Hu Kaiwei, Xie Zi-Ang, Wu Ping, Sun Jing, Li Li, Jia Chao, Zhang Shiping, Liu Chuanping, Wang Li
School of Mechanical Engineering, University of Science and Technology Beijing, 100083, China.
Soft Matter. 2014 Jun 28;10(24):4348-59. doi: 10.1039/c3sm53190b.
We studied the separation behaviour of binary granular particles in a vertically vibrated container. The final separation of the binary particle system exhibited the Brazil-Nut (BN) effect, though it was not complete. Particle convection occurred, and four different typical convection modes were observed when the frequency f changed from 20 Hz to 80 Hz at constant dimensionless acceleration Γ = 4πAf(2)/g. However, when Γ changed from 2 to 4 at constant f, the system's convection mode stayed almost the same. In our experiments, one type of particle generally moved much faster than the other, so the former was termed the 'convecting' particle, and the latter was termed the 'non-convecting' particle. To study the separation results qualitatively, we divided the system into vertical layers and calculated the mass distribution of the binary particles along the z axis. The results showed that when f increased at constant Γ or Γ decreased at constant f, the convecting particles, usually the smaller and lighter ones, distributed less to the top side and more to the bottom side of the container. Finally, to explain the experimental results, we derived a mass conservation equation for the convecting particles considering simultaneous convection and diffusion. The equation described the experimental results well. We also analysed the effects of f, Γ, diameter ratio, density ratio, etc., on the final separation results.
我们研究了二元颗粒在垂直振动容器中的分离行为。二元颗粒系统的最终分离呈现出巴西果效应，尽管并不完全。颗粒对流发生，当频率f在恒定无量纲加速度Γ = 4πAf(2)/g下从20 Hz变化到80 Hz时，观察到四种不同的典型对流模式。然而，当Γ在恒定f下从2变化到4时，系统的对流模式几乎保持不变。在我们的实验中，一种类型的颗粒通常比另一种移动得快得多，因此前者被称为“对流”颗粒，后者被称为“非对流”颗粒。为了定性研究分离结果，我们将系统划分为垂直层，并计算了二元颗粒沿z轴的质量分布。结果表明，当f在恒定Γ下增加或Γ在恒定f下减小时，对流颗粒，通常是较小且较轻的颗粒，在容器顶部的分布较少，而在底部的分布较多。最后，为了解释实验结果，我们推导了一个考虑同时存在对流和扩散的对流颗粒质量守恒方程。该方程很好地描述了实验结果。我们还分析了f、Γ、直径比、密度比等对最终分离结果的影响。
