Granular avalanches in a two-dimensional rotating drum with imposed vertical vibration

Laboratory experiment and discrete-element-method simulation of granular-heap flows under vertical vibration

Granular flow dynamics on a vertically vibrated pile is studied by means of both laboratory experiments and numerical simulations. As already revealed, the depth-averaged velocity of a fully fluidized granular pile under strong vibration, which is measured by a high-speed laser profiler in the experiment, can be explained by the nonlinear diffusion transport model proposed by our previous paper [Tsuji et al., Phys. Rev. Lett. 120, 128001 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.128001]. In this paper, we report that a similar transport model can be applied to the relation between the surface velocity and slope in the experiment. These facts are also reproduced by particle-scale numerical simulations based on the discrete element method. In addition, using these numerical results, the velocity profile inside the fluidized pile is measured. As a result, we show that the flow velocity decreases exponentially with depth from the surface of the pile, which means that a clearly fluidized region, also known as shear band structure, is localized around the surface. However, its thickness grows proportionally with the local height of the pile, i.e., the shear band does not consist of a fluidized layer with a constant thickness. From these features, we finally demonstrate that the integration of this exponentially decreasing velocity profile is consistent with the depth-averaged velocity predicted by the nonlinear diffusion transport model.

Planar granular shear flow under external vibration

We present results from a planar shear experiment in which a two-dimensional horizontal granular assembly of pentagonal particles sheared between two parallel walls is subjected to external vibration. Particle tracking and photoelastic measurements are used to quantify both grain scale motion and interparticle stresses with and without imposed vibrations. We characterize the particle motion in planar shear and find that flow of these strongly interlocking particles consists of transient vortex motion with a mean flow given by the sum of exponential profiles imposed by the shearing walls. Vibration is applied either through the shearing surface or as bulk vertical vibration of the entire shearing region with dimensionless accelerations Γ=A(2πf)^{2}/g≈0-2. In both cases, increasing amplitude of vibration A at fixed frequency f leads to failure of the force network, reduction in mean stress, and a corresponding reduction in imposed strain. Vibration of the shearing surface is shown to induce the preferential slipping of large-angle force chains. These effects are insensitive to changes in frequency in the range studied (f=30-120 Hz), as sufficiently large displacements are required to relieve the geometrical frustration of the jammed states.

Fluctuations of particle motion in granular avalanches - from the microscopic to the macroscopic scales

In this study, we have investigated the fluctuations of particle motion, i.e. the non-affine motion, during the avalanche process, discovering a rich dynamic from the microscopic to the macroscopic scales. We find that there is a strong correlation between the magnitude of the velocity fluctuation and the velocity magnitude in the spatial and temporal domains. The possible connection between this finding and the theory of the shear transformation zones is discussed based on the direct measurement of the T1 events. In addition, the velocity magnitude of the system and the stress fluctuations of the system are strongly temporally correlated. Our finding will pose challenges to the development of more rigorous theories to describe avalanche dynamics based on the microscopic approach. Moreover, our finding presents a plausible mechanism of particle entrainment in a simple system.

Spatiotemporal chaotic unjamming and jamming in granular avalanches

We have investigated the spatiotemporal chaotic dynamics of unjamming and jamming of particles in a model experiment – a rotating drum partially filled with bidisperse disks to create avalanches. The magnitudes of the first Lyapunov vector δu(t) and velocity v(t) of particles are directly measured for the first time to yield insights into their spatial correlation C_δu,v, which is on statistical average slightly larger near the unjamming than the value near the jamming transition. These results are consistent with the recent work of Banigan et al (Nature Phys. 2013), and it is for the first time to validate their theoretical models in a real scenario. v(t) shows rich dynamics: it grows exponentially for unstable particles and keeps increasing despite stochastic interactions; after the maximum, it decays with large fluctuations. Hence the spatiotemporal chaotic dynamics of avalanche particles are entangled, causing temporal correlations of macroscopic quantities of the system. We propose a simple model for these observations.