奈米自泳動粒子之擴散行為

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姓名

王辰戎(Chen-rong Wang) 查詢紙本館藏

畢業系所

化學工程與材料工程學系

論文名稱

奈米自泳動粒子之擴散行為
(Diffusion of Nano-Swimmers)

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摘要(中)

自泳動粒子為具備有自我推進通過周遭流體能力的物體，諸如魚類群游、鳥類群飛，或者是許多常見細菌如大腸桿菌、衣藻等，它們的運動行為都是近年來許多科學家欲探討的問題。然而在微觀尺度上這些自泳動細菌大多有著類似的運動方式，我們稱之為run-and-tumble motion。短時間內它們的運動軌跡近乎直線，經過一段時間後則會以極短暫的時間停住然後轉向，接著再重複同樣的過程，與布朗運動非常相似卻又不完全相同。而藉由其與周遭流體作用的方式又可分為從後方推進的pusher以及從前方驅動的puller。
本研究採用耗散粒子動力學法，依據run-and-tumble motion模型模擬pusher類型的奈米自泳動粒子於有限及無限邊界系統中的運動行為。首先，在無限邊界系統中，藉由三種測量方式皆得到了奈米自泳動粒子的擴散係數比一般不具有自我推進能力的粒子高，且在沉降平衡時自泳動粒子的濃度分佈情形也較為膨潤，此模擬結果與一般實驗結果相符。接著，在有限邊界系統中，我們同樣求得了奈米自泳動粒子的擴散係數，並發現相較於無限邊界系統時，由於彈道式軌跡的運動方式使奈米自泳動粒子容易滯留在邊界板面上，進而增加摩擦導致擴散係數的下降。我們以白金漢π理論與物理假設整理出影響變因的關係式，能夠成功地預測其擴散係數下降的量值，與其滯留在板面上的機率。最後依據Galajda等人的實驗，我們製造不對稱的漏斗型板子邊界，使奈米自泳動粒子在其中由於向左與向右的擴散係數不同，進而產生一往較大擴散係數方向移動的靜速度，藉以達到控制其運動方向的目的。

摘要(英)

Self-propelled micro-swimmers are biological organisms or synthetic objects that propel themselves through the surrounding fluids. Examples are a fish in a school, traveling birds, various swimming bacteria such as Escherichia coli and the green alga Chlamydomonas reinhardtii, etc. In the microscale living system, various self-propelled bacteria mostly have the same pattern of motion, which is called run-and-tumble motion. The trajectory of its motion is linear in a short interval, then punctuated by sudden and rapid randomizations in direction. The above process is repeated continually. This dynamics has something similar with Brownian motion but also something different. In addition, these swimmers can be classified as having pusher or puller polarity, which means that they are driven from the rear or the front fluids, respectively.
In this study, dissipative particle dynamics (DPD) based on the mode of run-and-tumble motion is employed to simulate self-propelled nano-swimmers in bounded/unbounded system. For the unbounded system, it is found that the diffusion coefficient of nano-swimmers is higher than that of passive swimmers. The sedimentation length is increasing for nano-swimmers at sedimentation equilibrium state which is consistent with results from experiments. For the bounded system, the diffusion coefficient of nano-swimmers was obtained as well. It has a high probability for nano-swimmers to detain at the wall because of the motion mode of ballistic trajectory, which leads to the increment of friction and decrement of diffusion coefficient. Based on Buckingham Pi theorem, the expression of diffusion coefficient is obtained which is associated with the velocity, distance between the two walls, and rotation characteristic time. Furthermore, when the walls are designed with a funnel shape, owing to the existence of diffusion coefficient difference between two opposite sites, the nano-swimmers tend to move toward the site with higher diffusion coefficient.

關鍵字(中)

★ 自泳動
★ 擴散

關鍵字(英)

★ self-propelled
★ swimmer
★ active particle
★ diffusivity

論文目次

摘要 I
Abstract II
誌謝 III
目錄 IV
圖目錄 VII
第一章緒論 1
1-1 簡介 1
1-2 常見的自泳動粒子 1
1-3 Run-and-tumble motion模型 3
1-4 自泳動粒子與周遭流體作用方式 4
1-5 自泳動粒子的特性與應用 6
1-5-1 擴散與沉降平衡 6
1-5-2 與物質表面間的作用 8
第二章模擬原理與方法 11
2-1 耗散粒子動力學(Dissipative Particle Dynamics) 11
2-2 DPD原理 13
2-2-1 DPD作用力 13
2-2-2 噪訊與時間尺度(Noise and Time Step) 16
2-2-3 斥力參數(Repulsion Parameters) 17
2-2-4 弗洛里-哈金斯理論(Flory-Huggins Theory) 18
2-2-5 長度、速度、時間尺度的無因次化 21
2-2-6 積分法求解 22
2-2-7 週期性邊界條件 23
2-2-8 Cell List表列法 25
2-3 模擬系統與參數 26
2-3-1 系統基本參數設定 26
2-3-2 自泳動粒子的設定 27
2-3-3 牆粒子的設定 30
2-4 擴散係數(Diffusion Coefficient, D) 31
2-4-1 平均平方位移(Mean Square Displacement, MSD) 31
2-4-2 速度自相關函數(Velocity Autocorrelation Function, VAF) 32
2-5 沉降平衡(Sedimentation Equilibrium, SE) 34
2-6 白金漢π定理(Buckingham π Theorem) 36
第三章奈米自泳動粒子於無邊界系統中擴散行為 37
3-1 自泳動粒子的可動性 37
3-2 MSD法量測擴散係數 39
3-3 VAF法量測擴散係數 40
3-4 沉降平衡的改變 41
第四章奈米自泳動粒子於有限邊界系統中運動行為 44
4-1 擴散係數於有限邊界系統中的改變 44
4-2 奈米自泳動粒子與板子間的作用 48
4-3 奈米自泳動粒子於板子表面的滯留行為 52
4-4 流體動力學作用對奈米自泳動粒子運動之影響 60
4-5 控制奈米自泳動粒子的運動方向 62
第五章結論 65
第六章參考文獻 66

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指導教授

曹恆光(Heng-kwong Tsao)

審核日期

2013-6-11

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