Single-particle motion in three-dimensional vibrofluidized granular beds

A technique to probe the interior of three-dimensional dynamic granular sys tems is presented. Positron emission particle tracking (PEPT) allows a sing le tracer particle to be followed around a three dimensional vibrofluidized granular bed for periods up to six hours. At present the technique is able to resolve the position of the grains to +/-4 mm, with an average temporal resolution of about 7 ms. Packing fraction profiles are calculated by maki ng use of the ergodicity of the system, and granular temperature profiles a re obtained, in the dilute case, from the short time behavior of the mean s quared displacement. At longer times, the mean squared displacement shows a range of behavior which can be explained by the presence of strong gradien ts in the packing fraction. Convection currents were observed, but were suf ficiently small in magnitude to be ignored during the analysis of grain mot ion. The system was modeled using the Smoluchowski equation, which was solv ed numerically, and the results compared with the experimentally determined displacement probability density functions. Good agreement between experim ent and numerical results was achieved using Brownian motion relationships modified to accommodate differences between granular systems and thermal sy stems.