Bidisperse Granular Flows Research Articles

Scale‐Dependent Processes and Runout in Bidisperse Granular Flows: Insights From Laboratory Experiments and Implications for Rock/Debris Avalanches

AbstractThe bidispersity observed in the particle‐size distribution of rock avalanches and volcanic debris avalanches (rock/debris avalanches) has been proposed as a factor contributing to their long runout. This has been supported by small‐scale analog experimental studies, which observe that a small proportion of fine particles mixed with coarser particles enhances granular avalanche runout. However, the mechanisms enabling this phenomenon and their resemblance to rock/debris avalanches have not been directly evaluated. Here, binary mixture granular avalanche experiments are employed to constrain the processes and conditions under which bidispersity enhances the runout of granular avalanches in experiments. Structure‐from‐motion photogrammetry is used to measure center of mass displacement and assess energy dissipation. Subsequently, this study evaluates the dynamic scaling and flow regimes in the lab and field to assess whether the runout‐enhancing mechanism is applicable to rock/debris avalanches. In small‐scale experiments, the granular mass propagates under a collisional regime, enabling kinetic sieving and size segregation. Fine particles migrate to the base where they reduce frictional areas between coarse particles and the substrate and encourage rolling. The reduced energy dissipation increases the kinetic energy conversion and avalanche mobility. However, rock/debris avalanches are unlikely to acquire a purely collisional regime; instead, they propagate under a frictional regime. The size segregation which is essential for the process observed at the lab‐scale is prohibited by the frictional regime, as evident by the sedimentology of rock/debris avalanche deposits. The proposal of bidispersity as a runout‐enhancing mechanism overlooks that scale‐dependent behaviors of natural events are often omitted in small‐scale experiments.

Segregation–rheology feedback in bidisperse granular flows: a coupled Stokes’ problem

The feedback between particle-size segregation and rheology in bidisperse granular flows is studied using the Stokes’ problem configuration. A method of lines scheme is implemented to solve the coupled momentum and segregation equations for a normally graded particle size distributed bulk at constant solids volume fraction. The velocity profiles develop quickly into a transient state, decoupled from segregation yet determined by the particle size. From this transient state, the velocity profile changes due to the particles’ relative movement, which redistributes the frictional response, hence its rheology. Additionally, the particles’ relative friction is modified via a frictional coefficient ratio, by analogy with the particles’ size ratio. While positive values of this coefficient exacerbate the nonlinearity of the velocity profiles induced by size differences, negative values dampen this behaviour. The numerical solutions reproduce well the analytical solutions for the velocity profile, which can be obtained from the steady-state conditions of the momentum and segregation equations for the transient and steady states, respectively. Segregation–momentum balances and four characteristic time scales can be established to propose two non-dimensional quantities, including specific Schmidt and Péclet numbers that describe broadly the segregation–rheology feedback. The proposed scheme, theoretical solutions and non-dimensional numbers offer a combined approach to understand segregation and flow dynamics within a granular bulk, extensible across many flow configurations.

Insights on the internal dynamics of bi-disperse granular flows from machine learning

In granular flows, grains exhibit heterogeneous dynamics featuring large distributions of forces and velocities. Conventional statistical methods have previously revealed how these dynamical properties scale with the grain size in monodisperse flows. We explore here whether they differ between small and large grains in bi-disperse flows. In simulated silo flows comprised of dense and collisional zones, we use a machine learning classifier to attempt to distinguish small from large grains based on features such as velocity, acceleration and force. Results show that a classification based on grain velocity is not possible, which suggests that large and small grains feature statistically similar velocities. In the dense zones, classification based on force only fails too, indicating that small and large grains are subjected to similar forces. However, classification based on force and acceleration succeeds. This indicates that the classifier is sensitive to the correlation between forces and acceleration, i.e. Newton’s second law, and can thus detect differences in grain size via their mass. These results highlight the potential for machine learning to assist with better understanding the behaviour of granular flows and similar disordered fluids.

Effect of base roughness on flow behaviour and size segregation in dry granular flows

Three bases with increasing roughness were designed by adjusting the geometric relationships of particles bonded to the base, to study the roughness effect on flow behaviour and size segregation in bidisperse granular chute flows. In light of limited research on accurate tracking of different particles in bidisperse granular flows, particle tracking velocimetry, which allows tracking of large and small particles down to the pixel level, was used to measure the velocity and displacement of large and small particles separately. Experimental results show that when the critical inclination θc increases from 31·9° to 36·1°, the mixing point of the large and small particles decreases from 67 to 39 cm. Moreover, the overall flow is suppressed in the stream-wise direction and promoted in the depth-wise direction as the base roughness increases.

3D structure of free-surface avalanche deposits from MRI: particle-size segregation in free-surface, bi-disperse granular flows

3D structure of free-surface avalanche deposits from MRI: particle-size segregation in free-surface, bi-disperse granular flows

Numerical and analytical analyses of the impact of monodisperse and bidisperse granular flows on a baffle structure

Numerical and analytical analyses of the impact of monodisperse and bidisperse granular flows on a baffle structure

Charge transport equation for bidisperse collisional granular flows with non-equipartitioned fluctuating kinetic energy

Starting from the Boltzmann–Enskog kinetic equations, the charge transport equation for bidisperse granular flows with contact electrification is derived with separate mean velocities, total kinetic energies, charges and charge variances for each solid phase. To close locally averaged transport equations, a Maxwellian distribution is presumed for both particle velocity and charge. The hydrodynamic equations for bidisperse solid mixtures are first revisited and the resulting model consisting of the transport equations of mass, momentum, total kinetic energy, which is the sum of the granular temperature and the trace of fluctuating kinetic tensor, and charge is then presented. The charge transfer between phases and the charge build-up within a phase are modelled with local charge and effective work function differences between phases and the local electric field. The revisited hydrodynamic equations and the derived charge transport equation with constitutive relations are assessed through hard-sphere simulations of three-dimensional spatially homogeneous, quasi-one-dimensional spatially inhomogeneous bidisperse granular gases and a three-dimensional segregating bidisperse granular flow with conducting walls.

Bridging the gap between particle-scale forces and continuum modelling of size segregation: application to bedload transport

Abstract

Breaking size-segregation waves and mobility feedback in dense granular avalanches

Through experiments and discrete particle method (DPM) simulations we present evidence for the existence of a recirculating structure, that exists near the front of dense granular avalanches, and is known as a breaking size-segregation (BSS) wave. This is achieved through the study of three-dimensional bidisperse granular flows in a moving-bed channel. Particle-size segregation gives rise to the formation of a large-particle-rich front and a small-particle-rich tail with a BSS wave positioned between the tail and front. We experimentally resolve the structure of the BSS wave using refractive-index matched scanning and find that it is qualitatively similar to the structure observed in DPM simulations. Our analysis demonstrates a relation between the concentration of small particles in the flow and the amount of basal slip, in which the structure of the BSS wave plays a key role. This leads to a feedback between the mean bulk flow velocity and the process of particle-size segregation. Ultimately, these findings shed new light on the recirculation of large and small grains near avalanche fronts and the effects of this behaviour on the mobility of the bulk flow.

Effect of pressure on segregation in granular shear flows.

The effect of confining pressure (overburden) on segregation of granular material is studied in discrete element method (DEM) simulations of horizontal planar shear flow. To mitigate changes to the shear rate due to the changing overburden, a linear with depth variation in the streamwise velocity component is imposed using a simple feedback scheme. Under these conditions, both the rate of segregation and the ultimate degree of segregation in size bidisperse and density bidisperse granular flows decrease with increasing overburden pressure and scale with the overburden pressure normalized by the lithostatic pressure of the particle bed. At overburdens greater than approximately 20 times the lithostatic pressure at the bottom of the bed, the density segregation rate is zero while the size segregation rate is small but nonzero, suggesting that different physical mechanisms drive the two types of segregation. The segregation rate scales close to linearly with the inertial number for both size bidisperse and density bidisperse mixtures under various flow conditions, leading to a proposed pressure dependence term for existing segregation velocity correlations. Surprisingly, particle stiffness has only a minor effect on segregation, although it significantly affects the packing density.

Axial segregation in spherical and cylindrical rotating tumblers

Monodisperse and bidisperse granular flows are studied in rotating tumblers using DEM. In spherical tumblers, flowing particles’ trajectories do not follow straight lines but are curved. At the same time particles near the surface drift toward the pole, inducing two global recirculation cells. Combined with radial segregation, drift and curvature compete to impose the axial segregation pattern: Small-Large-Small (SLS) or Large-Small-Large (LSL). Fill level, rotation speed and wall roughness influence drift and curvature, and modify the resulting segregation pattern. In cylindrical tumblers, equivalent recirculation cells occur next to the end walls. A second pair of recirculation cells with a weak drift in the opposite direction appears at the center for long enough tumblers. Unlike the sphere case, curvature and drift in the primary cells combine to push large particles toward the end walls, explaining why large particle bands appear at the end walls for axial segregation in cylinder.

Comparing and contrasting size-based particle segregation models

Over the last 12 years, numerous new theoretical continuum models have been formulated to predict particle segregation in the size-based bidisperse granular flows over inclined channels. Despite their presence, to our knowledge, no attempts have been made to compare and contrast the fundamental basis upon which these continuum models have been formulated. In this paper, firstly, we aim to illustrate the difference in these models including the incompatible nomenclature which impedes direct comparison. Secondly, we utilise (i) our robust and efficient in-house particle solver MercuryDPM, and (ii) our accurate micro–macro (discrete to continuum) mapping tool called coarse-graining, to compare several proposed models. Through our investigation involving size-bidisperse mixtures, we find that (i) the proposed total partial stress fraction expressions do not match the results obtained from our simulation, and (ii) the kinetic partial stress fraction dominates over the total partial stress fraction and the contact partial stress fraction. However, the proposed theoretical total stress fraction expressions do capture the kinetic partial stress fraction profile, obtained from simulations, very well, thus possibly highlighting the reason why mixture theory segregation models work for inclined channel flows. However, further investigation is required to strengthen the basis upon which the existing mixture theory segregation models are built upon.

Segregation time-scale in bi-disperse granular flows

Using a discrete simulation method, we investigate numerically two-dimensional bi-disperse chute flows formed of a layer of larger grains overlaid by a layer of smaller grains, and analyze their evolution for different slopes and different volume fraction of large beads. As size segregation occurs, the vertical position of the centre of mass of the large beads is shown to increase exponentially with time with a typical time scale decreasing with their volume fraction. A simple model balancing lift and drag forces acting on large particles recovers this dynamics, successfully predicts the typical time scale of segregation, and permits to relate this typical time scale to the flow dynamics.

Kinematics of monodisperse and bidisperse granular flows in quasi-two-dimensional bounded heaps

Quasi-two-dimensional bounded heap flow is a useful model for many granular flows in industry and nature. It belongs to a family of free surface flows—inclined chute flow, rotating tumbler flow and unbounded heap flow—but differs from the others in that uniform deposition of particles onto the static bed results in the uniform rise of the heap. The kinematics, however, are only partially understood. We performed discrete element method simulations to study granular flows in quasi-two-dimensional bounded heaps. The experimentally validated computational results show a universal functional form for the streamwise velocity profile for both monodisperse and bidisperse systems when velocities and coordinates are scaled by the local surface velocity and the local flowing layer thickness. This holds true regardless of streamwise location, feed rate, particle size distribution and, most surprisingly, the local particle concentration for bidisperse flows. The local surface velocity decreases linearly in the streamwise direction, while the flowing layer thickness remains nearly constant; both quantities depending only on local flow rate and local mean particle diameter. Additionally, the velocity profile normal to the overall flow, which is important in understanding segregation, can be predicted analytically from the streamwise velocity and matches the simulation results.