Wildman R D, Huntley J M, Hansen J P
Department of Mechanical Engineering, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Dec;60(6 Pt B):7066-75. doi: 10.1103/physreve.60.7066.
The analogy of vibrofluidized granular beds with a thermal gas of hard discs has been tested. Analysis of the mean squared displacement behavior of the grains allowed comparison of the measured diffusion with the predicted value at a particular combination of granular temperature and packing fraction. High speed photography, image analysis, and particle tracking software enabled accurate location of the grains. Appropriate analysis of the three mean squared displacement regimes, ballistic, diffusive, and crossover between the two extremes, allowed both the diffusion coefficient and the granular temperature to be measured at the same packing fraction. Broad agreement between Chapman-Enskog theory relating temperature to self-diffusion and observation was observed up to packing fractions of eta approximately equal to 0.7. At higher packing fractions the grains showed evidence of caging and jump diffusion, with the observed diffusion rapidly diverging from that predicted by theory. Measurement of self-diffusion coefficients and subsequent use of kinetic theory was found to be an accurate method to determine the granular temperature for intermediate packing fractions (eta=0.4-0.6), and would be particularly suitable for those situations where the time resolution of the experimental facility is insufficient to resolve the speed of the grain between collisions.
