A highly polydisperse granular gas is modeled by a continuous distribution of particle sizes, a, giving rise to a corresponding continuous temperature profile, T(a), which we compute approximately, generalizing previous results for binary or multicomponent mixtures. If the system is driven, it evolves towards a stationary temperature profile, which is discussed for several driving mechanisms in dependence on the variance of the size distribution. For a uniform distribution of sizes, the stationary temperature profile is nonuniform with either hot small particles (constant force driving) or hot large particles (constant velocity or constant energy driving). Polydispersity always gives rise to non-Gaussian velocity distributions. Depending on the driving mechanism the tails can be either overpopulated or underpopulated as compared to the molecular gas. The deviations are mainly due to small particles. In the case of free cooling the decay rate depends continuously on particle size, while all partial temperatures decay according to Haff's law. The analytical results are supported by event driven simulations for a large, but discrete number of species.
It is well-recognized that granular media under rapid flow conditions can be modeled as a gas of hard spheres with inelastic collisions. At moderate densities, a fundamental basis for the determination of the granular hydrodynamics is provided by the Enskog kinetic equation conveniently adapted to account for inelastic collisions. A surprising result (compared to its molecular gas counterpart) for granular mixtures is the failure of the energy equipartition, even in homogeneous states. This means that the partial temperatures $T_i$ (measuring the mean kinetic energy of each species) are differ…
We dynamically simulate fractionation (partitioning of particle species) during spinodal gas-liquid separation of a size-polydisperse colloid, using polydispersity up to ~40% and a skewed parent size distribution. We introduce a novel coarse-grained Voronoi method to minimise size bias in measuring local volume fraction, along with a variety of spatial correlation functions which detect fractionation without requiring a clear distinction between the phases. These can be applied whether or not a system is phase separated, to determine structural correlations in particle size, and generalise eas…
We report on experimentally measured drag force experienced by a solid cylinder penetrating a granular bed of glass beads including, specifically, a highly polydisperse sample with grain sizes in the range 1-100 μm. We consider both cases of lateral and axial intrusion in which the long axis of the cylinder is held horizontally and vertically, respectively. We explore different regimes of behavior for the drag force as a function of the penetration depth. In lateral intrusion, where the motion is effectively quasi-two-dimensional, we establish quantitative comparisons with existing theoretical…
We investigate the down-hill creep of a layer of granular material on a slope caused by an oscillatory variation of the size of the particles. The material is modeled as an athermal two dimensional polydisperse system of soft disks under the action of gravity. The slope angle is below the critical rest angle and therefore the system reaches an equilibrium configuration under static external conditions. However, under a protocol in which particles slowly change size in a quasistatic oscillatory way the system is observed to creep down in a synchronized way with the oscillation. We measure the c…
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…
Granular systems are not always homogeneous and can be composed of grains with very different mechanical properties. To improve our understanding of the behavior of real granular systems, in this experimental study, we compress 2D bidisperse systems made of both soft and rigid grains. By means of a recently developed experimental set-up, \md{from the measurement of the displacement field we can} follow all the mechanical observables of this granular medium from the inside of each particle up-to-the whole system scale. We \md{are able to} detect the jamming transition from these observables and…
Using simulations and a virtual-spring-based approach, we measure the segregation force, Fseg, over a range of size-bidisperse mixture concentrations, particle size ratios, and shear rates to develop a model for Fseg that extends its applicability from the well-studied non-interacting intruders regime to finite-concentration mixtures where cooperative phenomena occur. The model predicts the concentration below which the single intruder assumption applies and provides an accurate description of the pressure partitioning between species.
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…
Granular materials often present correlations between particle size and shape due to their geological formation and mechanisms of weathering and fragmentation. It is known that particle shape strongly affects shear strength. However, the effects of shape can be modified by the role the particle plays in a sample given its size. We explore the steady shear strength of samples composed of particles presenting size-shape correlations and we focus on the case of particle elongation in two opposite scenarios: (A) large elongated grains with finer circular grains and (B) large circular grains with e…
A pore-scale model is introduced for two-phase flow in dense packings of polydisperse spheres. The model is developed as a component of a more general hydromechanical coupling framework based on the discrete element method, which will be elaborated in future papers. Here the emphasis is on the generation of a network of pores mapping the void space between spherical grains, and the definition of local criteria governing the primary drainage process. The pore space is decomposed by Regular Triangulation, from which a set of pores connected by throats are identified. A local entry capillary pres…
We describe the development of a new software tool, called "Pomelo", for the calculation of Set Voronoi diagrams. Voronoi diagrams are a spatial partition of the space around the particles into separate Voronoi cells, e.g. applicable to granular materials. A generalization of the conventional Voronoi diagram for points or monodisperse spheres is the Set Voronoi diagram, also known as navigational map or tessellation by zone of influence. In this construction, a Set Voronoi cell contains the volume that is closer to the surface of one particle than to the surface of any other particle. This is …
Size segregation in bedload transport is studied numerically with a coupled fluid-discrete element model. Starting from an initial deposit of small spherical particles on top of a large particle bed, the segregation dynamics of the bed is studied as it is driven by the fluid flow. Focusing on the quasi-static part of the bed, the small particles are observed to segregate as a layer of constant thickness at a velocity constant in time and independent of the number of small particles. The segregation velocity is observed to be directly linked to the inertial number at the bottom of the layer, an…
