Propagating waves in a monolayer of gas-fluidized rods

Abstract

We report on an observation of propagating compression waves in a quasi-two-dimensional monolayer of apolar granular rods fluidized by an upflow of air. The collective wave speed is an order of magnitude faster than the speed of the particles. This gives rise to anomalously large number fluctuations, ΔN~N 0.72±0.04 , which are greater than ordinary number fluctuations of N 1/2 . We characterize the waves by calculating the spatiotemporal power spectrum of the density. The position of observed peaks, as a function of frequency ω and wave vector k, yields a linear dispersion relationship in the long-time, long-wavelength limit and a wave speed c=ω/k. Repeating this analysis for systems at different densities and air speeds, we observe a linear increase in the wave speed with increasing packing fraction with almost no dependence on the air flow. We also observe that the parallel and perpendicular root-mean-square speeds of the rods are identical when waves are present, but become different at low packing fractions where there are no waves. Based on this apparent exclusivity, we map out the phase behavior for the existence of waves vs speed anisotropy as a function of density and fluidizing air flow. Disciplines Physical Sciences and Mathematics | PhysicsThis journal article is available at ScholarlyCommons: https://repository.upenn.edu/physics_papers/607PHYSICAL REVIEW E 83, 061304 (2011) Propagating waves in a monolayer of gas-fluidized rods We report on an observation of propagating compression waves in a quasi-two-dimensional monolayer of apolar granular rods fluidized by an upflow of air. The collective wave speed is an order of magnitude faster than the speed of the particles. This gives rise to anomalously large number fluctuations, N ∼ N 0.72±0.04 , which are greater than ordinary number fluctuations of N 1/2 . We characterize the waves by calculating the spatiotemporal power spectrum of the density. The position of observed peaks, as a function of frequency ω and wave vector k, yields a linear dispersion relationship in the long-time, long-wavelength limit and a wave speed c = ω/k. Repeating this analysis for systems at different densities and air speeds, we observe a linear increase in the wave speed with increasing packing fraction with almost no dependence on the air flow. We also observe that the parallel and perpendicular root-mean-square speeds of the rods are identical when waves are present, but become different at low packing fractions where there are no waves. Based on this apparent exclusivity, we map out the phase behavior for the existence of waves vs speed anisotropy as a function of density and fluidizing air flow.

Granular materials composed of shape-anisotropic grains

“…by vibro-uidization [149][150][151] or in an upow of air. 152,153 As we will see, shape anisotropy of the grains matters in many respects.…”

“…The time scales where the mean square displacements parallel and perpendicular to the rod axes became diffusive differ. In a subsequent study, the authors reported propagating compression waves [153]. The speed of the collective waves was found to be an order of magnitude faster than the average particle.…”

“…Since collisions in real granular systems are dissipative, a permanent kinetic energy supply is needed to maintain a stationary particle dynamics. A gas-like state of shapeanisotropic grains has been achieved in experiments e. g. by vibro-fluidization [149][150][151] or in an upflow of air [152,153]. As we will see, shape anisotropy of the grains matters in many respects.…”

Sounds and hydrodynamics of polar active fluids

“…2a and 2b that the time correlations of ρ q and v q oscillate over several periods before being damped, thereby demonstrating that both density and velocity waves propagate in the active liquid, see also Supplementary Videos 2 and 3. We emphasize, that we here consider the propagation of linear waves as opposed to the density fronts, or bands, seen at the onset of collective motion [1,8,26,27]. In Fig.…”

Three-dimensional (3D) experimental realization and observation of a granular gas in microgravity

“…This can be achieved by levitating the particles using electro-magnetic fields Kohlstedt et al, 2005;Maa et al, 2008) or by air flow beneath the grains (Daniels et al, 2009;Daniels and Durian, 2011;Nichol and Daniels, 2012;Burton et al, 2013a,b). In 3D granular gases, the bias due to gravity cannot be eliminated in ground-based labs.…”