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We analyze stress transmission in wet granular media in the pendular state by means of three-dimensional molecular-dynamics simulations. We show that the tensile action of capillary bonds induces a self-stressed particle network organized in two percolating \"phases\" of positive and negative particle pressures. Various statistical descriptors of the microstructure and bond force network are used to characterize this partition. Two basic properties emerge: 1) the highest particle pressure is located in the bulk of each phase; 2) the lowest pressure level occurs at the interface between the two phases, involving also the largest connectivity of the particles via tensile and compressive bonds. When a confining pressure is applied, the number of tensile bonds falls off and the negative phase breaks into aggregates and isolated sites.

In the past ten years much work has been undertaken on developing mixture theory continuum models to describe kinetic sieving-driven size segregation. We propose an extension to these models that allows their application to bidisperse flows over inclined channels, with particles varying in density and size. Our model incorporates both a recently proposed explicit formula for how the total pressure is distributed among different species of particles, which is one of the key elements of mixture theory-based kinetic sieving models, and a shear rate-dependent drag. The resulting model is used to predict the range of particle sizes and densities for which the mixture segregates. The prediction of no segregation in the model is benchmarked by using discrete particle simulations, and good agreement is found when a single fitting parameter is used which determines whether the pressure scales with the diameter, surface area or volume of the particle.

We investigate the macroscopic mechanical behaviour of wet polydisperse granular media. Capillary bonding between two grains of unequal diameters is described by a realistic force law implemented in a molecular-dynamics algorithm together with a protocol for the distribution of water in the bulk. Axial-compression tests are simulated for granular samples at different levels of water content, and compared to experiments performed in similar conditions. We find good agreement between numerical and experimental data in terms of the rupture strength as a function of water content. Our results show the importance of the distribution of water for the mechanical behaviour.

It is well-known that in a dense, gravity-driven flow, large particles typically rise to the top relative to smaller equal-density particles. In dense flows, this has historically been attributed to gravity alone. However, recently kinetic stress gradients have been shown to segregate large particles to regions with higher granular temperature, in contrast to sparse energetic granular mixtures where the large particles segregate to regions with lower granular temperature. We present a segregation theory for dense gravity-driven granular flows that explicitly accounts for the effects of both gravity and kinetic stress gradients involving a separate partitioning of contact and kinetic stresses among the mixture constituents. We use discrete-element-method (DEM) simulations of different-sized particles in a rotated drum to validate the model and determine diffusion, drag, and stress partition coefficients. The model and simulations together indicate, surprisingly, that gravity-driven kinetic sieving is not active in these flows. Rather, a gradient in kinetic stress is the key segregation driving mechanism, while gravity plays primarily an implicit role through the kinetic stress gradients. Finally, we demonstrate that this framework captures the experimentally observed segregation reversal of larger particles downward in particle mixtures where the larger particles are sufficiently denser than their smaller counterparts.

A constitutive model is developed for the complex rheology of rate-independent granular materials. The closures for the pressure and the macroscopic friction coefficient are linked to microstructure through evolution equations for coordination number and fabric. The material constants in the model are functions of particle-level properties and are calibrated using data generated through simulations of steady and unsteady simple shear using the discrete element method (DEM). This model is verified against DEM simulations at complex loading conditions.

The steady-state shear rheology of granular materials is investigated in slow quasistatic and inertial flows. The effect of gravity (thus the local pressure) and the often-neglected contact stiffness are the focus of this study. A series of particle simulations are performed on a weakly frictional granular assembly in a split-bottom geometry considering various magnitudes of gravity and contact stiffnesses. While traditionally the inertial number, i.e., the ratio of stress to strain-rate time scales, is used to describe the flow rheology, we report that a second dimensionless number, the ratio of softness and stress time scales, must also be included to characterize the bulk flow behavior. For slow, quasistatic flows, the density increases while the effective (macroscopic) friction decreases with increase in either particle softness or local pressure. This trend is added to the rheology and can be traced back to the anisotropy in the contact network, displaying a linear correlation between the effective friction coefficient and deviatoric fabric in the steady state. When the external rotation rate is increased towards the inertial regime, for a given gravity field and contact stiffness, the effective friction increases faster than linearly with the deviatoric fabric.

Despite their widespread adoption, particle-scale simulation methods, such as the Discrete Element Method (DEM), for electrically charged particles in several natural processes and industrial transformations do not include realistic polarization effects. At close distances, these can dominate the particle motion and are impossible to predict by the commonly adopted Coulomb point-charge approximation. Sophisticated mathematical tools can account for uneven charge distributions, predicting an attractive force between a charged particle and a neutral particle or possible attraction between two like-charged particles. Such approaches are accurate but too complex for implementation in DEM simulations of many interacting particles. We propose a novel, simpler yet realistically accurate effective dipole model. By attributing a net charge and an induced effective dipole to each sphere, the interaction force between charged polarizable particles is computed in closed form. A comparison of a rigorous solution and the proposed dipole approach for two spherical particles reveals significant improvement over the commonly employed Coulomb law. The effects of particle size ratio and charge ratio on the interaction force are discussed. Then, the dynamic DEM simulation of a shaker filled with a binary mixture of differently sized particles that are all positively charged is shown to predict the counterintuitive formation of fine-on-coarse aggregates.

There is a large amount of experimental and numerical work dealing with dry granular flows (such as sand, glass beads, etc.) that supports the so-called $\\ensuremath{\\mu} (I)$-rheology. The reliability of the $\\ensuremath{\\mu} (I)$-rheology in the case of complex transient flows is not fully ascertained, however. From this perspective, the granular column collapse experiment provides an interesting benchmark. In this paper we implement the $\\ensuremath{\\mu} (I)$-rheology in a Navier–Stokes solver (Gerris) and compare the resulting solutions with both analytical solutions and two-dimensional contact dynamics discrete simulations. In a first series of simulations, we check the numerical model in the case of a steady infinite two-dimensional granular layer avalanching on an inclined plane. A second layer of Newtonian fluid is then added over the granular layer in order to recover a close approximation of a free-surface condition. Comparisons with analytical and semi-analytical solutions provide conclusive validation of the numerical implementation of the $\\ensuremath{\\mu} (I)$-rheology. In a second part, we simulate the unsteady two-dimensional collapse of granular columns over a wide range of aspect ratios. Systematic comparisons with discrete two-dimensional contact dynamics simulations show good agreement between the two methods for the inner deformations and the time evolution of the shape during most of the flow, while a systematic underestimation of the final run-out is observed. The experimental scalings of spreading of the column as a function of the aspect ratio available from the literature are also recovered. A discussion follows on the performances of other rheologies, and on the sensitivity of the simulations to the parameters of the $\\ensuremath{\\mu} (I)$-rheology.

The Enskog kinetic theory is used as a starting point to model a suspension of solid particles in a viscous gas. Unlike previous efforts for similar suspensions, the gas-phase contribution to the instantaneous particle acceleration appearing in the Enskog equation is modelled using a Langevin equation, which can be applied to a wide parameter space (e.g. high Reynolds number). Attention here is limited to low Reynolds number flow, however, in order to assess the influence of the gas phase on the constitutive relations, which was assumed to be negligible in a previous analytical treatment. The Chapman–Enskog method is used to derive the constitutive relations needed for the conservation of mass, momentum and granular energy. The results indicate that the Langevin model for instantaneous gas–solid force matches the form of the previous analytical treatment, indicating the promise of this method for regions of the parameter space outside of those attainable by analytical methods (e.g. higher Reynolds number). The results also indicate that the effect of the gas phase on the constitutive relations for the solid-phase shear viscosity and Dufour coefficient is non-negligible, particularly in relatively dilute systems. Moreover, unlike their granular (no gas phase) counterparts, the shear viscosity in gas–solid systems is found to be zero in the dilute limit and the Dufour coefficient is found to be non-zero in the elastic limit.