分格顆粒氣體之分子動力學模擬與顆粒通量模型之研究

On Molecular Dynamics Simulations and Particle Flux Model for Compartmentalized Granular Gases

林祺皓(Chi-Hao Lin)

指導教授 ： 陳國慶教授

國立臺灣大學/工學院/應用力學研究所/博士(2010年)

https://doi.org/10.6342/NTU.2010.10638

摘要

本文主要在探討分格容器中顆粒物質受到底部垂直震動的運動行為。因為該系統中，顆粒的碰撞時間遠小於顆粒連續兩次碰撞的間隔時間，故此系統可視為顆粒氣體(granular gases)。吾人建立了分子動力學方法(molecular dynamics simulations，MD)來模擬二元顆粒物質受外部振動所產生的各類狀態(如均勻分布、單格聚集、顆粒振盪與二格聚集等狀態)。在顆粒振盪狀態時，顆粒溫度的計算證實了該過程中，溫度確實呈現了振盪狀態。然而，溫度振盪過程產生的二區溫度差異，並非整體宏觀行為的唯一機制(高溫流向低溫)。
因此，吾人將振盪過程區分為二個階段，分別為輕顆粒流動階段(L-stage)與重顆粒流動階段(H-stage)，其中L階段又區分為2個階段(L1與L2)。L1階段顆粒流動方向與溫度差異互為相反方向，故吾人針對此一階段提出濃度驅動的機制來解釋宏觀行為。為了進一步地證實濃度驅動的概念，吾人將分格容器拓展至非對稱分格系統。由實驗觀察，因左右二室體積不同使得顆粒的濃度造成差異，導致顆粒由大區流動至小區的時間與反向流動時間產生了差異，且時間差異隨著非對稱比值的增加有愈顯著差距。
除此之外，二元顆粒振盪亦會受到二元顆粒數目的多寡而有相反的差異。當顆粒數較少時，顆粒由小區流動至大區的時間較反向流動長；而在顆粒較多的時候，顆粒由小區流動至大區的時間卻較反向流動短。對於此一特殊又有趣的現象，吾人以能量低點解釋了其物理機制，並由MD的方式得到了證實。當顆粒數較少時，顆粒聚集於小區的能量低於顆粒聚集於大區，相較而言小區較為穩定，故停留時間較長；而顆粒數較多時卻是恰為相反，使得大區較為穩定進而顆粒的停留時間較長。
最後，吾人針對Hsieh的侵入顆粒議題，提出了2T模型來描述凝結溫度的下降。2T模型主要結合了二室間的通量平衡與驅動力平衡。藉由二個平衡概念，證實了侵入顆粒愈重，則凝結溫度下降愈大的結果。

關鍵字

顆粒氣體 ； 顆粒振盪 ； 分子動力學 ； 顆粒通量 ； 凝結溫度

並列摘要

This article studies the behavior of granular materials in a compartmentalized container by the vertical vibration. Because the time of the collision between particles is much smaller than the time interval between two successive collisions, so the system can be regarded as granular gases. We establish a molecular dynamics (molecular dynamics simulations, MD) to simulate the vibration of binary particles generated by various external input energy. There are several states can be observed, such as uniform state, one clustering state, granule oscillation and two-clustering state). In granular oscillation, the granular temperature shows an oscillatory state. Furthermore, the temperature difference between two zones is not the only mechanism for granular oscillation.
The oscillation process is divided into two stages. One is L-stage to describe the movement of light particles, and another one is H-stage to describe the movement of heavy particles. L-stage can be divided into two stages (L1 and L2). In L1-stage, the of difference of concentration is the macro-driven mechanism. In order to further confirm the concept of concentration, we extended to non-symmetrical systems. From the experimental observations, the concentration difference leads to time differences between the movement of particles from large zone to small zone and the reverse flow. Furthermore, the time difference will increase with the increase of the non-symmetrical ratio .
In addition, we observed that there are two types of granular oscillations. When the number of particles is small, the time required for particles moved from the large zone to small zone is smaller than the reverse direction. However, when the number of particles is large, the time required for particles moved from the large zone to small zone is larger than the reverse direction. For this special phenomenon, we use the particle flux model calculate the period bifurcation and the period switch. Besides, we use the concept of energy to explain the physical mechanism by the MD simulations. When the number of particles is small, the averaged energy for particles cluster in the small zone is smaller than the one for particles cluster in the large zone. However, when the number of particles is much more, the averaged energy for particles cluster in the small zone is greater than the one for particles cluster in the large zone.
Finally, we propose the 2T model to describe the intruder effect. The intruder effect is that the condensation temperature will drop when the intruder is added into the based particles. 2T model combine the flux balance with the balance of driving force. By the two balanced concepts, we successfully calculate the drop of the condensation temperature.

並列關鍵字

granular gases ； granular oscillation ； molecular dynamics ； particle flux ； condensation temperature

參考文獻

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