Scaling behavior in the convection-driven Brazil nut effect

Decompaction wave propagation in a vibrated fine-powder bed

We experimentally study the crack formation and decompaction-wave propagating in a vibrated powder bed consisting of glass beads of 5 μm in diameter. The vibrated powder bed exhibits three distinct phases depending on the vibration conditions: consolidation (CS), static fracture (SF), and dynamic fracture (DF). Particularly, we found an upward wave propagation in the DF regime when the powder bed is strongly vibrated. As a remarkable feature, we found that in fine cohesive powders, the decompaction-wave propagation speed normalized to gravitational speed is independent of the shaking strength. This result implies that the wave propagation speed is governed by the balance between gravity and cohesion effect rather than vibration strength. We also explore the universality of wave propagation phenomenon in coarser and low-density granular powders.

Characterization of the Clogging Transition in Vibrated Granular Media

The existence of a transition from a clogged to an unclogged state has been recently proposed for the flow of macroscopic particles through bottlenecks in systems as diverse as colloidal suspensions, granular matter, or live beings. Here, we experimentally demonstrate that, for vibrated granular media, such a transition genuinely exists, and we characterize it as a function of the outlet size and vibration intensity. We confirm the suitability of the "flowing parameter" as the order parameter, and we find out that the rescaled maximum acceleration of the system should be replaced as the control parameter by a dimensionless velocity that can be seen as the square root of the ratio between kinetic and potential energy. In all the investigated scenarios, we observe that, for a critical value of this control parameter S_{c}, there seems to be a continuous transition to an unclogged state. The data can be rescaled with this critical value, which, as expected, decreases with the orifice size D. This leads to a phase diagram in the S-D plane in which clogging appears as a concave surface.

How universal is the vibration-velocity controlled granular convection?

Recently, a number of articles have reported that granular convection induced by continuous vibration is controlled by vibration velocity, in contrast with some previous studies. We have reported such an example for the Brazil nut effect when the vibration is given discontinuously, using a one-layer granular bed in a cell with down-facing side walls. Here, we report the effect of vibration phase and wall friction using the same experimental system, to confirm rising motion of an intruder induced by granular convection is again governed by vibration velocity. We compare two different cases of vibration phase for giving intermittent vibration cycles, and found one, in which granular packing is well established before grains start to lose contacts due to vibration, provides distinctly high reproducibility. We further control the side wall friction using a microfabrication technique, and found that significantly high reproducibility is attained in a cell with vertical side walls when a millimeter texture is introduced on the side walls. Our results indicate that the granular convection is universally controlled by vibration velocity. The present study opens a way to conduct highly reproducible experiments on granular dynamics, which is indispensable for deep physical understanding of granular flow and segregation.

Rising obstacle in a one-layer granular bed induced by continuous vibrations: two dynamical regimes governed by vibration velocity

The rising motion of an obstacle in a vibrated granular medium is a classic problem of granular segregation, and called the Brazil nut (BN) effect. Identification of the controlling vibration parameters of the effect is a long-standing problem. The simple possibility that the BN effect can be characterized solely by vibration velocity has recently been pointed out. The issue has become controversial over the long history of research, with only a few systems providing evidence for this simple possibility. Here, we investigate the rising motion of an obstacle in a vertically positioned one-layer granular bed under continuous vibrations. We find the rising motion is composed of two distinct regimes, and the first and second regimes are both governed, in terms of vibration parameters, solely by the vibration velocity. We further demonstrate simple scaling laws that well describe the two regimes. Our results support the emergent simple possibility for the controlling parameters of the BN effect and suggest that this feature could be universal. We propose two possible mechanisms of convection and arch effect for the two distinct regimes and demonstrate that these mechanisms explain the scaling laws followed by our experimental data.

Effect of viscosity on the shaking-induced fluidization in a liquid-immersed granular medium

A liquid-immersed granular medium is shaken vertically under a wide range of accelerations (Γ in dimensionless form) and frequencies (f) and its fluidization process is studied. The granular medium is formed by settling and consists of two size-graded layers (particle diameter d) such that the upper layer is fine grained and is less permeable. When Γ>Γ(c), a liquid-rich layer formed by the accumulated liquid at the two-layer boundary causes a gravitational instability. The upwellings of the instability are separated horizontally by a distance (wavelength) λ, and their amplitude grows exponentially with time [∝exp(pt)] at a growth rate p. We conduct experiments for two liquid viscosity cases such that the particle settling velocity (V(s)) of the same particle differs by a factor of 17. We find that for both cases, Γ(c) is at a minimum in an optimum frequency band centered at f∼100 Hz. However, the high-viscosity (HV) case has a smaller Γ(c), a shorter λ, and a faster dimensionless growth rate [p'=p/(V(s)/d)]. We also measure granular rheology under an oscillatory shear and find that (i) interparticle friction decreases when the strain amplitude becomes large and (ii) friction is smaller for the HV case. From (i), we infer that the shear strain of the shaking experiments becomes largest at around f∼100 Hz. We consider that (ii) is a consequence of liquid lubrication and is a reason for a smaller Γ(c) for the HV case. We show that the low- and high-frequency limits of the optimum frequency band can be explained by introducing critical values of dimensionless jerk (i.e., time derivative of acceleration) J and dimensionless shaking energy S. The low-frequency limit corresponds to the requirement that in order to unjam the particles, the period of shaking (1/f) must be shorter than the time needed for the particles to rearrange by settling (d/V(s)), which also explains why the HV case is fluidized at a lower f compared to the LV case. We apply the results of the linear stability analyses for Rayleigh-Taylor instability. Using the measured λ and p, we infer that (i) only a thin layer beneath the two-layer boundary is mobile and the rest of the lower layer remains jammed and (ii) the effective viscosity of the upper granular layer relative to the liquid is smaller for the HV case as a result of smaller friction.

Symmetrically periodic segregation in a vertically vibrated binary granular bed

Periodic segregation behaviors in fine mixtures of copper and alumina particles, including both percolation and eruption stages, are experimentally investigated by varying the ambient air pressure and vibrational acceleration. For the cases with moderate air pressure, the heaping profile of the granular bed keeps symmetrical in the whole periodic segregation. The symmetrical shape of the upper surface of the granular bed in the eruption stage, which resembles a miniature volcanic eruption, could be described by the Mogi model that illuminates the genuine volcanic eruption in the geography. When the air pressure increases, an asymmetrical heaping profile is observed in the eruption stage of periodic segregation. With using the image processing technique, we estimate a relative height difference between the copper and the alumina particles as the order parameter to quantitatively characterize the evolution of periodic segregation. Both eruption and percolation time, extracted from the order parameter, are plotted as a function of the vibration strength. Finally, we briefly discuss the air effect on the granular segregation behaviors.

Granular convection and the Brazil nut effect in reduced gravity

We present laboratory experiments of a vertically vibrated granular medium consisting of 1-mm-diameter glass beads with embedded 8-mm-diameter intruder glass beads. The experiments were performed in the laboratory as well as in a parabolic flight under reduced-gravity conditions (on Martian and Lunar gravity levels). We measured the mean rise velocity of the large glass beads and present its dependence on the fill height of the sample containers, the excitation acceleration, and the ambient gravity level. We find that the rise velocity scales in the same manner for all three gravity regimes and roughly linearly with gravity.