Self-diffusion in inhomogeneous granular shearing flows.

In this Letter, we discuss how flow inhomogeneity affects the self-diffusion behavior in granular flows. Whereas self-diffusion scalings have been well characterized in the past for homogeneous shearing, the effect of shear localization and nonlocality of the flow has not been studied. We, therefore, present measurements of self-diffusion coefficients in discrete numerical simulations of steady, inhomogeneous, and collisional shearing flows of nearly identical, frictional, and inelastic spheres. We focus on a wide range of dense solid volume fractions, that correspond to geophysical and industrial shearing flows that are dominated by collisional interactions. We compare the measured values first with a scaling based on shear rate and, then, on a scaling based on the granular temperature. We find that the latter does much better than the former in collapsing the data. The results lay the foundations of diffusion models for inhomogeneous shearing flows, which should be useful in treating problems of mixing and segregation.

Simulation of the Attrition of Recycled Concrete Aggregates during Concrete Mixing.

Concrete mixing can lead to mechanical degradation of aggregates, particularly when dealing with recycled concrete aggregates. In this work, the attrition of such materials during mixing is studied by means of experiments and simulations. The effect of the presence of fines, water addition, flow configuration of the mixer (co- or counter-current) and impeller frequency is discussed. Experiments were performed in a laboratory Eirich mixer. Discrete element numerical simulations (DEM) were performed on the same geometry by mimicking the behaviour of the material and, in particular, the cohesion induced by water and the cement paste using either Hertz-Mindlin or Hertz-Mindlin with Johnson-Kendall-Roberts (JKR) contact laws. The combination of the collision energy spectra extracted from the DEM simulations and an attrition model allowed the prediction of the mass loss due to attrition in 1-min experiments. Semi-quantitative agreement was observed between experiments and simulations, with a mean relative error of 26.4%. These showed that higher mass losses resulted from operation at the highest impeller speeds, co-current operation, and also with the wet aggregate. Mixing of the agglomerate in the concrete mix resulted in a significant reduction in attrition when compared to mixing aggregates alone. With further validation, the proposed simulation approach can become a valuable tool in the optimization of mixing by allowing the effects of material, machine and process variables to be studied on the mass loss due to attrition.

Self-diffusion scalings in dense granular flows.

We report on measurements of self-diffusion coefficients in discrete numerical simulations of steady, homogeneous, collisional shearing flows of nearly identical, frictional, inelastic spheres. We focus on a range of relatively high solid volume fractions that are important in those terrestrial gravitational shearing flows that are dominated by collisional interactions. Diffusion over this range of solid fraction has not been well characterized in previous studies. We first compare the measured values with an empirical scaling based on shear rate previously proposed in the literature, and highlight the presence of anisotropy and the solid fraction dependence. We then compare the numerical measurements with those predicted by the kinetic theory for shearing flows of inelastic spheres and offer an explanation for why the measured and predicted values differ.

Effective Wall Friction in Wall-Bounded 3D Dense Granular Flows.

We report numerical simulations on granular shear flows confined between two flat but frictional sidewalls. Novel regimes differing by their strain localization features are observed. They originate from the competition between dissipation at the sidewalls and dissipation in the bulk of the flow. The effective friction at sidewalls is characterized (effective friction coefficient and orientation of the friction force) for each regime, and its interdependence with slip and force fluctuations is pointed out. We propose a simple scaling law linking the slip velocity to the granular temperature in the main flow direction which leads naturally to another scaling law for the effective friction.

Average balance equations, scale dependence, and energy cascade for granular materials.

A new averaging method linking discrete to continuum variables of granular materials is developed and used to derive average balance equations. Its novelty lies in the choice of the decomposition between mean values and fluctuations of properties which takes into account the effect of gradients. Thanks to a local homogeneity hypothesis, whose validity is discussed, simplified balance equations are obtained. This original approach solves the problem of dependence of some variables on the size of the averaging domain obtained in previous approaches which can lead to huge relative errors (several hundred percentages). It also clearly separates affine and nonaffine fields in the balance equations. The resulting energy cascade picture is discussed, with a particular focus on unidirectional steady and fully developed flows for which it appears that the contact terms are dissipated locally unlike the kinetic terms which contribute to a nonlocal balance. Application of the method is demonstrated in the determination of the macroscopic properties such as volume fraction, velocity, stress, and energy of a simple shear flow, where the discrete results are generated by means of discrete particle simulation.

Texture analysis as a tool to study the kinetics of wet agglomeration processes.

In this work wet granulation experiments were carried out in a planetary mixer with the aim to develop a novel analytical tool based on surface texture analysis. The evolution of a simple formulation (300g of microcrystalline cellulose with a solid binders pre-dispersed in water) was monitored from the very beginning up to the end point and information on the kinetics of granulation as well as on the effect of liquid binder amount were collected. Agreement between texture analysis and granules particle size distribution obtained by sieving analysis was always found. The method proved to be robust enough to easily monitor the process and its use for more refined analyses on the different rate processes occurring during granulation is also suggested.

Scaling laws for the slip velocity in dense granular flows.

In this Letter, the two-dimensional dense flow of polygonal particles on an incline with a flat frictional inferior boundary is analyzed by means of contact dynamics discrete element simulations, in order to develop boundary conditions for continuum models of dense granular flows. We show the evidence that the global slip phenomenon deviates significantly from simple sliding: a finite slip velocity is generally found for shear forces lower than the sliding threshold for particle-wall contacts. We determined simple scaling laws for the dependence of the slip velocity on shear rate, normal and shear stresses, and material parameters. The importance of a correct determination of the slip at the base of the incline, which is crucial for the calculation of flow rates, is discussed in relation to natural flows.

Hysteresis in a hydrodynamic model of dense granular flows.

A hydrodynamic model for dense granular flows, previously developed for confined flows, has been extended to address free surface flow down an inclined chute. Results show that the model can predict the existence of two critical inclination angles, namely, the avalanche starting angle θ(start) above which the granular bed begins flowing from an initially jammed configuration, and an avalanche stopping angle θ(stop), which is the minimum to maintain flowing conditions, in agreement with experiments and numerical simulations available from the literature. The dependence of these critical angles on the bed depth is also analytically formulated, reflecting the expected qualitative behavior. Such a hysteretic behavior is specific of granular flow and its prediction provides indications of consistence of the modeling approach. The improved model also captures the scaling of the velocity profiles down the bed depth.

Effective boundary conditions for dense granular flows.

We derive an effective boundary condition for dense granular flow taking into account the effect of the heterogeneity of the force network on sliding friction dynamics. This yields an intermediate boundary condition which lies in the limit between no slip and Coulomb friction; two simple functions relating wall stress, velocity, and velocity variance are found from numerical simulations. Moreover, we show that this effective boundary condition corresponds to Navier slip condition when the model of G. D. R. Midi [Eur. Phys. J. E 14, 341 (2004)] is assumed to be valid, and that the slip length depends on the length scale that characterizes the system, viz. the particle diameter.