Nuclear magnetic resonance measurements of velocity distributions in an ultrasonically vibrated granular bed

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.