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

Rheology of nonconvex granular flows based on particle rotational characteristics

Particle shape has a profound impact on the flow behaviors of granular materials, yet effectively incorporating the role of particle shape into granular rheology remains challenging. In this study, we employ three representative types of nonconvex particles generated through the multisphere approach and identify a consistent one-to-one relationship between the rescaled friction coefficient and the inertial number I across both inertial and quasistatic flow regimes. However, variations in particle shape cause notable deviations in rheological data compared to their spherical counterparts. Based on the observed dependence of rheological data on I for various nonconvex particles and their convergence at high I, we propose an inertial number I_{s} to effectively capture the impact of particle shape on flow states. The model parameters defining I_{s} are shown to be nearly independent of flow states and configurations, with physical interpretations related to particle rotational characteristics during shear. For practical application, we propose an empirical formula to capture the dependence of model parameters on particle geometrical shapes. The robustness of the proposed model is validated by predicting flow in an inclined flow configuration and applying it to additional nonconvex particles with more irregular and asymmetric features. This establishes a crucial foundation for extending the application of this generalized rheological model to other complex granular flows.

Controlling rheology via boundary conditions in dense granular flows

Boundary shape, particularly roughness, strongly controls the amount of wall slip in dense granular flows. In this paper, we aim to quantify and understand which aspects of a dense granular flow are controlled by the boundary conditions, and to incorporate these observations into a cooperative nonlocal model characterizing slow granular flows. To examine the influence of boundary properties, we perform experiments on a quasi-2D annular shear cell with a rotating inner wall and a fixed outer wall; the latter is selected among 6 walls with various roughnesses, local concavity, and compliance. We find that we can successfully capture the full flow profile using a single set of empirically determined model parameters, with only the wall slip velocity set by direct observation. Through the use of photoelastic particles, we observe how the internal stresses fluctuate more for rougher boundaries, corresponding to a lower wall slip, and connect this observation to the propagation of nonlocal effects originating from the wall. Our measurements indicate a universal relationship between dimensionless fluidity and velocity.

Interplay between hysteresis and nonlocality during onset and arrest of flow in granular materials

The jamming transition in granular materials is well-known for exhibiting hysteresis, wherein the level of shear stress required to trigger flow is larger than that below which flow stops. Although such behavior is typically modeled as a simple non-monotonic flow rule, the rheology of granular materials is also nonlocal due to cooperativity at the grain scale, leading for instance to increased strengthening of the flow threshold as system size is reduced. We investigate how these two effects - hysteresis and nonlocality - couple with each other by incorporating non-monotonicity of the flow rule into the nonlocal granular fluidity (NGF) model, a nonlocal constitutive model for granular flows. By artificially tuning the strength of nonlocal diffusion, we demonstrate that both ingredients are key to explaining certain features of the hysteretic transition between flow and arrest. Finally, we assess the ability of the NGF model to quantitatively predict material behavior both around the transition and in the flowing regime, through stress-driven discrete element method (DEM) simulations of flow onset and arrest in various geometries. Along the way, we develop a new methodology to compare deterministic model predictions with the stochastic behavior exhibited by the DEM simulations around the jamming transition.

Sidewall friction in confined surface flows of granular materials

We report numerical simulations of surface granular flows confined between two sidewalls. These systems exhibit both very slow and very energetic flows. Zhu et al. [1] have shown that in energetic confined systems, the Froude number at sidewalls and the sidewall effective friction coefficient are linked through a unique relation. We show that this relation is also valid for creep flows. It is independent of the angle of the flow but depends on the sidewall-grain friction coefficient. Our results shed light on boundary conditions that have to be used at sidewalls in continuum theories aiming to capture the behavior of granular systems from creeping to energetic flows.

Influence of granular temperature and grain rotation on the wall friction coefficient in confined shear granular flows

A depth-weakening wall friction coefficient, µw, has been reported from three-dimensional numerical simulations of steady and transient dense granular flows. To understand the degradation mechanisms, a scaling law for µw/ f and χ has been proposed where f is the intrinsic particle-wall friction and χ is the ratio of slip velocity to square root of granular temperature (Artoni & Richard, Phys. Rev. Lett., vol. 115 (15), 2015, 158001). Independently, a friction degradation model has been derived which describes a monotonically diminishing friction depends on a ratio of grain angular and slip velocities, Ω (Yang & Huang, Granular Matter, vol. 18 (4), 2016, 77). In search of experimental evidence for how these two parameters degrade the µw, an annular shear cell experiment was performed to estimate the bulk granular temperature, angular and slip velocities at sidewall through image-processing. Meanwhile, µw was measured by a force sensor to confirm the weakening towards the creep zone. The measured µw/ f − χ and µw/ f − Ω were both well-fitted to the corresponding models showing that both granular temperature and angular velocity are significant mechanisms to degrade the µw which broadens the research perspective on modeling the boundary condition of dense granular flows.

Analytical nonlocal model for shear localization in wall-bounded dense granular flow

This work employs a Landau-Ginzburg-type nonlocal rheology model to account for shear localization in a wall-bounded dense granular flow. The configuration is a 3D shear cell in which the bottom bumpy wall moves at a constant speed, while a load pressure is applied at the top bumpy wall, with flat but frictional lateral walls. At a fixed pressure, shear zones transit from the top to the bottom when increasing lateral wall friction coefficient. With a quasi-2D model simplification, asymptotic solutions for fluidization order parameters near the top and bottom boundaries are sought separately. Both solutions are the Airy function in terms of a depth coordinate scaled by a characteristic length which measures the width of the corresponding shear zone. The theoretical predictions for the shear zone widths against lateral wall friction coefficient and load pressure agree well with data extracted from particle-based simulation for the flow.

Force fluctuations at the transition from quasi-static to inertial granular flow

We analyse the rheology of gravity-driven, dry granular flows in experiments where individual forces within the flow bulk are measured. We release photoelastic discs at the top of an incline to create a quasi-static erodible bed over which flows a steady 2D avalanche. The flowing layers we produce are dense (φ ≈ 0.8), thin (h ≈ 10d), and in the slow to intermediate flow regime (I = 0.1 to 1). Using particle tracking and photoelastic force measurements we report coarse-grained profiles for packing fraction, velocity, shear rate, inertial number, and stress tensor components. In addition, we define a quantitative measure for the rate of generation of new force chain networks and we observe that fluctuations extend below the boundary between dense flow and quasi-static layers. Finally, we evaluate several existing definitions for granular fluidity, and make comparisons among them and the behaviour of our experimentally-measured stress tensor components. Our measurements of the non-dimensional stress ratio μ show that our experiments lie within the local rheological regime, yet we observe rearrangements of the force network extending into the quasi-static layer where shear rates vanish. This elucidates why non-local rheological models rely on the notion of stress diffusion, and we thus propose non-local effects may in fact be dependent on the local force network fluctuation rate.

On the influence of rotational motion on MRI velocimetry of granular flows - Theoretical predictions and comparison to experimental data

Continuum dynamics of granular materials are known to be influenced by rotational, as well as translational, motion. Few experimental techniques exist that are sensitive to rotational motion. Here we demonstrate that MRI is sensitive to the rotation of granules and that we can quantify its effect on the MRI signal. In order to demonstrate the importance of rotational motion, we perform discrete element method (DEM) simulations of spherical particles inside a Couette shear cell. The variance of the velocity distribution was determined from DEM data using two approaches. (1) Direct averaging of the individual particle velocities. (2) Numerical simulation of the pulsed field gradient (PFG) MRI signal acquisition based on the DEM data. Rotational motion is found to be a significant effect, typically contributing up to 50% of the signal attenuation, thus amplifying the calculated velocity variance. A theoretical model was derived to relate an MRI signal to the angular velocity distribution. This model for the signal was compared to previously published experimental data as well as simulated MRI results and found to be consistent.

Erodible, granular beds are fragile

Geophysical flows that involve the transport of grains and the shearing of colloids and non-Brownian suspensions often take place above a substrate composed of the same particles that can be incorporated into the flow. Despite the importance of understanding such erodible beds to the phrasing of appropriate boundary conditions for the solution of continuum models, a rigorous definition of the erodible bed and the constitutive relations for the stresses within it are still lacking. Here, we use discrete-element simulations to show that the intense, intermittent forming and breaking of contact chains marks the transition to the erodible bed at a critical solid volume fraction, as in shear jamming of steady, homogeneous flows. However, the compressible, collisional flow that confines the bed is not strong enough to insure the stability of the contact network, resulting in a bulk stiffness that is three orders of magnitude less than in shear jamming.

Inclined granular flow in a narrow chute

In this paper we presents a detailed description of granular flow down a flat, narrow chute using discrete element method simulations, with emphasis on the influence of sidewalls on the flow. The overall phase diagram is provided and it is found that there are four flow regimes (no flow, bulk flow, surface flow, and gas flow). The H̃_stop curve is very complicated and quite different from that in the case without sidewalls. The effective friction coefficient [Formula: see text] increases with pile height H̃ and a surface flow occurs when the inclination angle [Formula: see text] exceeds a critical value. The profile of [Formula: see text] shows that the [Formula: see text] rheology is valid in boundary layers. Furthermore, [Formula: see text] increases with the velocity of particles and there is a saturation to a nonzero value in static heap. For small H̃, the static heap vanishes and there is a bulk flow. A similarity between basal particles and sidewall particles indicates a universal role of the boundaries. In this bulk flow, there is a transition of the velocity profile with wall friction [Formula: see text]. When [Formula: see text] is large, the velocity is linear and decreases with increasing height. With small [Formula: see text], the velocity is nonlinear and the flow rate is roughly proportional to H̃^3/2.

Rheology of dense granular flows for elongated particles

We study the rheology of dense granular flows for frictionless spherocylinders by means of 3D numerical simulations. As in the case of spherical particles, the effective friction μ is an increasing function of the inertial number I, and we systematically investigate the dependence of μ on the particle aspect ratio Q, as well as that of the normal stress differences, the volume fraction, and the coordination number. We show in particular that the quasistatic friction coefficient is nonmonotonic with Q: from the spherical case Q=1, it first sharply increases, reaches a maximum around Q≃1.05, and then gently decreases until Q=3, passing its initial value at Q≃2. We provide a microscopic interpretation for this unexpected behavior through the analysis of the distribution of dissipative contacts around the particles: as compared to spheres, slightly elongated grains enhance contacts in their central cylindrical band, whereas at larger aspect ratios particles tend to align and dissipate by preferential contacts at their hemispherical caps.

Microscopic Description of the Granular Fluidity Field in Nonlocal Flow Modeling

A recent granular rheology based on an implicit "granular fluidity" field has been shown to quantitatively predict many nonlocal phenomena. However, the physical nature of the field has not been identified. Here, the granular fluidity is found to be a kinematic variable given by the velocity fluctuation and packing fraction. This is verified with many discrete element simulations, which show that the operational fluidity definition, solutions of the fluidity model, and the proposed microscopic formula all agree. Kinetic theoretical and Eyring-like explanations shed insight into the obtained form.

Characterization of base roughness for granular chute flows

Base roughness plays an important role in the dynamics of granular flows but is still poorly understood due to the difficulty of its quantification. For a bumpy base made of spheres, at least two factors should be considered in order to characterize its geometric roughness, namely, the size ratio of flow to base particles and the packing arrangement of base particles. In this paper, we propose an alternative definition of base roughness, R_{a}, as a function of both the size ratio and the distribution of base particles. This definition is generalized for random and regular packings of multilayered spheres. The range of possible values of R_{a} is presented, and optimal arrangements for maximizing base roughness are studied. Our definition is applied to granular chute flows in both two- and three-dimensional configurations, and is shown to successfully predict whether slip occurs at the base. A transition is observed from slip to nonslip conditions as R_{a} increases. Critical values of R_{a} are identified for the construction of a nonslip base at various angles of inclination.

Clusters of polyhedra in spherical confinement

Dense particle packing in a confining volume remains a rich, largely unexplored problem, despite applications in blood clotting, plasmonics, industrial packaging and transport, colloidal molecule design, and information storage. Here, we report densest found clusters of the Platonic solids in spherical confinement, for up to [Formula: see text] constituent polyhedral particles. We examine the interplay between anisotropic particle shape and isotropic 3D confinement. Densest clusters exhibit a wide variety of symmetry point groups and form in up to three layers at higher N. For many N values, icosahedra and dodecahedra form clusters that resemble sphere clusters. These common structures are layers of optimal spherical codes in most cases, a surprising fact given the significant faceting of the icosahedron and dodecahedron. We also investigate cluster density as a function of N for each particle shape. We find that, in contrast to what happens in bulk, polyhedra often pack less densely than spheres. We also find especially dense clusters at so-called magic numbers of constituent particles. Our results showcase the structural diversity and experimental utility of families of solutions to the packing in confinement problem.