介觀強耦合庫倫液之剪帶:數值模擬

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姓名

李嘉駿(Kar-Chun Li) 查詢紙本館藏

畢業系所

物理學系

論文名稱

介觀強耦合庫倫液之剪帶:數值模擬
(Shear banding in strongly coupled Coulomb liquids under mesoscopic confinement: numerical simulation)

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摘要(中)

受剪力的液體會沿剪力向方流動，越遠離剪力作用的區域，其速度越小。當液體的黏滯係數不隨剪力改變，其速度場為線性分佈，擁有這種性質的液體稱為牛頓液體(例如：水)。黏滯係數隨剪力改變的液體，其速度場為非線性分佈，這種非線性分佈的現象稱為剪帶：受力處有較大的剪率，剪率為液體每單位時間的形變。擁有這種性質的液體稱為非牛頓液體(例如:高分子溶液)。到目前為止，剪帶的微觀起源並不清楚。
另一方面，侷限在分子尺度(介觀)狹逢中液體的特性跟巨觀的液體不同。研究者發現，臨侷限板邊界的液體分子傾向沿邊界排列成層狀結構。這種超薄液體受剪力時，跟非牛頓液體一樣，同樣展示出剪帶與剪薄(黏滯力隨剪力增加而降低)。瞭解上述奇異現象，不僅對基礎物理研究有貢獻外，在奈米科技應用上，也非常重要。但受限於實驗觀察尺度，我們無法得知超薄液體中液體分子在剪帶與剪薄發生時的微觀運動與結構重組。故在本論文中，藉由數值模擬的介觀強耦合庫倫液體來比擬上述超薄液體的奇特行為。
介觀強耦合庫倫系統是由一群帶負電的粒子被侷限在均勻分佈的正電荷背景所產生的位能井中所組成。調整系統的熱擾動能使此系統呈現液體狀態。藉由數值模擬方法追蹤系統受剪力下每個粒子的運動軌跡來探討超薄液體的剪帶及剪薄現象的微觀起源。
我們發現這種超薄液體的黏滯係數會隨剪力增大而改變(先減少，後增加)，同時速度場隨剪力展示非線性的變化。藉由一些統計運算分析，例如：速度場與黏滯係數對外力的關係、時間結構關連函數等，我們深入探討剪力如何改變系統的黏滯係數從而影響其速度場的分佈。

摘要(英)

Shear banding is the non-linear mean velocity profile in the non-Newtonian liquid under shear stress. Unlike the sheared Newtonian liquid whose viscosity is independent of shear stress and mean velocity profile is linear, the non-Newtonian liquid is the liquid whose viscosity is a function of shear stress. It exhibits shear banding accompanied with shear thinning (viscosity decreases with shear stress) or shear thickening (viscosity increases with shear stress). Also, shear banding can be due to the non-uniform spatial distribution of the shear stress or the viscosity.
When the liquid is under the mesoscopic confinement (the molecular-scale gap), it also exhibits shear banding accompanied with shear thinning. Actually, the micro-structure and the micro-dynamics of the confined liquid are more complicated than those of the bulk liquid because of the confinement which causes the formation of the layered structure with anisotropic motion nearby each boundary. How the shear stress changes the viscosity and then affects the mean velocity profile in the confined liquid are not clear.
Using the molecular dynamics simulation, we investigate the velocity profiles and the local viscosity of the mesoscopically confined 2D Coulomb liquids steadily sheared by opposite stresses along the two opposite boundaries. The narrow Coulomb liquids about a few inter-particle distance in width are formed by particles interacting through 1/r type repulsive force in a uniformly counter ion background which generates an effective parabolic type transverse confining potential well.
In the confined Coulomb liquid, the local heating caused by the shear stress and the shear banding are observed. The local heating may cause the non-uniform spatial distribution of the viscosity. Also, the background drag which locally dissipates the stress causes the non-uniform spatial distribution of the shear stress. Therefore, the shear banding can be due to the non-uniform spatial distribution of the shear stress and the viscosity. On the other hand, the local viscosity and the curvature of the mean velocity profile normalized by the shear speed are non-monotonic in the shear stress. The system undergoes a transition from shear thinning to shear thickening.

關鍵字(中)

★ 介觀
★ 黏滯係數
★ 剪帶
★ 強耦合庫倫液

關鍵字(英)

★ mesoscopic confinement
★ viscosity
★ strongly coupled Coulomb liquid
★ shear banding

論文目次

1 Introduction 1
2 Background and theory 7
2.1 Rheology of fluids . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Rheology of Newtonian fluids . . . . . . . . . . . . . . 8
2.1.2 Rheology of non-Newtonian fluids: shear banding, thinning
and thickening . . . . . . . . . . . . . . . . . . . . 8
2.2 Liquids at the discrete level . . . . . . . . . . . . . . . . . . . 10
2.2.1 Microscopic picture of the bulk liquid . . . . . . . . . . 10
2.2.2 Liquids under mesoscopic confinement . . . . . . . . . 10
2.3 Rheological response of mesoscopically confined liquids . . . . 13
2.3.1 Shear banding and thinning in mesoscopically confined
liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.2 The micro-origin of viscosity . . . . . . . . . . . . . . . 15
2.3.3 The possible micro-origin of shear banding . . . . . . . 15
2.4 2D Strongly Coupled Coulomb Systems (SCCSs) . . . . . . . . 16
2.4.1 Experimental systems of 2D SCCSs . . . . . . . . . . . 16
2.4.2 Numerical systems of 2D SCCSs . . . . . . . . . . . . . 17
2.5 Statistical measurement . . . . . . . . . . . . . . . . . . . . . 18
2.5.1 Topological defects . . . . . . . . . . . . . . . . . . . . 18
2.5.2 Spatiotemporal correlation of local bond-orientational
order . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 Numerical Methods 23
3.1 The numerical system . . . . . . . . . . . . . . . . . . . . . . 23
3.2 The equation of motion . . . . . . . . . . . . . . . . . . . . . 24
4 Result and Discussion 26
4.1 Confined Coulomb liquids . . . . . . . . . . . . . . . . . . . . 27
4.1.1 The motion and the structure of confined liquids . . . 27
4.1.2 Structural relaxation time of confined liquids . . . . . . 31
4.2 Sheared Coulomb liquids . . . . . . . . . . . . . . . . . . . . 31
4.2.1 The motion and the structure of sheared liquids . . . . 34
4.2.2 Velocity profiles of sheared liquids . . . . . . . . . . . . 35
4.2.3 The local viscosity of liquids . . . . . . . . . . . . . . . 38
4.2.4 The effects on viscosity . . . . . . . . . . . . . . . . . . 38
4.3 The structural memory and the local viscosity . . . . . . . . . 44
5 Conclusion 47

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指導教授

伊林(Lin I)

審核日期

2009-7-17

推文