Eric I. Corwin

Structural signature of jamming in granular media

Glasses are rigid, but flow when the temperature is increased. Similarly, granular materials are rigid, but become unjammed and flow if sufficient shear stress is applied. The rigid and flowing phases are strikingly different, yet measurements reveal that the structures of glass and liquid are virtually indistinguishable. It is therefore natural to ask whether there is a structural signature of the jammed granular state that distinguishes it from its flowing counterpart. Here we find evidence for such a signature, by measuring the contact-force distribution between particles during shearing. Because the forces are sensitive to minute variations in particle position, the distribution of forces can serve as a microscope with which to observe correlations in the positions of nearest neighbours. We find a qualitative change in the force distribution at the onset of jamming. If, as has been proposed, the jamming and glass transitions are related, our observation of a structural signature associated with jamming hints at the existence of a similar structural difference at the glass transition—presumably too subtle for conventional scattering techniques to uncover. Our measurements also provide a determination of a granular temperature that is the counterpart in granular systems to the glass-transition temperature in liquids.

A ‘granocentric’ model for random packing of jammed emulsions

Packing problems are ubiquitous, ranging from oil extraction through porous rocks to grain storage in silos and the compaction of pharmaceutical powders into tablets. At a given density, particulate systems pack into a mechanically stable and amorphous jammed state. Previous theoretical studies have explored a connection between this jammed state and the glass transition, the thermodynamics of jamming and geometric modelling of random packings. Nevertheless, a simple underlying mechanism for the random assembly of athermal particles, analogous to crystalline ordering, remains unknown. Here we use three-dimensional measurements of packings of polydisperse emulsion droplets to build a simple statistical model in which the complexity of the global packing is distilled into a local stochastic process. From the perspective of a single particle, the packing problem is reduced to the random formation of nearest neighbours, followed by a choice of contacts among them. The two key parameters in the model—the available space around a particle and the ratio of contacts to neighbours—are directly obtained from experiments. We demonstrate that this ‘granocentric’ view captures the properties of the polydisperse emulsion packing—ranging from the microscopic distributions of nearest neighbours and contacts, to local density fluctuations, to the global packing density. Application of our results to monodisperse and bidisperse systems produces quantitative agreement with previously measured trends in global density. Our model therefore reveals a general principle of organization for random packing and may provide the foundations for a theory of jammed matter.

Universal microstructure and mechanical stability of jammed packings.

The mechanical properties of jammed packings depend sensitively on their detailed local structure. Here we provide a complete characterization of the pair correlation close to contact and of the force distribution of jammed frictionless spheres. In particular we discover a set of new scaling relations that connect the behavior of particles bearing small forces and those bearing no force but that are almost in contact. By performing systematic investigations for spatial dimensions d=3-10, in a wide density range and using different preparation protocols, we show that these scalings are indeed universal. We therefore establish clear milestones for the emergence of a complete microscopic theory of jamming. This description is also crucial for high-precision force experiments in granular systems.

The role of interstitial gas in determining the impact response of granular beds

We examine the impact of a solid sphere into a fine-grained granular bed. Using high-speed X-ray radiography we track both the motion of the sphere and local changes in the bed packing fraction. Varying the initial packing density as well as the ambient gas pressure, we find a complete reversal in the effect of interstitial gas on the impact response of the bed: The dynamic coupling between gas and grains allows for easier penetration in initially loose beds but impedes penetration in more densely packed beds. High-speed imaging of the local packing density shows that these seemingly incongruous effects have a common origin in the resistance to bed packing changes caused by interstitial air.

Jamming criticality revealed by removing localized buckling excitations

Recent theoretical advances offer an exact, first-principles theory of jamming criticality in infinite dimension as well as universal scaling relations between critical exponents in all dimensions. For packings of frictionless spheres near the jamming transition, these advances predict that nontrivial power-law exponents characterize the critical distribution of (i) small interparticle gaps and (ii) weak contact forces, both of which are crucial for mechanical stability. The scaling of the interparticle gaps is known to be constant in all spatial dimensions d-including the physically relevant d=2 and 3, but the value of the weak force exponent remains the object of debate and confusion. Here, we resolve this ambiguity by numerical simulations. We construct isostatic jammed packings with extremely high accuracy, and introduce a simple criterion to separate the contribution of particles that give rise to localized buckling excitations, i.e., bucklers, from the others. This analysis reveals the remarkable dimensional robustness of mean-field marginality and its associated criticality.

Model for random packing of polydisperse frictionless spheres

We propose a statistical model for the random packing of frictionless polydisperse spheres in which the complexity of the global packing is distilled into a local stochastic process. We simplify the problem by considering the “granocentric” point of view of a single particle in the bulk, thereby reducing random packing to the assembly of nearest neighbours, followed by a random choice of contacts among them. The model is based on only two parameters, the available solid angle around each particle and the ratio of contacts to neighbors, which are both directly obtainable from experiments or simulations. As a result, the model analytically predicts the microscopic distributions of nearest neighbours and contacts, the local density fluctuations as well as the global density of the packing. We find that this granocentric view captures the essential properties of the polydisperse emulsion packing. This model suggests a general principle of organization for random packing and provides a statistical tool for quantifying the effect of the particle size distribution on the geometry of random packing in a variety of contexts of industrial relevance.

Universal Non-Debye Scaling in the Density of States of Amorphous Solids.

At the jamming transition, amorphous packings are known to display anomalous vibrational modes with a density of states (DOS) that remains constant at low frequency. The scaling of the DOS at higher packing fractions remains, however, unclear. One might expect to find a simple Debye scaling, but recent results from effective medium theory and the exact solution of mean-field models both predict an anomalous, non-Debye scaling. Being mean-field in nature, however, these solutions are only strictly valid in the limit of infinite spatial dimension, and it is unclear what value they have for finite-dimensional systems. Here, we study packings of soft spheres in dimensions 3 through 7 and find, away from jamming, a universal non-Debye scaling of the DOS that is consistent with the mean-field predictions. We also consider how the soft mode participation ratio evolves as dimension increases.

Gas-Mediated Impact Dynamics in Fine-Grained Granular Materials

Noncohesive granular media exhibit complex responses to sudden impact that often differ from those of ordinary solids and liquids. We investigate how this response is mediated by the presence of interstitial gas between the grains. Using high-speed x-ray radiography we track the motion of a steel sphere through the interior of a bed of fine, loose granular material. We find a crossover from nearly incompressible, fluidlike behavior at atmospheric pressure to a highly compressible, dissipative response once most of the gas is evacuated. We discuss these results in light of recent proposals for the drag force in granular media.

Structure of marginally jammed polydisperse packings of frictionless spheres.

We model the packing structure of a marginally jammed bulk ensemble of polydisperse spheres. To this end we expand on the granocentric model [Clusel et al., Nature (London) 460, 611 (2009)], explicitly taking into account rattlers. This leads to a relationship between the characteristic parameters of the packing, such as the mean number of neighbors and the fraction of rattlers, and the radial distribution function g(r). We find excellent agreement between the model predictions for g(r) and packing simulations, as well as experiments on jammed emulsion droplets. The observed quantitative agreement opens the path towards a full structural characterization of jammed particle systems for imaging and scattering experiments.

Mean-field granocentric approach in 2D & 3D polydisperse, frictionless packings

Abstract We have studied the contact network properties of two- and three-dimensional polydisperse, frictionless sphere packings at the random closed packing density through simulations. We observe universal correlations between particle size and contact number that are independent of the polydispersity of the packing. This allows us to formulate a mean field version of the granocentric model to predict the contact number distribution . We find the predictions to be in good agreement with a wide range of discrete and continuous size distributions. The values of the two parameters that appear in the model are also independent of the polydispersity of the packing. Finally, we look at the nearest neighbour spatial correlations to investigate the validity of the granocentric approach. We find that both particle size and contact number are anti-correlated which contrasts with the assumptions of the granocentric model. Despite this shortcoming, the correlations are sufficiently weak which explains the good approximation of obtained from the model.