顆粒震盪臨界現象之探討

On the Critical Conditions of Granular Oscillation

李家杰(Chia-Chieh Li)

指導教授 ： 陳國慶

國立臺灣大學/工學院/應用力學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.03129

摘要

顆粒的震盪現象(granular oscillation)是近幾年來才發現的一種屬於顆粒材料的特殊現象。在2005年首先由學者R. Lambiotte團隊以分子動力模擬(MD simulation)發現，並將之命名為「顆粒鐘」(Granular Clock)。在2006年由Viridi團隊成功地進行實驗來驗證顆粒震盪的存在。在2008年，Hou團隊首度使用顆粒溫度(granular temperature)的概念來解釋顆粒的振盪行為，並且將顆粒的振盪行為做為一種顆粒溫度震盪的表現。
本文主要以實驗的方式來探討顆粒震盪行為的產生原因；此外，在理論部分細部推討了van der Meer團隊建立的通量模型( flux model)，並且嘗試加以修改此通量模型，使之能包含不同顆粒溫度的呈現。
實驗的第一部分討論由於改變容器縱深與所加入系統之大顆粒數目關係的實驗觀察結果，提出了一個相對應的物理模型來說明顆粒振盪的行為是如何被驅動。實驗的第二部分採取了粒子影像追蹤法去記錄顆粒震盪時之顆粒數目的聚集轉移變化，並且量測震盪時之顆粒溫度變化，進一步支持本文中提出之物理模型。實驗的第三部分配合通量模型中的顆粒溫度估算，間接測量單種顆粒聚集時之臨界顆粒溫度；此部分實驗選用了粒子影像追蹤法(PTV)去測量單種顆粒在實際聚集時之顆粒溫度，並且將兩者結果拿來做比較分析。實驗的最後一個部分呈現了三種顆粒混合之震盪測試，發現三種顆粒規律震盪之存在，同時也提供了顆粒震盪的本質可能包含了質量驅動(mass-driven)之初步想法。

關鍵字

顆粒鐘 ； 顆粒震盪 ； 顆粒追隨 ； 顆粒溫度 ； 顆粒材料 ； 巴西堅果效應 ； 反巴西堅果效應 ； 通量模型 ； 粒子影像追蹤法 ； 統計力學

並列摘要

Recently, the spectacular phenomenon of granular oscillation had been found in a vibrated binary granular mixture in a compartmentalized container. It was first observed by R. Lambiotte et al. in 2005 through MD simulation, and named the phenomenon the “granular clock.” Viridi et al. successfully provided the experimental evidence of the existence of granular oscillation. In 2008, Hou et al. interpreted the granular oscillation as the oscillation in the coexisting granular temperatures of large and small spheres.
In this thesis, experimental results are brought to explain the mechanisms that drive the granular oscillation. Besides, the derivation of flux model of van der Meer et al. is also carried with detail in the thesis. Moreover, the flux function is modified to be able to present the coexistence of two different granular temperatures in a system.
The first part of the experiment is the depth discussion. From the observation of this experiment, a physical model named “expeller-trapper” is delivered to explain the mechanism of granular oscillation and the associated experiments. The second part of the experiment reveals the measurement of the granular temperatures of two different species of particles under granular oscillation to support the physical model we introduced in this thesis.
The third part of the experiment is the indirect measurement of the characteristic granular temperature under mono-disperse clustering. PTV method is also used to measure the actual clustering temperature of the grains, and then the comparisons between these two approaches are made to present in the thesis. The final part of the experiment is to present the experimental observation of the tri-disperse granular oscillation, which contributes to the conjecture of mass-driven oscillation left for the future work.

並列關鍵字

granular clock ； granular follower ； granular temperature ； granular material ； Brazil nut effect ； reverse Brazil nut effect ； flux model ； PTV ； statistical mechanics

參考文獻

2. E. Ben-Naim, P. L. Krapivsky, and S. Redner, Kinetics of clustering in traffic flows. Physical Review E, 1994. 50(2): p. 822.

3. B. S. Kerner and P. Konhauser, Cluster effect in initially homogeneous traffic flow. Physical Review E, 1993. 48(4): p. R2335.

5. J. Eggers, Sand as Maxwell's Demon. Physical Review Letters, 1999. 83(25): p. 5322.

6. R. Lambiotte, J. M. Salazar, and L. Brenig, From particle segregation to the granular clock. Physics Letters A, 2005. 343(1-3): p. 224-230.

7. I. Goldhirsch and G. Zanetti, Clustering instability in dissipative gases. Physical Review Letters, 1993. 70(11): p. 1619.