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振动驱动颗粒气体体系的局域态本构关系的实验验证*
Experimental study on the local equation of state for vibrated granular gases*
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摘要: 对准二维、水平边界振动驱动的颗粒气体体系的流体力学参量进行了局域态本构关系的实验研究。实验观测结果与经典动力学理论预测进行了比较。由于颗粒气体空间分布的不均匀性，颗粒体系的整体本构关系不成立，有必要对局域态进行分析。局域态本构关系是指颗粒系统的局域温度、局域压强和局域数密度之间的关系。通过颗粒速度的方向变化，可以得到颗粒的碰撞点。因此在计算压力张量的对角线项时，除了动力学部分之外，我们计入了颗粒碰撞的影响，得到了一个约为常数的压力张量迹，即颗粒压强的空间分布，与流体力学理论预测以及分子动力学模拟结果相符合；但是颗粒温度和数密度的空间分布，在振动的正反两个方向的分量出现差异，并且温度、压强和数密度之间的局域本构关系，无论在低密度或高密度区域，实验与理论预测在定性上一致，但定量上都有较大差别。因此经典流体力学理论在描述这样的体系时需加以修正。Abstract: We experimentally measure the local equation of state for two-dimensional horizontal fluidize granular gases confined in a rect-angle box. Local equation of state can be seen as a local constitutive equation of temperature, pressure and the number density. Except the kinetic parts, the collision parts of the stress tensor are included. The diagonal components of the stress tensor are almost constant, which is consistent with the results from the simulation and hydrodynamic theory. Furthermore, the spacial profiles of the temperature and the number density are shown to be consistent with the experimental results of micro-gravity. Finally the local equations of state for different area fractions are found to have great discrepancies with the theoretical predictions no matter how the low or dense the density is.
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