Data from: 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.本研究报道了经超声频率垂直振动流化的芥菜籽颗粒床的核磁共振成像（Nuclear Magnetic Resonance Imaging）实验结果。针对多组振动频率、振幅及颗粒数量条件，我们在三维样品池中测量了颗粒温度（granular temperature）与填充率（packing fraction）随高度的变化规律。研究发现，振动频率的小幅提升会导致颗粒温度大幅降低，这与经典“硬球（hard-sphere）”模型关于振动边界能量通量的预测相悖。通过采用实验测得的赫兹接触刚度系数（Hertzian contact stiffness coefficients）开展颗粒-壁面相互作用的数值模拟，结果显示：当振动周期趋近于颗粒-壁面接触时间时，能量通量会出现显著下降。本实验由此证明，在超声频率条件下，亟需针对“软球（soft-sphere）”边界条件构建新的理论模型。