侵入者對顆粒氣體臨界聚集溫度之探討

On the Critical Clustering Temperature of Granular Gases with Intruders

謝萬霖(Wan-Lin Hsieh)

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(2010年)

https://doi.org/10.6342/NTU.2010.10657

摘要

顆粒氣體在外界給予適當的能量輸入下，由於顆粒與顆粒之間為非彈性碰撞，顆粒最後會發生聚集的狀態。若加入侵入顆粒於單種基底顆粒系統後，將會增加或者降低系統聚集時的凝聚溫度。系統臨界聚集溫度的增加主要由於侵入顆粒發生巴西堅果效應。

本文第一部分所探討的是各種參數對於顆粒臨界聚集溫度的影響。這些參數主要分為三類：材料參數(密度、恢復係數、粒徑)、容器參數(隔板寬度、底面積大小)以及其他參數(侵入顆粒之數目、基底顆粒的質量)。此部分主要發現加入侵入顆粒的密度、恢復係數、以及容器底面積加大，系統的臨界聚集溫度將會下降。

第二部分主要藉由實驗、模擬、理論三種方法計算侵入顆粒於原系統之臨界聚集溫度。此部分實驗的方法採用粒子影像追蹤法測量實際的顆粒溫度；接著藉由顆粒力學計算模擬的方法來探討在單種基底顆粒系統中加入一顆侵入顆粒後，其對於原系統臨界聚集溫度的影響；最後將以上兩種方法與理論計算方法來做比較分析。

最後一個部分為將原尺度縮小後其臨界聚集溫度的討論。

關鍵字

顆粒氣體 ； 侵入顆粒 ； 臨界聚集 ； 巴西堅果效應 ； 粒子影像追蹤法

並列摘要

In some energy input condition, the system of granular gas will come into being clustering state which results from inelastic collision between particles. However, the critical clustering temperature of a mono-disperse gas will be changed with intruding particle. The increasing value of the critical clustering temperature is because of the system occur the Brazil-nut effect

The first part of this thesis is the parameters discussion. All of these parameters are divided into three different types: the material parameters (density, coefficient of restitution, and diameter of particle), the container parameters (width of the compartments, bottom area) and the other parameters (number of the intruder, mass of the base particle). In addition, we found out that both of density and coefficient of restitution of intruding particle and bottom area of container are able to decrease the critical granular temperature.

In the second part, PTV method is used to measure the actual granular temperature. And we also use the discrete element method to explore the effect of the critical clustering temperature of a mono-disperse gas with an intruding particle. And compare the value of theory with above of two methods.

The final part of this thesis is to lessen the scale of all the system, and discuss the influence of critical clustering temperature.

並列關鍵字

ranular gas ； intruder ； critical clustering ； Brazil-nut effect ； PTV

參考文獻

[28] 邱方志, "顆粒氣體於非對稱容器之聚集與振盪," 國立台灣大學應用力學研究所碩士論文, 2009.

[1] S. Hsiau and S. Pan, "Motion state transitions in a vibrated granular bed," Powder Technology, vol. 96, pp. 219-226, 1998.

[2] O. Sano, "Dilatancy, buckling, and undulations on a vertically vibrating granular layer," Physical Review E, vol. 72, p. 51302, 2005.

[3] A. Ugawa and O. Sano, "Undulations of a thin granular layer induced by vertical vibration," JOURNAL-PHYSICAL SOCIETY OF JAPAN, vol. 72, pp. 1390-1395, 2003.

[4] J. Eggers, "Sand as Maxwell's demon," Physical Review Letters, vol. 83, pp. 5322-5325, 1999.