a quasi-stationary state, which is characterized by time-independent, finite correlations of spin and linear velocity. The latter are analysed systematically for a wide range of system parameters, including the coefficients of tangential and normal res…
Role of Friction on the Formation of Confined Granular Structures
Faculdade de Engenharia Mecânica, UNICAMP-Universidade Estadual de Campinas（坎皮纳斯州立大学机械工程学院）；Laboratoire PIMM, CNRS, Arts et Métiers Institute of Technology, Cnam（国立工艺学院PIMM实验室）；Faculty of Physics, University of Duisburg-Essen（杜伊斯堡-埃森大学物理系）
Granular materials such as sand, powders, and grains are omnipresent in daily life, industrial applications, and earth-science [1]. When unperturbed, they form stable structures that resemble the ones of other amorphous solids like metallic and colloidal glasses [2]. It is commonly conjectured that all these amorphous materials show a universal mechanical response when sheared slowly, i.e., to have an elastic regime, followed by yielding [3]. Here we use X-ray tomography to determine the microscopic dynamics of a cyclically sheared granular system in three dimensions. Independent of the shear …
The most widely used model for granular gases is perhaps the inelastic hard-sphere model (IHSM), where the grains are assumed to be perfectly smooth spheres colliding with a constant coefficient of normal restitution. A much more tractable model is the inelastic Maxwell model (IMM), in which the velocity-dependent collision rate is replaced by an effective mean-field constant. This simplification has been taken advantage of by many researchers to find a number of exact results within the IMM. On the other hand, both the IHSM and IMM neglect the impact of roughness -- generally present in real …
In this work we address the question of whether a low-density system composed of identical rough particles may reach hydrodynamic states (also called \textit{normal} states), even if energy is not conserved in particle collisions. As a way to measure the ability of the system to present a hydrodynamic behavior, we focus on the so-called homogeneous cooling state of the granular gas and look at the corresponding relaxation time as a function of inelasticity and roughness. We report computer simulation results of the sixth- and eighth-order cumulants of the particle velocity distribution functio…
Effective particle size governs structure and dynamics in rough hard-particle fluids
College of Physics, Chengdu University of Technology（成都理工大学物理学院）；Department of Physics, University of Montpellier, CNRS（蒙彼利埃大学物理系）；State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology（成都理工大学地质灾害防治与地质环境国家重点实验室）；School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）
Sediment transport occurs when the nondimensional fluid shear stress $Θ$ at the bed surface exceeds a minimum value $Θ_c$. A large collection of data, known as the Shields curve, shows that $Θ_c$ is primarily a function of the shear Reynolds number ${\rm{Re}}_*$. It is commonly assumed that $Θ>Θ_c({\rm{Re}}_*)$ occurs when the ${\rm Re}_*$-dependent fluid forces are too large to maintain static equilibrium for a typical surface grain. A complimentary approach, which remains relatively unexplored, is to identify $Θ_c({\rm{Re}}_*)$ as the applied shear stress at which grains cannot stop moving. …
