Anomalous diffusion in a monolayer of lightweight spheres fluidized in air flow.

Shihori Koyama,Tomoki Matsuno,Takashi Noguchi

doi:10.1103/physreve.104.054901

Abstract

This paper presents statistical analyses of random motions in a single layer of fluidized lightweight spherical particles. Foam polystyrene spheres were driven by an upward airflow through the sieve mesh, and their two-dimensional motion was acquired using image analysis. In the bulk region, the particle velocity distributions changed from Gaussian to heavy-tailed distribution as the bulk packing fraction ϕ_{b} was increased. The mean square displacement of the particles exhibited transition to subdiffusion at much lower ϕ_{b} than observed in previous studies using similar setup but with heavier particles. A slight superdiffusion and significant growth of the correlation length in the two-body velocity correlation was observed at further large ϕ_{b}. The effect of the wall on the dynamics of the particles was also investigated, and the anisotropy of the granular temperature was found to be a useful index to discriminate between the wall region and the bulk. The turbulence statistics in the wake of a particle indicated a strong wall-normal asymmetry of aerodynamic forcing as the "thermal" agitation in the wall region.

Highlights

IntroductionGranular systems can be fluidized when one is placed in an upward fluid flow so as that each constituting particle is levitated and agitated by turbulent aerodynamic force
Granular systems can be fluidized when one is placed in an upward fluid flow so as that each constituting particle is levitated and agitated by turbulent aerodynamic force. The particles lose their kinetic energy through rolling friction, fluid viscosity, and inelastic mutual collisions as well as the negative part of work done by the aerodynamic forces
Previous laboratory studies on the air-fluidized granular materials have, to the best of our knowledge, implicitly limited their observation area to the bulk region, i.e., the central region detached from solid wall, focusing on homogeneous properties

Summary

Introduction

Granular systems can be fluidized when one is placed in an upward fluid flow so as that each constituting particle is levitated and agitated by turbulent aerodynamic force. Fluidized systems are in a subtle dynamic state in which perpetual aerodynamic agitation is required to compensate for the energy loss in order for particles to behave collectively like a fluid. When the number of particles is large, the aerodynamic force and the collisions between particles are considered to be sufficiently complicated, and it is often hoped that the agitation is Gaussian. This leads to an analogy to the thermal system despite the dissipative and macroscopic dynamics in the many-particle system. Many studies in recent years have found that various macroscopic, strongly dissipative (and out-of-equilibrium) systems such as particles agitated by turbulent airflow [3,4,5,6,7,8] or by mechanical vibration [9,10,11] can mimic Brownian behavior to an appreciable degree, which has long been considered mainly in the context of energetically

Results

Discussion

Conclusion