本文主要研究不可壓縮之牛頓流體，模擬液滴藉由噴墨系統噴出。為了讓液滴形狀變化的過程更加準確，有必要配合理論的基礎，建立一套完整的數學模式，藉以尋求最佳的製程參數。本文將針對不同入口最大壓力、不同表面張力、不同黏滯係數、不同噴嘴孔徑及不同平板速度對於液滴之影響來進行研究，探討液滴生成、液滴在飛行的過程及撞擊底板之形狀變化。在數值方法計算上，使用有限體積法以離散控制方程式計算流體運動，以求解連續方程式和動量方程式，並利用分離-隱式(segregated-implicit)法求解統御方程式。在液滴受到擠壓噴出的飛行形狀變化因為包含了空氣與液滴兩相的問題，且曲率變化大，為了有效地模擬這些現象，採用流體體積法(VOF)來計算網格內兩相的體積變化，並選用SIMPLEC演算法則求得速度及壓力的分佈。

This research mainly aims at incompressible Newtonian fluid and simulates fluid droplet formation process of inkjet system. In the design of inkjet system, it is important to establish a complete mathematical model to simulate the ejection of fluid and find the best operating condition. This research investigates on different maximum pressures, surface tensions, viscosities, sizes of nozzle and different velocities of rigid body to evaluate the droplet ejection parameters. FVM（Finite Volume Method） is used in this research to calculate fluid motion and solve continuity equation and momentum equation. The governing equations were then solved using segregated-implicit method. The ejecting system of interesting includes liquid and gas. In order to simulate the system with co-exist of two phases, VOF（Volume of Fluid） method is adopted. Using SIMPLEC algorithm solve the distributive of velocity and pressure.

中文摘要 i
英文摘要 ii
誌謝 iii
目錄 iv
表目錄 vi
圖目錄 vii
符號說明 xiii

第一章 緒論 1
1.1 研究目的與動機 1
1.2 噴墨種類與原理 2
1.2.1 連續式（Continuous） 3
1.2.2 依需求式（Drop-on-Demand） 5
1.3 文獻回顧 13
1.4 本文架構 18

第二章 理論基礎 19
2.1 理論分析 19
2.2 控制方程式 20
2.3 表面張力 20
2.4 自由表面 21
2.5 邊界條件 23
2.5.1 自由液面之邊界條件 23
2.5.2 入口之邊界條件 24
2.5.3 固體壁面之邊界條件 24

第三章 數值分析 26
3.1 數值方法 26
3.1.1 有限差分法（FDM） 26
3.1.2 有限元素法（FEM） 26
3.1.3 有限體積法（FVM） 27
3.2 SIMPLEC演算法則 28
3.3 自由表面處理 31
3.4 步驟與流程 34

第四章 結果分析與討論 36
4.1 模型驗證 36
4.2 物理模型 41
4.3 製程參數對液滴噴射行為之影響分析 44
4.3.1 入口最大壓力對液滴噴射行為之影響 45
4.3.2 表面張力對液滴噴射行為之影響 58
4.3.3 黏滯係數對液滴噴射行為之影響 71
4.3.4 噴嘴孔徑對液滴噴射行為之影響 84
4.3.5 平板速度對液滴噴射行為之影響 97

第五章 總結 110
5.1 結論 110
5.2 未來展望 117

參考文獻 118
附錄A 連續方程式和動量方程式之推導 124
作者介紹 130

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