Experiments and characterization of low-frequency oscillations in a granular column

Abstract

The behavior of a vertically vibrated granular bed is reminiscent of a liquid in that it exhibits many phenomena such as convection and Faraday-like surface waves. However, when the lateral dimensions of the bed are confined such that a quasi-one-dimensional geometry is formed, the only phenomena that remain are bouncing bed and the granular Leidenfrost effect. This permits the observation of the granular Leidenfrost state for a wide range of energy injection parameters and more specifically allows for a thorough characterization of the low-frequency oscillation (LFO) that is present in this state. In both experiments and particle simulations we determine the LFO frequency from the power spectral density of the center-of-mass signal of the grains, varying the amplitude and frequency of the driving, the particle diameter, and the number of layers in the system. We thus find that the LFO frequency (i) is inversely proportional to the fast inertial timescale and (ii) decorrelates with a typical decay time proportional to the slow dissipative timescale in the system. The latter is consistent with the view that the LFO is driven by the inherent noise that is present in the granular Leidenfrost state with a low number of particles.

Macroscopically equivalent granular systems with different numbers of particles

“…0 behaviour shows. This further suggests that LFOs are an intrinsic characteristic of density inverted states, as argued in [23,29]. The situation is curious, as the mode is a macroscopic phenomenon, but its amplitude is driven by microscopic effects.…”

“…Furthermore, the evolution of z cm (t) is seen to become less chaotic and closer to a harmonic oscillation with a clearly defined frequency as  d 0, as increasingly steep peaks in the Fourier transforms indicate (not shown) [29]; this is another sign that low-frequency oscillations are driven by finite-number fluctuations.…”

“…Shaken beds of grains in density inverted states undergo collective semi-periodic oscillations, referred to as lowfrequency oscillations (LFOs) [15,23,28,29]. These are clearly identifiable in all simulations, making it possible to study their properties in equivalent macroscopic systems with different N. Their characteristic amplitude, quantified by the standard deviation of the evolution of the vertical centre of mass, s º ( ( )) a z t LFO cm , is seen to be proportional to -N 1 2 (d 1 2 ), as shown in figure 4(a).…”