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An experiment to measure granular temperature in a sheared low density granular bed containing a range of sizes of particles has been performed. Using positron emission particle tracking, a single particle was tracked from different size phases. From the coordinate data, the second moment of the velocity fluctuations about the mean flow in each direction was determined. It was found that the larger particles are 'hotter' and that most of the energy is contained in the θ (shearing) direction fluctuations. Evidence was found for Knudsen layer and higher order Burnett effects, suggesting extensions of the Navier-Stokes approaches are necessary to describe heat transport in polydisperse systems. [ABSTRACT FROM AUTHOR]

We study convective motion in vertically vibrated three-dimensional granular beds by comparing the predictions of a model based on a hydrodynamic description to Navier–Stokes order with experimental results obtained using positron emission particle tracking (PEPT). The three-dimensional conservation equations relating mass, momentum and energy are solved using the finite element (FE) method for a viscous vibrofluidized bed by using only observable system parameters such as particle number, size, mass and coefficients of restitution. The mean velocity profiles from the viscous model show reasonable agreement with the experimental results at relatively low altitudes for the range of experimental values studied, though the velocity fields at higher altitudes were systematically underestimated by the model. We confirm that the convection rolls are influenced by the sidewall coefficient of restitution and demonstrate the scaling relationships that operate, where increasing amplitude of vibration leads to a reduction in the angular velocity of the rolls. [ABSTRACT FROM PUBLISHER]

The three-dimensional conservation equations relating energy and momentum transfer in a vibrated three-dimensional granular bed have been solved numerically by the finite element method. Two closures based on granular kinetic theory were used: one, the standard Fourier law relating heat flux to temperature gradient and the other, including an additional concentration gradient term. Each prediction of the two-dimensional axisymmetric granular temperature and packing fraction fields was compared against a one-dimensional model and three-dimensional experimental results, acquired using the technique of positron emission particle tracking. Both closures resulted in solutions that were in reasonable agreement with the experimental results, but it was found that differences between the predictions of each of the closures were relatively small in comparison to the anisotropy of the experimentally determined temperature distribution. [ABSTRACT FROM AUTHOR]

The velocity autocorrelation functions of grains moving in highly fluidized three-dimensional granular beds have been determined for the first time. Positron emission particle tracking was used to determine the location of a tracer particle. The velocity auto- and cross-correlation functions were then calculated following estimation of the velocities of the grains. The cross-correlations were found to be about zero for all times and the velocity autocorrelation functions differed in the x and y directions. A numerical study was performed to model the velocity auto-correlation function in the y-direction and this analysis was found to capture many of the observed experimental features. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We report the results of nuclear magnetic resonance imaging experiments on granular beds of mustard grains fluidized by vertical vibration at ultrasonic frequencies. The variation of both granular temperature and packing fraction with height was measured within the three-dimensional cell for a range of vibration frequencies, amplitudes and numbers of grains. Small increases in vibration frequency were found--contrary to the predictions of classical 'hard-sphere' expressions for the energy flux through a vibrating boundary--to result in dramatic reductions in granular temperature. Numerical simulations of the grain-wall interactions, using experimentally determined Hertzian contact stiffness coefficients, showed that energy flux drops significantly as the vibration period approaches the grain-wall contact time. The experiments thus demonstrate the need for new models for 'soft-sphere' boundary conditions at ultrasonic frequencies. [ABSTRACT FROM AUTHOR]