臺灣博碩士論文加值系統

本文探討在受振動的顆粒群中植入少數尺寸較大的相異顆粒後，這些相異顆粒的行為。過去的研究大部分是把重點擺在垂直振動的系統，即有重力影響的系統。這些研究發現，混合顆粒中體積較大的會聚集在上層。一般稱這種現象作巴西堅果效應(Brazil Nut Effect, BNE)[32]。若適當選擇混合顆粒的質量比與半徑比，也能使較大的顆粒聚集在下層，稱為反巴西堅果效應(Reverse Brazil Nut Effect, RBNE)[41]。
利用分子動力學模擬，本文發現二維顆粒系統受到與重力方向垂直的簡諧振動時，被植入的相異顆粒也會因其大小，質量的不同而有類似BNE和RBNE的兩種傾向 。一是往背景顆粒群的質心靠攏，二是被排擠在背景顆粒群之外。由於這個系統的重力及其它間隙流體的複雜影響可以忽略，因此本文認為理解這類系統的現象對理解一般混合顆粒的分離機制會有很大的幫助。
通過模擬及實驗的佐證，本文認為相異顆粒的傾向不同是由於顆粒之間碰撞頻率及慣性的差異性所造成的。而引發的傾向則決定於因振動引起顆粒分布的不對稱性有關。一個顆粒的碰撞頻率越大，運動狀態的改變越劇烈，而顆粒的質量越大則可以抵抗運動狀態的變化。本文稱這種因運動狀態改變的多寡造成的顆粒分離現象為慣性分離效應。這種效應也成功解釋了二維顆粒系統在無重力下受二維振動時，被植入相異顆粒的分離現象。

This report discusses the behavior of the intruded particles in a group of background particles which are agitated by external force. The intruded particles population is minority and have larger size than the background particles and also different in mass. The main researches for the last 30 years mostly focused on systems in which the vibrated direction is parallel to gravitational field. Some reports found the so called Brazil Nut Effect(BNE) [32] that the larger particles always accumulate on the top layer after agitation.And also the larger particles may sink to bottom (Reverse BNE) [41] if the size ratio and mass ratio are selected appropriately.
By the Molecular dynamics (MD) simulation, this report found the similar phenomenon of BNE in the 2 dimensional granular systems in the absence from gravitational field. The intruder in the system migrates either to the center or the edge of the cluster of the background particles. Since this system has negligible influence by gravity and the interstitial fluid, it may be an easier and important way to understand the mechanisms of particles segregation. Furthermore, it can be approximately realized by horizontal shaken experiment in gravitational field.
With the aids of simulation and experiment, this report suggests a mechanism for migration of an intruder in the shaking granular bed. The mechanism suggests that the migration of the intruder is due to the competition between the collision frequency and the inertia of the intruder. Since the collision frequency and the inertia is proportional to the size and the mass respectively, that explain why the size ratio and mass ratio become the main control parameters in particles migration. This mechanism also explains well the results in the system shaken in two dimensions.

目錄
中文摘要 i

英文摘要 ii

目錄 iii

圖表目次 v

第一章 簡介

一、顆粒物理簡介 1

二、混合顆粒的分離 2

第二章 實驗裝置與模擬方法

一、實驗裝置 5

二、電腦模擬方法 9

三、數值測試與比較 14

第三章 混合顆粒在一維簡諧振動下的行為

一、實驗 18

二、模擬結果與討論 21

三、大顆粒遷移方向的判據 25

四、大顆粒的遷移速度 28

五、偏差隨機行走模型 33



第四章: 混合顆粒在水平二維振動的圓形盤中的遷移現象

一、實驗 34

二、模擬結果與討論 35

三、小顆粒群的自旋 36

四、偏差隨機行走模型 41

第五章 : 水平振動系統的相變

一、顆粒系統的冷卻與加熱 48

二、顆粒系統的動力學與結構相變 48

第六章 : 結論 53

附錄A 55

參考文獻 65

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