外場下流體相分離的數值模擬

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姓名

羅尉彰(Wei-Jhang Luo) 查詢紙本館藏

畢業系所

物理學系

論文名稱

外場下流體相分離的數值模擬
(Numerical Simulation of Phase Separation in Binary Fluids with an External Field)

相關論文

★ 黏彈介質中高分子之動力學

★ 層狀液晶缺陷結構之彈性

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摘要(中)

外場下相變的動力學在過去十年中已經被廣泛地研究。在這個研究工作中，我們執行數值模擬來研究在均勻電場下的流體相分離現象。當流體歷經相分離時會變為非均質材料，它的介電常數會隨著區域的濃度改變。因此電場能夠影響系統的圖案形成。在我們的模擬中所用的動力學模型遵循著H模型，並且在Ginzburg-Landau自由能中額外加入一個由電場引發的項。分離的相會被排列形成圖案，在其中界面的法向量都垂直於電場。這個系統初期階段的動力學將透過線性分析與雙淬火過程來研究。

摘要(英)

The dynamics of phase transitions with an external field is studied extensively in the last decade. In this work, we perform numerical simulations to study the phase separation in binary fluids with a uniform electric field. The binary fluid is inhomogeneous while it undergoes the phase separation, and its dielectric constant varies with the local composition. Therefore the electric field would affect the pattern formation of the system. The dynamic model in our simulation follows the model H with an additional term in the Ginzburg-Landau free energy, which is induced by the electric field. The separated phases are arranged to form patterns where the normal vector of interfaces is perpendicular to the field. The dynamics of this system in the early stage is investigated through the linear analysis and the biquenching process.

關鍵字(中)

★ 外加場
★ 相分離

關鍵字(英)

★ phase separation
★ external field

論文目次

1. Introduction......1
2. Dynamics of Phase Separation......4
2.1. The Cahn-Hilliard Equation......4
2.2. Hydrodynamic Flow......6
2.3. Growth Laws......7
2.4. Free Energy Under the External Electric Field......8
2.4.1. Thermodynamic Relations......8
2.4.2. Fixed Potential......9
2.5. Equations of Motion......11
2.5.1. Chemical Potential Correction......11
2.5.2. The Ginzburg-Landau Equation......11
2.5.3. Electric Forces in a Fluid Dielectric......12
3. Numerical Simulation......14
3.1 Methods......14
3.1.1. Numerical Scheme Using the Fourier Transform......14
3.1.2. Integration of Time Evolution Equation......15
3.1.3. Initial and Boundary Conditions......16
3.2. Two-dimensional Simulations......17
3.3. Three-dimensional Simulations......22
4. Analyses and Discussion......24
4.1. Linear Analysis......24
4.2. Growth Rate......27
4.3. Coarsening Mechanism in an Electric Field......31
5. Conclusions......39
A. Non-dimensionalizng of the Ginzburg-Landau Equation......41

參考文獻

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指導教授

陸駿逸(Chun-Yi Lu)

審核日期

2004-7-1

推文