Vertical ordering of rods under vertical vibration

Structural evolution of granular cubes packing during shear-induced ordering

Packings of granular particles may transform into ordered structures under external agitation, which is a special type of out-of-equilibrium self-assembly. Here, evolution of the internal packing structures of granular cubes under cyclic rotating shearing has been analyzed using magnetic resonance imaging techniques. Various order parameters, different types of contacts and clusters composed of face-contacting cubes, as well as the free volume regions in which each cube can move freely have been analyzed systematically to quantify the ordering process and the underlying mechanism of this granular self-assembly. The compaction process is featured by a first rapid formation of orientationally ordered local structures with faceted contacts, followed by further densification driven by free-volume maximization with an almost saturated degree of order. The ordered structures are strongly anisotropic with contacting ordered layers in the vertical direction while remaining liquid-like in the horizontal directions. Therefore, the constraint of mechanical stability for granular packings and the thermodynamic principle of entropy maximization are both effective in this system, which we propose can be reconciled by considering different depths of supercooling associated with various degrees of freedom.

Cubatic structural transformation of the packing of granular cylinders

Packing structures of granular cylinders with the aspect ratio close to one have been reconstructed with the help of magnetic resonance imaging techniques. By controlling the container boundary conditions and preparation protocols, a structural transformation from a disordered liquid-like state to an orientationally ordered state with cubatic symmetry at a high packing fraction is observed. This ordering process is accompanied by the formation of more faceted contacts, which lower the elastic energy between jammed granular particles to drive the transformation. With the help of Edwards' volume ensemble theory, this granular structural transformation is explained using a phenomenological thermodynamic model and a self-consistent mean-field statistical mechanical model. Both models predict a sharp but continuous change of order parameter when the effective granular temperature is lowered. The intrinsic difference and connection between this granular structural transformation and the entropy-driven phase transition of conventional thermal hard-particle systems are discussed.

Structural disorder, filament growth and self-poisoning in short rods confined onto a flat wall

Confocal microscopy was used to directly observe the structural coarsening of the first layer of short colloidal rods sedimented onto a flat wall. Based on an image analysis algorithm we devised, quantitative information on the location, orientation and length of each particle can be extracted with high precision. At high density the system undergoes structural arrest, and becomes trapped in a disordered state of randomly arranged filaments that are composed of side-by-side aligned rods. The frustration of structural order is signalled by a new peak that emerges in the radial distribution function. Configuration analysis shows that the peak is primarily due to pairs of particles that are arranged in a "T" shape, a configuration that is compatible with neither crystallization nor filament growth. Our results point to a self-poisoning mechanism for the frustration of structural order, and highlight the importance of particle shape in controlling colloidal assembly thus materials properties.

Clustering in vibrated monolayers of granular rods

We investigate the ordering properties of vertically-vibrated monolayers of granular cylinders in a circular container at high packing fraction. In line with previous works by other groups, we identify liquid-crystalline ordering behaviour similar to that of two-dimensional hard rectangular particles subject to thermal equilibrium fluctuations. However, due to dissipation, there is a much stronger tendency for particles to cluster into parallel arrangements in the granular system. These clusters behave as a polydisperse mixture of long life-time 'superparticles', and some aspects of the system behaviour can be understood by applying mean-field theories for equilibrium hard rectangles, based on two-body correlations, to these 'superparticles'. Many other features of the granular system are different: (i) for small particle length-to-breadth ratio κ, we identify tetratic ordering at moderate packing fractions and smectic fluctuations at higher packing fractions, with no sharp transition between the two states. Both types of ordering can be explained in terms of clustering. (ii) For large κ, strong clustering precludes the stabilisation of a uniaxial nematic state, and the system exhibits a mixture of randomly-oriented clusters which, as packing fraction is increased, develops into states with smectic fluctuations, again through a diffuse transition. (iii) Vorticity excitations of the velocity field compete with smectic ordering, causing dynamic fluctuations and the absence of steady states at high densities; the tetratic state, by contrast, is very stiff against vorticity, and long-standing steady states, spatially and orientationally homogeneous except for four symmetrical defects located close to the wall, can be observed.

Modifying self-assembly and species separation in three-dimensional systems of shape-anisotropic particles

The behaviors of large, dynamic assemblies of macroscopic particles are of direct relevance to geophysical and industrial processes and may also be used as easily studied analogs to micro- or nano-scale systems, or model systems for microbiological, zoological, and even anthropological phenomena. We study vibrated mixtures of elongated particles, demonstrating that the inclusion of differing particle "species" may profoundly alter a system's dynamics and physical structure in various diverse manners. The phase behavior observed suggests that our system, despite its athermal nature, obeys a minimum free energy principle analogous to that observed for thermodynamic systems. We demonstrate that systems of exclusively spherical objects, which form the basis of numerous theoretical frameworks in many scientific disciplines, represent only a narrow region of a wide, multidimensional phase space. Thus, our results raise significant questions as to whether such models can accurately describe the behaviors of systems outside this highly specialized case.

Effect of aspect ratio on the development of order in vibrated granular rods

We investigate ordering of granular rods in a container subject to vibrations in a gravitational field as a function of number density of the rods. We study rods with three different length to diameter aspect ratios A(r)= 5, 10, and 15. The measurements are performed in three dimensions using x-ray computer tomography to visualize the rods in the entire container. We first discuss a method to extract the position and orientation of the rods from the scans which enables us to obtain statistical measures of the degree of order in the packing. We find that the rods with A(r)=5 phase separate into domains with vertical and horizontal orientation as the number density of the rods is increased, whereas, for A(r)=10 and 15 the rods are predominately oriented vertically in layers. By calculating two-point spatial correlation functions, we further show that long range hexagonal order occurs within a layer when the rods are oriented along the vertical axis. Thus, our experiments find that long range order increases rapidly in granular rods with growing anisotropy.

X-ray microtomography study of the compaction process of rods under tapping

We present an x-ray microtomography study of the compaction process of cylindrical rods under tapping. The process is monitored by measuring the evolution of the orientational order parameter, local, and overall packing densities as a function of the tapping number for different tapping intensities. The slow relaxation dynamics of the orientational order parameter can be well fitted with a stretched-exponential law with stretching exponents ranging from 0.9 to 1.6. The corresponding relaxation time versus tapping intensity follows an Arrhenius behavior which is reminiscent of the slow dynamics in thermal glassy systems. We also investigated the boundary effect on the ordering process and found that boundary rods order faster than interior ones. In searching for the underlying mechanism of the slow dynamics, we estimated the initial random velocities of the rods under tapping and found that the ordering process is compatible with a diffusion mechanism. The average coordination number as a function of the tapping number at different tapping intensities has also been measured, which spans a range from 6 to 8.

Relation between self-organized criticality and grain aspect ratio in granular piles

We investigate experimentally whether self-organized criticality (SOC) occurs in granular piles composed of different grains, namely, rice, lentils, quinoa, and mung beans. These four grains were selected to have different aspect ratios, from oblong to oblate. As a function of aspect ratio, we determined the growth (β) and roughness (α) exponents, the avalanche fractal dimension (D), the avalanche size distribution exponent (τ), the critical angle (γ), and its fluctuation. At superficial inspection, three types of grains seem to have power-law-distributed avalanches with a well-defined τ. However, only rice is truly SOC if we take three criteria into account: a power-law-shaped avalanche size distribution, finite size scaling, and a universal scaling relation relating characteristic exponents. We study SOC as a spatiotemporal fractal; in particular, we study the spatial structure of criticality from local observation of the slope angle. From the fluctuation of the slope angle we conclude that greater fluctuation (and thus bigger avalanches) happen in piles consisting of grains with larger aspect ratio.

Column collapse of granular rods

We investigate the collapse of granular rodpiles as a function of particle (length/diameter) and pile (height/radius) aspect ratio. We find that, for all particle aspect ratios below 24, there exists a critical height Hl below which the pile never collapses, maintaining its initial shape as a solid, and a second height Hu above which the pile always collapses. Intermediate heights between Hl and Hu collapse with a probability that increases linearly with increasing height. The linear increase in probability is independent of particle length, width, or aspect ratio. When piles collapse, the runoff scales as a piecewise power law with pile height, with rf ~H(1.2±0.1) for pile heights below H(c) ≈ 0.74 and r(f) ≈ H(0.6±0.1) for taller piles.

Geometric aspects of particle segregation

Size segregation is a natural occurrence both in everyday life and in industrial processes. Understanding and research of the phenomenon has overwhelmingly been from a mechanistic point of view. This paper demonstrates through simulations that segregation can also be explained and trends predicted geometrically. The algorithm used in this study contains three simple elements: random walks combined with a rebounding probability to encourage particles to settle, plus the non-overlap constraint. It is implemented digitally in a regular lattice grid, to make it easy to deal with arbitrary shapes. It does not explicitly consider any particle interaction forces, and it does not include any rules specifically designed to promote or suppress segregation. Yet particle movement, which occurs within a digitized cubic grid, leads to shaking-induced segregation comparable to that observed in physical tests. The paper details the comparison of shaking-induced particle segregation between a series of computer based simulations and those of physical experiments undertaken in the laboratory. A range of mixtures, comprising nonspherical, arbitrary shaped/sized particles are investigated, having been packed into pseudo-two-dimensional containers. The simulation results suggest that segregation can be adequately explained, from a geometrical point of view, as a result of the relative motion between particles of different sizes and shapes. The geometrical algorithm thus provides a fast and qualitative prediction as to how likely segregation is to occur for any given mixture of arbitrary shapes.

Energy dissipation and dispersion effects in granular media

The strong interactions between particles will make the energy within the granular materials propagate through the network of contacts and be partly dissipated. Establishing a model that can clearly classify the dissipation and dispersion effects is crucial for the understanding of the global behaviors in the granular materials. For particles with rate-independent material, the dissipation effects come from the local plastic deformation and can be constrained at the energy level by using energetic restitution coefficients. On the other hand, the dispersion effects should depend on the intrinsic nature of the interaction law between two particles. In terms of a bistiffness compliant contact model that obeys the energetical constraint defined by the energetic coefficients, our recent work related to the issue of multiple impacts indicates that the propagation of energy during collisions can be represented by a distributing law. In particular, this law shows that the dispersion effects are dominated by the relative contact stiffness and the relative potential energy stored at the contact points. In this paper, we will apply our theory to the investigation of the wave behavior in granular chain systems. The comparisons between our numerical results and the experimental ones by Falcon, [Eur. Phys. J. B 5, 111 (1998)] for a column of beads colliding against a wall show very good agreement and confirm some conclusions proposed by Falcon Other numerical results associated with the case of several particles impacting a chain, and the collisions between two so-called solitary waves in a Hertzian type chain are also presented.

Coupled tomography and distinct-element-method approach to exploring the granular media microstructure in a jamming hourglass

We describe an approach for exploring microscopic properties of granular media that couples x-ray microtomography and distinct-element-method (DEM) simulations through image analysis. We illustrate it via the study of the intriguing phenomenon of instant arching in an hourglass (in our case a cylinder filled with a polydisperse mixture of glass beads that has a small circular shutter in the bottom). X-ray tomography provides three-dimensional snapshots of the microscopic conditions of the system both prior to opening the shutter, and thereafter, once jamming is completed. The process time in between is bridged using DEM simulation, which settles to positions in remarkably good agreement with the x-ray images. Specifically designed image analysis procedures accurately extract the geometrical information, i.e., the positions and sizes of the beads, from the raw x-ray tomographs, and compress the data representation from initially 5 gigabytes to a few tens of kilobytes per tomograph. The scope of the approach is explored through a sensitivity analysis to input data perturbations in both bead sizes and positions. We establish that accuracy of size--much more than position--estimates is critical, thus explaining the difficulty in considering a mixture of beads of different sizes. We further point to limits in the replication ability of granular flows away from equilibrium; i.e., the difficulty of numerically reproducing chaotic motion.