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.
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.
In this work, we discuss experiments and discrete element simulations of wall-bounded shear flows of slightly polydisperse spheres under gravity. Experiments were performed in an annular shear cell in which the bottom bumpy wall rotates at fixed velocity, while a pressure is applied at the top bumpy wall. The coaxial cylinders delimiting the flow are flat, frictional and transparent, allowing visualization of the flow. Velocity profiles were obtained by particle image velocimetry, and are characterized by an exponential profile, the decay length of which depends on the applied load, but not on the wall velocity. A force sensor was installed at different vertical positions on the outer sidewall in order to measure wall forces. The effective streamwise and transverse wall friction coefficients were thus estimated, showing wall friction weakening in creep zones. In order to better understand these results, contact dynamics simulations were carried out in a simplified configuration (Artoni & Richard, Phys. Rev. Lett., vol. 115 (15), 2015, 158001). In this case, profiting from the possibility of varying the particle–wall friction coefficient, different flow regimes were observed. In particular, shear can either be localized (1) at the bottom or (2) at the top of the shear cell, or (3) it can be quite evenly distributed in the vertical direction. Through an averaging technique that explicitly takes into account gradient effects (Artoni & Richard, Phys. Rev. E, vol. 91 (3), 2015, 032202), relevant, coarse-grained, continuum fields (solid fraction, velocity, stresses, velocity fluctuations) were obtained. They allow a discussion of the relevance of velocity fluctuations (i.e. granular temperature) for describing non-locality in granular flow. The case of solid-like fluctuations is also addressed. Finally, a simplified stress analysis is devoted to explain the emergence of complex shear localization patterns by the heterogeneity of effective bulk friction, which is due to the joint effect of gravity and wall friction.
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, 3412004 is assumed to be valid, and that the slip length depends on the length scale that characterizes the system, viz. the particle diameter
In this Letter, the 2-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.PACS numbers: 47.57. Gc, 83.80.Fg Despite the large number of studies devoted to understanding the rheology of dense granular flows, the boundary behavior -i.e. the interaction of an ensemble of flowing particles with a wall -is still poorly understood. The issue is relevant for nearly all the situations in which granular materials are processed (silo or chute flows, sampling, die filling and compression) or are observed in nature (avalanches, landslides). A complete understanding of the boundary behavior requires us to study the relationships among the amount of wall slip, stresses and deformation rates in the material, possibly arriving at a quantitative average characterization to be used for characterization and for continuum modeling. This was extensively done with respect to rapid, dilute granular flows [1][2][3], but the results from those analyses cannot be applied to dense, slow flows of granular materials since the phenomenology is largely different. Longlasting contacts, dynamics of force chain networks, and dissipation mainly due to friction are the most significant distinctions between dense and collisional flow regimes. From the practical point of view, in the dense flow of granular materials in silos and hoppers, wall friction is usually described by means of the effective wall friction coefficient µ w = σT σN , which is a bulk, not a particle property, where σ T is the shear stress and σ N is the normal stress in the direction perpendicular to the wall. Such a coefficient, often presented as the angle of wall friction (defined as tan −1 µ w ), is not necessarily a constant property of the couple of particle and wall materials [4,5]. In presence of shear, in a recent work we argued [5] that shear-induced fluctuations of the force network could determine a dependence of the effective wall friction coefficient on flow properties, such as slip velocity, shear rate and stresses. The main point of the theory is that the stronger the phenomenon of force chains breaking and forming in the material, the larger will be the deviation from the condition of steady sliding for the particles at a boundary, implying generally that µ w < µ pw , where µ pw is the particle-wall friction coefficient, and suggesting...
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