不同表面粗糙度的大顆粒在垂直式振動床中動態行為之研究

The dynamics of intruders differing in surface roughness in a vertical vibrated granular bed

吳啟碩(Chi-shou Wu)

指導教授 ： 蕭述三

國立中央大學/工學院/能源工程研究所/碩士(2011年)

摘要

本研究探討在類二維的振動床系統中，不同表面粗糙度的大顆粒(或稱Intruder)在顆粒床中的巴西豆現象。所謂的巴西豆現象是指顆粒因為大小的不同，粒徑較大的顆粒會隨著時間上升至自由表面，而較小的顆粒會沉在容器底部。本研究以高速攝影機擷取大顆粒在顆粒床裡的動態行為，並藉由改變不同的振動條件以及顆粒床填充高度，觀察這些條件對不同表面粗糙度的大顆粒上升行為的影響。
本研究的實驗結果顯示，大顆粒的上升時間隨著無因次振動加速度增加而增長，隨著振動頻率增加而減少，上升速度隨著填充高度增加而減少。而且摩擦係數比較大的大顆粒，因為上升過程中，摩擦力造成的能量消散較大，從容器底部上升到自由表面的時間會比較長，摩擦係數較小的大顆粒，則因為摩擦力對它上升過程中的影響較小，所以上升地較快。而且不同摩擦係數大顆粒的上升時間，在較小無因次振動加速度、較大振動頻率以及較大的填充高度下，差異較為明顯。

關鍵字

顆粒流 ； 振動床 ； 表面粗糙度 ； 巴西豆效應

並列摘要

This study investigates experimentally the Brazil-nut effect in a quasi-2D vertical vibrated granular bed, the only difference lying in the surface roughness of the larger disks (or called intruders). The so-called “Brazil nut problem” means the larger particle rises to the top of the container and the smaller particles move to the bottom. The dynamics of the larger disk is recorded by using a high speed camera. The effects of vibration conditions and filling height of the granular bed on the dynamics of intruder are investigated in the study.
The results show that the rising velocity decreases with increasing granular bed filling height. It also shows that the rising time becomes faster with the larger dimensionless vibration acceleration and smaller vibration frequency is applied in the granular system. However, the rise time of the rough disks is smaller than the smooth one because of the larger energy dissipation of the rough disks. Additionally, the difference in the rising time between the rough and smooth intruders is more significant with the smaller dimensionless vibration acceleration, higher vibration frequency and higher granular bed filling height.

並列關鍵字

Granular flow ； Vibrated bed ； Brazil-nut effect ； Surface roughness

參考文獻

Kondic, L., Hartley, R. R., Tennakoon, S. G. K., Painter, B. and Behringer R. P., 2003, “Segregation by friction,” Europhysics Letters, Vol. 61, pp. 742-748.

Aoki, K. M., Akiyama T., Maki Y. and Watanabe T., 1996, “Convective roll patterns in vertically vibrated beds of granules,” Physical Review E, Vol. 54, pp. 874-883.

Bates, L., 1997, User Guide to Segregation

Bose, M. and Rhodes, M., 2007, “Dynamics of an intruder in a shaken granular bed,” Powder Technology, Vol. 179, pp. 25-30.

Breu, A. P. J., Ensner, H. M., Kruelle, C. A. and Rehberg I., 2003, “Reversing the Brazil-nut effect: Competition between percolation and condensation,” Physical Review Letters, Vol. 90, 014302.