Self-diffusion of grains in a two-dimensional vibrofluidized bed

The analogy of vibrofluidized granular beds with a thermal gas of hard disc s has been tested. Analysis of the mean squared displacement behavior of th e grains allowed comparison of the measured diffusion with the predicted va lue at a particular combination of granular temperature and packing fractio n. High speed photography, image analysis, and particle tracking software e nabled accurate location of the grains. Appropriate analysis of the three m ean squared displacement regimes, ballistic, diffusive, and crossover betwe en the two extremes, allowed both the diffusion coefficient and the granula r temperature to be measured at the same packing fraction. Broad agreement between Chapman-Enskog theory relating temperature to self-diffusion and ob servation was observed up to packing fractions of eta similar to 0.7. At hi gher packing fractions the grains showed evidence of caging and jump diffus ion, with the observed diffusion rapidly diverging from that predicted by t heory. Measurement of self-diffusion coefficients and subsequent use of kin etic theory was found to be an accurate method to determine the granular te mperature for intermediate packing fractions (eta=0.4-0.6), and would be pa rticularly suitable for those situations where the time resolution of the e xperimental facility is insufficient to resolve the speed of the grain betw een collisions. [S1063-651X(99)02012-7].