Pattern transition, microstructure, and dynamics in a two-dimensional vibrofluidized granular bed

Abstract

Experiments are conducted in a two-dimensional monolayer vibrofluidized bed of glass beads, with a goal to understand the transition scenario and the underlying microstructure and dynamics in different patterned states. At small shaking accelerations (Γ=Aω^{2}/g<1, where A and ω=2πf are the amplitude and angular frequency of shaking and g is the gravitational acceleration), the particles remain attached to the base of the vibrating container; this is known as the solid bed (SB). With increasing Γ (at large enough shaking amplitude A/d) and/or with increasing A/d (at large enough Γ), the sequence of transitions/bifurcations unfolds as follows: SB ("solid bed") to BB ("bouncing bed") to LS ("Leidenfrost state") to "2-roll convection" to "1-roll convection" and finally to a gas-like state. For a given length of the container, the coarsening of multiple convection rolls leading to the genesis of a "single-roll" structure (dubbed the multiroll transition) and its subsequent transition to a granular gas are two findings of this work. We show that the critical shaking intensity (Γ_{BB}^{LS}) for the BB→LS transition has a power-law dependence on the particle loading (F=h_{0}/d, where h_{0} is the number of particle layers at rest and d is the particle diameter) and the shaking amplitude (A/d). The characteristics of BB and LS states are studied by calculating (i) the coarse-grained density and temperature profiles and (ii) the pair correlation function. It is shown that while the contact network of particles in the BB state represents a hexagonal-packed structure, the contact network within the "floating cluster" of the LS resembles a liquid-like state. An unsteadiness of the Leidenfrost state has been uncovered wherein the interface (between the floating cluster and the dilute collisional layer underneath) and the top of the bed are found to oscillate sinusoidally, with the oscillation frequency closely matching the frequency of external shaking. Therefore, the granular Leidenfrost state is a period-1 wave as is the case for the BB state.

Phase-coexisting patterns, horizontal segregation, and controlled convection in vertically vibrated binary granular mixtures

“…(This analogy of a floating granular-layer with the original Leidenfrost-effect [30] of a liquid-drop hovering over its own vapour-cushion was suggested by Eshuis et al [16].) It has been established recently [23] that the floating dense-layer has a liquid-like structure as confirmed via an analysis of its paircorrelation function, and the LS moves synchronously with the vibrating container and hence this represents a period-1 pattern. Therefore, the mixed state of "Gas & LS" in Fig.…”

“…5(c) -there are strong correlated motions along both horizontal and vertical directions. Such correlated motion constitutes one characteristic feature of the Leidenfrost state that distinguishes it from the BB-state [23] as it is evident from a comparison of Fig. 5(c) with the velocity-vector plots in Fig.…”

“…The related experimental details of image-analysis and the PIV methodology are documented in Ref. [23].…”

Heat flux of a granular gas with homogeneous temperature

“…However, the term proportional to the density gradient becomes important in regions of the system where the temperature gradient is small enough, situation that usually requires the application of an external force. The presence of the new term in the heat low explains, for example, the non-monotonic temperature dependence on position observed in simulations and experiments [14,15]. In the present work, we identify and fully study the limiting case, namely, a state with homogeneous granular temperature and non-homogeneous density.…”

“…At the first order in the gradients, the Chapman-Enskog method applied to a wide variety of models provides constitutive relations that closes system ( 13)- (15). They read…”