Dynamics of Air-Fluidized Granular System Measured by the Modulated Gradient Spin-echo.pdf

a r X i v : p h y s i c s / 0 5 0 5 2 1 4 v 7 [ p h y s i c s .f l u - d y n ] 5 O c t 2 0 0 5 version 2 Dynamics of Air-Fluidized Granular System Measured by the Modulated Gradient Spin-echo Janez Stepi?snik,1, ? Samo Lasic?,1 Igor Sers?a,2 Ales? Mohoric?,1 and Gorazd Planins?ic?1 1University of Ljubljana, Faculty of Mathematics and Physics, Physics Department, Jadranska 19, 1000 Ljubljana, Slovenia? 2Josef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia (Dated: February 2, 2008) Abstract The power spectrum of displacement fluctuation of beads in the air-fluidized granular system is measured by a novel NMR technique of modulated gradient spin-echo. The results of measurement together with the related spectrum of the velocity fluctuation autocorrelation function fit well to an empiric formula based on to the model of bead caging between nearest neighbours; the cage breaks up after a few collisions [1]. The fit yields the characteristic collision time, the size of bead caging and the diffusion-like constant for different degrees of system fluidization. The resulting mean squared displacement increases proportionally to the second power of time in the short- time ballistic regime and increases linearly with time in the long-time diffusion regime as already confirmed by other experiments and simulations. PACS numbers: 45.70.Mg, 76.60.Lz 1 INTRODUCTION Sand dunes, grain silos, building materials, catalytic beds, filtration towers, riverbeds, snowfields, and many foods are granular systems consisting of large number of randomly arranged macroscopic grains. Despite their apparent simplicity granular materials exhibit a host of unusual behaviours, whose unravelling more often than not appears to challenge existing wisdom of science [2, 3]. Fluidized granular bed is a system of randomly arranged, macroscopic grains in which the driving force of motion is container shaking or gas flow through the granular system. Al- though, these systems are of tremendous tech