臺灣博碩士論文加值系統

本文旨在以理論分析探討浸泡塗層的流場分佈與塗層厚度、液膜長度的關係。藉由適當的因次分析，可定義出三個不同的流場形式分別為：低毛細數流場、中毛細數流場、高毛細數流場。而每單一個流場又可依不同的特徵區分成三個區域，分別為：區域一，固定厚度區；區域二，類一維流域動態區；區域三，靜態區。區域二及區域三將分別透過雙精度五階的數值方法（Runge-Kutta- Fehlberg Method）求得其解，並將其解平滑的接在一起以便得到整個流場的邊界形狀。經由計算的結果可以得知，可拉附的薄層液體長度將隨著重力效應愈趨明顯（當To變大時）而縮短。所以，當浸泡塗層此項技術應用在微重力的環境下時，需要更長的拉附距離才能使欲塗附的材料達到一固定的厚度。此外，當液體的表面張力變強時（即當Ca變小時），其拉附的薄層液體表面將愈趨凹陷，因此，其拉附的距離將會增加。

The present study is aimed at investigating theoretically the dip-coating processes. Based on the appropriate scaling analysis, three flow regimes are defined; they are the low-capillary number flows, the viscocapillary flows, and the high-capillary number flows. The whole flow domain is further decomposed into three regions with specific flow characteristics; they are Region I, the constant-thickness region, Region II, the nearly one-dimensional dynamic region, and Region III, the static region. Numerical calculations using the fifth-order Runge-Kutta- Fehlberg method are needed for the dynamic region, which is then matched smoothly to Region I and III to give the solution for the whole flow domain. The results indicate that the liquid film is reduced when the gravity effect becomes important or the value of To increases. Thus, in micro-gravity environment, a larger distance is necessary to attain a uniform thickness of coating material on the substrate when the dip-coating process is applied. In addition, with stronger surface tension or a smaller value of Ca the free surface of the liquid film becomes more concave and, consequently, the length of the liquid film before reaching the constant-thickness region, L, increases.

致謝 i
摘要 ii
Abstract iii
Contents iv
List of Figures v
List of Symbols vi

Chapter 1 Introduction 1

1-1 Introduction 1
1-2 Literature Review 3
1-3 Scope of the Present Study 5

Chapter 2 Mathematical Formulations 6

2-1 Governing Equations 6
2-2 Boundary Conditions 7
2-3 Nondimensionalization 8
2-4 Flow Regimes and Decomposition of Flow Domain 10
2-5 Low Capillary Number Flows 12
2-6 Gravity Effects 14

Chapter 3 Numerical Calculations and Discussion 18

3-1 Calculations of h(x) in Region II 18
3-2 Results and Discussion 21
3-3 Simplified Model for Blade Coating Processes 22

Chapter 4 Conclusions 23

Reference 24
Appendix A 26 Appendix B 27
Figures 28

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