以耗散粒子動力學法研究奈米自泳動粒子輸送現象

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賴達昇(Da-sheng Lai) 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

以耗散粒子動力學法研究奈米自泳動粒子輸送現象
(Transport Phenomena of Nano-Swimmers: DPD study)

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摘要(中)

自泳動粒子是具備自我推進能力，得以通過周遭流體的物體，在自然界
中諸如魚類群游、鳥類群飛，或是許多常見細菌如大腸桿菌、衣藻等，都
可以觀察到其獨特的運動行為，近幾年成為科學家極力探討的問題。從微
觀尺度觀察，這些自泳動粒子都有著類似的移動方式，首先，它們會朝一
個方向作直線運動，經過一段時間後，以極短暫的時間停住然後轉向，接
著再朝新的方向作直線運動，不斷地重複兩階段步驟，稱為run-and-tumble motion。
本研究採用耗散粒子動力學法，模擬自泳動粒子的擴散行為及對流場的
影響。首先，在無邊界系統探討自泳動粒子透過不同作用方式移動，竟是
兩種完全不同的擴散行為。第一種為pusher成對作用型，粒子藉由推動後方流體使自己前進，藉由計算粒子及溶劑的平均平方位移量，透過斜率得到擴散係數，進一步修正自泳動粒子擴散係數的關係式:Dp=D0+f(fp)*v^2*t，而周遭溶劑的擴散係數關係式為:Ds=D0+fp*v^2；另一種則是external force單一作用型，粒子移動時不與周遭流體產生作用，其平均平方位移量和時間為冪次關係(t^a)，當a介於1和2之間，稱為superdiffusion，且ap和fp呈冪次關係。接著在有限邊界系統中，探討自泳動粒子對流場的影響，當自泳動粒子為球狀粒子時，隨著作用力(Fa)愈大，自泳動粒子會在邊界產生聚集，導致系統內流速愈來愈慢；而當自泳動粒子為桿狀粒子時，隨著作用力增加，系統內的整體流速是先上升而後下降，因為硬桿變得較有指向性，其平均指向是與重力施加的方向相反，產生polar order的現象，更準確的說，由於系統內流場速度差的影響，造成硬桿在中間流動時，其指向和重力同向，而當位置越靠近邊界，其指向則和重力方向相反，產生逆流行為。

摘要(英)

Nano-swimmers in nature such as microorganisms can utilize different propulsion mechanisms to achieve directed locomotion in a viscous environment.For nature microswimmers, such as E. coli, the locomotion can be described by a run-and-tumble model in which straight runs are depicted by swimming speed (va) and tumbles associated with complete randomizations in the direction take place with mean duration (t). For sufficiently large time and length scales, the diffusive behavior is displayed for run-and-tumble organisms.
In this study, the diffusive behavior of nanoswimmers and the flow rate were investigated by active colloids with DPD simulation (Dissipative Particle Dynamics simulation). In an unbounded system, nano-swimmers were observed to display two different diffusion behaviors from a variety of motions. The first type is called as pusher with a random dipole force. Active colloids acted on a surrounding solvent bead to move at each time step. The mean square displacement of active colloids and solvent were linear dependent with the time. After calculation, the diffusion coefficient could be determined by slope and adjusted the relationship between the concentration of active colloids (fp) and related factors, including active force (Fa) and run time(t). For an active colloid’s diffusion coefficient relationship is
Dp=D0+f(fp)*v^2*t, and the solvent’s diffusion coefficient relationship is Ds=D0+fp*v^2.
The second type was called as external force with a point force. For this type, active colloids didn’t act on the surrounding solvent beads. In this way, the mean square displacement of active colloids was exponential dependent with the time (t^a). When a was between 1 and 2, this condition was called superdiffusion, and the active colloid’s diffusion index (ap) was generally exponential dependent with fp.
For the bounded system under gravity, the effect of flow to nano-swimmers. There were two shapes of active colloids. One was spherical and another was rod-like. For a spherical colloid, the higher active force was, the lower flow rate was. It was assumed that active colloids would aggregate close to the boundary so as to enhance the friction. And the flow rate was decreasing. However, for the rod-like colloid with rising active force, the flow rate was not decreasing continuously. The flow rate was observed to increase in the beginning. It was predicted that the rod-like colloids became directional so that the active rods exhibit polar order. And the average orientation was reversed to the direction of gravity. Exactly speaking, when the active rod was in the middle of the system, the orientation of colloids was the same with the direction of gravity. Otherwise, when the active rod was near to the boundary, the orientation of colloids was opposite to the direction of gravity. This phenomenon was due to the difference of flow rate.

關鍵字(中)

★ 耗散粒子動力學
★ 自泳動粒子
★ 輸送現象

關鍵字(英)

★ DPD
★ Self-propelled particles
★ Transport phenomena

論文目次

摘要................................................... I
Abstract.............................................. II
致謝.................................................. IV
目錄................................................... V
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 自泳動粒子與作用方式................................. 5
1-5 自泳動粒子的特性與應用............................... 7
1-5-1 擴散與沉降平衡.................................... 7
1-5-2 自泳動粒子與物質表面間的作用....................... 11
1-5-3 逆流而上的行為................................... 13
第二章模擬原理與方法................................... 15
2-1 耗散粒子動力學(Dissipative Particle Dynamics)...... 15
2-2 DPD 原理.......................................... 17
2-2-1 DPD 作用力...................................... 17
2-2-2 噪訊與時間尺度................................... 21
2-2-3 斥力參數(Repulsion Parameters)................... 22
2-2-4 弗洛里-哈金斯理論(Flory-Huggins Theory)........... 24
2-2-5 長度、速度、時間尺度的無因次化..................... 27
2-2-6 積分法求解....................................... 28
2-2-7 週期性邊界條件................................... 30
2-2-8 Cell List 表列法................................ 31
2-3 模擬系統與參數..................................... 32
2-3-1 系統基本參數設定.................................. 32
2-3-2 自泳動粒子的設定.................................. 33
2-3-3 牆粒子的設定..................................... 35
2-4 擴散係數(Diffusion Coefficient, D)................. 36
2-4-1 平均平方位移(Mean Square Displacement, MSD)...... 37
2-4-2 速度自相關函數(Velocity Autocorrelation Function, VAF).................................................. 39
第三章自泳動粒子於無邊界系統中擴散行為................... 42
3-1 Pusher 型自泳動粒子 (Dipole force)................. 42
3-2 External force 型自泳動粒子 (Point force).......... 53
第四章自泳動粒子於流場中運動行為........................ 59
4-1 自泳動球狀粒子對流場的影響........................... 59
4-2 自泳動桿狀粒子對流場的影響........................... 64
第五章結論............................................ 72
第六章參考文獻........................................ 73

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指導教授

曹恆光(Heng-kwong Tsao)

審核日期

2015-6-11

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