Pattern formation and fluidization in vibrated granular layers, and grain dynamics and jamming in a water fluidized bed

Goldman, Daniel Ivan
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This work examines the behavior of granular materials forced away from equilibrium in two different experimental systems. We study pattern formation in vibrated granular layers, and fluidization of grains near the onset of fluidization in a water fluidized bed. When a thin layer of grains is subject to sufficiently strong vertical vibration of frequency fd, standing wave patterns are excited and oscillate sub-harmonically at fd/2. The patterns form when Γ, the peak plate acceleration normalized by gravity, exceeds a critical value, Γ ≈ 2.5. To gain understanding of this transition, we studied the behavior of the layer near the onset of patterns. Below onset, for Γ < 2.5, we found that although no visible patterns were excited, the noisy state contained spatial structure. In addition, we studied the formation and the evolution of order in square patterns after a rapid change in Γ from below to above onset. We found that the pattern formed in two distinct stages: a rapid ordering with universal properties, followed by a slower non-universal ordering. We also examined the behavior of the average wavelength of the patterns during the first stage ordering, and found that the evolution of the wavelength was accompanied by a change in the effective fluid depth of the layer. The condition for a rapid layer fluidization was shown to be governed by a previously studied grain mobility transition. In the asymptotically formed square patterns, we found that the dynamics of the nodes of the patterns displayed normal modes and dispersion relations analogous to those of a two-dimensional crystal lattice. In addition, the normal modes could be resonantly excited; if the amplitude of a mode became large enough, the crystal melted, in accord with the Lindemann criterion for 2D melting. At higher values of Γ, we performed experiments on patterns that displayed phase discontinuities, called kinks. We observed that localized transient kinks called phase bubbles prevented the formation of stable patterns that would oscillate at fd/6. By preparing the system with a uniform initial condition, we were able to observe transient fd/6 patterns. In addition, we found that a convective motion associated with kinks led to segregation of different-sized particles: large particles were pulled into the kink and remained trapped. Fluidization in a water fluidized bed occurs when the pressure drop ∆P developed by the flow Q through packed grains balances the buoyant weight of the grains, (ρp −ρf )gh, where ρp and ρf are the solid and fluid densities and h is the height of the grains. For increasing Q, fluidization is characterized by an increase in void fraction, 1 − Φ, where Φ is the solid particle fraction. Using a light scattering technique called Diffusing Wave Spectroscopy, we studied the dynamics of grains for smooth increases and decreases of Q near the onset of fluidization. We found that the behavior was strongly influenced by the initial packing fraction of the grains. Loosely packed grains near Random Loose Packed (RLP), with 1 − Φ ≈ 0.45, moved immediately at the onset of fluidization and remained in motion. In contrast, tightly packed grains displayed a range in Q above onset during which voidage changes were followed by a rapid settling into a motionless state. We found that this was a result of yield stresses developed in the packed material due to the creation of a stress-bearing network; the network resulted from jamming of the grains due to frictional contacts between the grains and the walls of the cell. We also found that behavior of the bed upon defluidization was analogous to the behavior of a supercooled liquid near the glass transition: for 1 − Φ > 0.45, the bed resembled a liquid. For 1 − Φ < 0.45, motion in the bed was hindered due to local regions of largely immobile particles. These regions grew in size as Q was decreased until ∆P < (ρp − ρf )gh, at which point all translational dynamics of the grains ceased.