Time dependence and density inversion in simulations of vertically oscillated granular layers

Abstract

We study a layer of grains atop a plate which oscillates sinusoidally in the direction of gravity, using three-dimensional, time-dependent numerical solutions of continuum equations to Navier-Stokes order as well as hard-sphere molecular dynamics simulations. For high accelerational amplitudes of the plate, the layer exhibits a steady-state "density inversion" in which a high-density portion of the layer is supported by a lower-density portion. At low accelerational amplitudes, the layer exhibits oscillatory time dependence that is strongly correlated to the motion of the plate. We show that continuum simulations yield results consistent with molecular dynamics results in both regimes. 05.65.+b,47.57.Gc Although experimental [1,2] and computational [3][4][5][6][7] evidence demonstrate the potential for hydrodynamic models to describe important aspects of granular flow, a general set of governing equations for granular media is not yet recognized [8,9]. Several proposed rapid granular flow models use binary, inelastic hard-sphere collision operators in kinetic theory to derive equations of motion for the continuum fields: number density n, velocity u, and granular temperature T [10-12]. As Eshuis, et al [9] stated in 2010, "The holy grail question in research on granular dynamics is [13,14], To what extent can granular flow be described by a continuum approach?" Density inversion, in which a low-density region near the bottom of a granular layer supports a higher-density region above it, has proven to be significant for the study of granular hydrodynamics. This phenomenon has been identified in vertically shaken layers [7,9,[15][16][17] as well as in layers flowing parallel to a surface, such as in gravity-driven flow down an incline [18,19].In their seminal investigation [7], Lan and Rosato studied density inversion in vertically vibrated granular media. A layer of grains with depth H and uniform diameter σ atop a plate that oscillates sinusoidally with frequency f and amplitude A will leave the plate at some time in the oscillation cycle if the maximum acceleration of the plate a max = A (2πf ) 2 exceeds the acceleration of gravity g. The oscillating plate can be characterized by the dimensionless parameters Γ = a max /g and f * = f H/g. Lan and Rosato studied density inversion in such a system by conducting soft-sphere discrete element method (DEM) simulations and comparing these results to kinetic theory predictions of Richman and Martin [20].These continuum predictions did not account for the time dependence of the layer or the plate, but rather treated the oscillating plate as a source of thermal energy and assumed one-dimensional (1-D) steady-state density and temperature distributions as functions of height in the cell. To characterize the rate of kinetic energy input through shaking, they used the dimensionless RMS speed of the bottom plate V b = (2πf A) / √ 2σg as their control parameter. It has since become common to instead use the dimensionless shaking strength [15]In Fig. 5 of their manuscript, L...

A robust numerical method for granular hydrodynamics in three dimensions

“…Similar results were obtained before by e.g. Bougie, Policht & Pearce (2012). There, however, mild driving conditions are considered which lead to maximum volume fractions way below 0.3.…”

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

“…To isolate the possible effects of the two-dimensionality of our experiments on height-oscillations, additional experiments (not shown) were conducted in a quasi-2D box (of width of about 5 particle diameter, W/d = 5.5, and length L/d = 100) with a shallow granular layer (F = h 0 /d = 6); increasing the shaking intensity from 30 to 40, however, we found that the Leidenfrost state remains a "period-1" wave, implying that the LS is synchronized with the shaking frequency even in a quasi-2D vibro-fluidized bed. Simulations in a 2D-box and/or additional experiments may help to resolve the disagreement between the above simulations [46,49] and our experiments about the synchronous time-dependence of the Leidenfrost state.…”

“…(It may be noted that the low-and high-Γ regimes in simulations of Ref. [49] correspond to the same shaking strength (S = Γ(A/d) = constant) but having small-and large-A/d, respectively.) To isolate the possible effects of the two-dimensionality of our experiments on height-oscillations, additional experiments (not shown) were conducted in a quasi-2D box (of width of about 5 particle diameter, W/d = 5.5, and length L/d = 100) with a shallow granular layer (F = h 0 /d = 6); increasing the shaking intensity from 30 to 40, however, we found that the Leidenfrost state remains a "period-1" wave, implying that the LS is synchronized with the shaking frequency even in a quasi-2D vibro-fluidized bed.…”

“…4b)-while the former may be connected to the f -wave nature of the LS as found in our work, the implications of the peaks at the harmonics of f remain unclear. On the other hand, the simulation work of Bougie et al [49] probed the time-dependence and density inversion in a vertically vibrated 3D-box filled with shallow layers (F = h 0 /d = 4.3) of granular materials. While they found that the density-inverted state is indeed an f -wave in the low-Γ regime (Γ = 5.68), the density profiles become time-invariant in the high-Γ regime (Γ = 56.5).…”

Geological evidence: New insights into rock avalanche dynamics

“…If a granular Leidenfrost effect truly exists during the emplacement of RAs, a relatively dispersed basal layer should be generated at the base of RAs 41,42 . Does this truly exist?…”