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The influence of hopper width on dense granular flow in a two$-$dimensional hopper is investigated through experiments and simulations. Though the flow rate remains stable for larger hopper widths, a slight reduction in hopper width results in a significant increase in flow rate for smaller hopper widths. Both Beverloo\('\)s and Janda\('\)s formula accurately capture the relationship between the flow rate and outlet size. Flow characteristics in the regions near the outlet exhibit local self$-$similarity, supporting Beverloo and Janda's principles. Moreover, global self$-$similarity is analysed, indicated by the transition in flow state from mass flow in regions far from the outlet to funnel flow near the outlet. The earlier occurrence of this transition favors to enhance the grain velocity and consequently increases the dense flow rate. An exponential scaling law is proposed to describe the dependencies of flow rate, grain velocity, and transition height between the mass flow pattern and the funnel flow pattern on silo width., Comment: 17 papges, 9 figures

This study numerically investigates the nonlinear interaction of head-on solitary waves in a granular chain (a nonintegrable system) and compares the simulation results with the theoretical results in fluid (an integrable system). Three stages (i.e., pre-in-phase traveling stage, central-collision stage, and post-in-phase traveling stage) are identified to describe the nonlinear interaction processes in the granular chain. The nonlinear scattering effect occurs in the central-collision stage, which decreases the amplitude of incident solitary waves. Compared with the leading-time phase in the incident and separation collision processes, the lagging-time phase in the separation collision process is smaller. This asymmetrical nonlinear collision results in an occurrence of leading phase shifts of time and space in the post-in-phase traveling stage. We next find that solitary wave amplitude does not influence the immediate space-phase shift in the granular chain. The space$-$phase shift of the post-in-phase traveling stage is only determined by measurement position rather than wave amplitude. The results are reversed in the fluid. An increase in solitary wave amplitude leads to decreased attachment, detachment and residence times for granular chain and fluid. For the immediate time-phase shift, leading and lagging phenomena appear in the granular chain and the fluid, respectively. These results offer new knowledge for designing mechanical metamaterials and energy-mitigating systems.

This paper presents the experiments and simulations on the resonance-induced acceleration of the reverse Brazil nut effect (RBNE)-Brazil nut effect (BNE) segregation inversion of binary mixtures in flat-bottom and circular-bottom containers. Both experimental and simulation results indicate that the starting location of the sinkage of heavier grains at the top layer is triggered with certain randomness in the flat-bottom container, whereas it first occurs at either of the lateral edges of the bottom in the circular-bottom container. The quantified segregation factors in simulations show that the transition from the RBNE segregation state to the BNE segregation state happens faster in the circular-bottom container than that in the flat-bottom container. The occurrence of standing-wave resonant spots of higher and lower granular temperature accelerates the RBNE-BNE segregation inversion. From the elastic collision model of single grain, the bottom with a larger angle leads to more energy transfer from the vertical direction to the horizontal direction. The theoretical predictions are confirmed by the simulations of a monodisperse granular bed. The flat-bottom container has a uniform distribution with a standing-wave period of granular temperature and packing density, whereas the circular-bottom container possesses a higher granular temperature in the horizontal direction and a lower packing density at the lateral edges of the circular bottom. Owing to the buoyancy effect, heavier grains easily sink first at the resonant spots with higher temperature., Comment: 12 pages, 10 figures

This study presents numerical simulations of the resonance of a finite-length granular chain of dissipative grains driven by a harmonically vibrated tube. Multiple gradual resonant modes, namely, non-resonance mode, partial-resonance mode, and complete-resonance mode, are identified. With a fixed vibration frequency, increased vibration acceleration leads to a one-by-one increase in the number of grains participating in resonance, which is equal to the number of grain-wall collisions in a vibration period. Compared with the characteristic time of the grain-grain and the grain-wall collisions, the time of free flight plays a dominant role in grain motion. This condition results in the occurrence of large opening gaps between the grains and independent grain-grain and gain-wall collisions. A general master equation that describes the dependence of the system energy on the length of the granular chain and the number of grain-wall collisions is established, and it is in good agreement with the simulation results. We observe a gradual step-jump increase in system energy when the vibration acceleration is continuously increased, which is dedicated to an individual energy injection. Moreover, two typical phase diagrams are discussed in the spaces of $\phi-\it{\Gamma}$ and $N-\it\Gamma$., Comment: 19 pages, 7 figures

Discrete element method is conducted to investigate the bidisperse dense granular flow having big and small grains in a two dimensional hopper. A half-circular dynamical force arch is observed above the outlet and Beverloo's law is verified to describe the relationship between flow rate and outlet size. The bidisperse flow can reach the maximum flow rate when a small fraction of big grains is added into the monodisperse flow with only small grains. The distributions of contact force, packing fraction and grain velocity indicate that the flow properties in the hopper are closely related to the local flow characteristics of the key area which almost overlaps with the force arch. The interior packing structures, i.e., ordered arrangement for monodisperse flow and disordered arrangement for bidisperse flow, play a dominant role in the flow pattern transition from mass flow to funnel flow. The earlier occurrence of the transition can effectively increase the grain velocity and therefore improve the flow rate., Comment: 17 pages, 9 figures

The rectification effect on the propagation of solitary waves in the symmetric Y-shaped granular chain is numerically investigated in this Letter. A heterojunction with mass mismatch occurs at the position of Y-junction by adjusting the branch angle. And the heavy-light heterojunction is more favorable for the solitary wave passing. The energy rectification efficiency can be improved by adjusting the branch angle and the direction of incident solitary wave. The results have particularly practical significance for the potential design of acoustic diode devices., Comment: 5 pages, 6 figures

We present molecular dynamics simulations on the segregation of binary mixtures in a high-velocity rotating drum. Depending on the ratio of particle's radius and density, the ring-like spin segregation patterns in radial direction show similarities to the Brazil-nut effect and its reverse form. The smaller and heavier particles are easier to accumulate towards the drum wall and the bigger and lighter ones towards the drum center. Furthermore, we quantify the effects of particle's radius and density on the segregation states and plot the phase diagram of segregation in the ${\rho_b}/{\rho_s}$ - ${r_b}/{r_s}$ space. The observed phenomena can also be well explained by the combined actions, i.e., the percolation effect and the buoyancy effect., Comment: 6 figures