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研究生：	吳鉉忠 Wu, Hsuan-Chung
論文名稱：	壓電式微液滴噴射數學模擬系統之開發與實驗研究 Development of a Mathematical Model for Piezoelectric Micro-droplet Ejection and Its Experimental Study
指導教授：	黃文星 Hwang, Weng-Sing
學位類別：	博士 Doctor
系所名稱：	工學院 - 材料科學及工程學系 Department of Materials Science and Engineering
論文出版年：	2004
畢業學年度：	92
語文別：	中文
論文頁數：	173
中文關鍵詞：	噴墨列印製程、微液滴、流體體積法、壓電式噴墨
外文關鍵詞：	micro-droplet, piezoelectric inkjet, inkjet printing, volume of fluid, piecewise linear interface calculation
相關次數：	點閱：63 下載：3
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面對工業製造技術對自動化、微小化、降低成本、減少環境污染的要求與趨勢，噴墨列印在許多工業製造技術上，成為極具吸引力之材料分配與成形的替代技術。在建立一可模擬壓電式噴墨系統於噴射過程中之液滴生成、飛行與擊打到標的之目標下，本研究成功開發一套三維電腦輔助分析系統。

本研究之模擬系統在速度與壓力的求解上是使用SOLA (SOLution Algorithm) 數值技術，在界面重建及液體體積的傳遞問題上採用PLIC (Piecewise Linear Interface Calculation) 並耦合VOF (Volume of Fluid) 法來計算，在表面張力的處理上是使用CSF (Continuum Surface Force) 模式，壓電材料經受電壓影響而產生變形所造成的噴嘴壓力隨時間變化關係則是採用聲波傳遞理論處理。實驗上所採用的噴墨頭其驅動方式為壓電式-收縮管型。使用CCD (Charge Couple Device) Camera擷取液滴影像，控制LED (Light Emitting Diodes) 發光的時間以獲取不同時間的液滴生成、飛行過程之影像。藉由不同時間所擷取的液滴影像來計算液滴的飛行距離與速度。

模擬系統以壓電式-收縮管型噴墨頭為載具，模擬液滴生成、飛行與擊打到標的之完整過程，並以實驗觀測與量測結果來驗證模擬系統的準確性。模擬與實驗結果在液滴型態、斷裂時間、飛行距離與液滴體積四方面具有良好的一致性。在模擬系統被驗證可靠之後，再據以進行數值實驗來評估物性參數 (噴液的表面張力與黏滯係數) 與製程參數 (壓力波型態與噴墨頭長度) 對液滴噴射行為的影響。

在實驗方面為探討壓電式微液滴噴射裝置在單脈衝電壓型態下液滴的生成及噴射行為。研究的對象包括去離子水及乙二醇兩種液體，實驗結果並結合壓力波傳導理論來探討操作頻率、正電壓維持時間與電壓大小對液滴體積及速度之影響。

The development of manufacturing technologies has been driven by the need for automation, miniaturization, and the reduction of costs and environmental impact. To meet these needs, ink-jet printing technology is an increasingly attractive alternative for the distribution and patterning of material in a wide variety of applications. A three-dimensional computer-aided analysis system has been developed in this study to simulate the formation, ejection, and impact of a liquid droplet in a squeeze mode piezoelectric inkjet printing device.

The computer simulation system is based on a SOLA (Light Emitting Diode) scheme for the solution of velocity and pressure fields. It is coupled with VOF (Volume of Fluid) and PLIC (Piecewise Linear Interface Calculation) techniques for the transport of volume fractions of liquid in the cells, and construction of the interface. For the treatment of surface tension effects, a CSF (Continuum Surface Force) model is employed. The pressure at the nozzle inlet, which is related to the applied voltage, imposed on the simulation system is determined by the propagation theory of acoustic waves. For the experimental setup, a squeeze mode piezoelectric print head is employed. By coordinating an LED (Light Emitting Diodes) flash with droplet ejection, a CCD (Charge Couple Device) camera could be used to capture images of the droplets at different points in the formation and ejection process. These images were then used to estimate the volume and velocity of the droplets.

The simulation system simulated the formation, ejection and impact of a micro-droplet on the substrate for a piezoelectric inkjet printing device as well as to validate the mathematical model by comparing the simulated results with experimental observations/measurements. The simulated results are rather consistent with the experimental observations in terms of droplet morphology, breaking time, flight distance, and droplet volume. The effects of ink physical properties (including surface tension and viscosity) and operation characteristics (including pressure wave type and cavity length) on the ejection behavior of the droplet are presented by the validated simulation system.

In the experimental study, the formation and ejection behavior of droplets created by a squeeze mode piezoelectric ink-jet printing device using a single pulse voltage pattern are investigated. The test liquids are water and ethylene glycol. The experimental results and acoustic wave theory are used to discuss the effects of operating frequency, positive voltage keeping time and pulse voltage magnitude on the volume and velocity of the droplets.

中文摘要	                               I
英文摘要	                               III
目錄	                                 V
表目錄	                                VIII
圖目錄	                                IX
符號說明	                               XII
英文縮寫及全名對照表	                 XIV

第一章	緒論	                      1
1-1 研究背景	                       1
1-1-1 噴墨種類與原理	                    1
1-1-2 噴墨列印製程的應用	                  3
1-2 文獻回顧	                       5 
1-3 研究目的與內容	                    8

第二章	理論基礎	                    15
2-1 噴墨現象與聲波傳導理論     	        15
2-2 數學模式的理論	                    17
2-2-1 控制方程式	                      18
2-2-2表面張力的處理	                    19
2-2-3 自由表面的處理	                    21
2-2-4 邊界條件	                       22
2-2-4-1 自由表面邊界	                     22
2-2-4-2 固體邊牆邊界	                     23
2-2-4-3 入口邊界	                       24

第三章	數值方法	                    30
3-1 系統的分割與變數設置	                 30
3-2 動量方程式的差分化	                  31
3-3 連續方程式的差分化及流場壓力的解法	  32
3-4 表面張力的數值處理	                  34
3-5 自由表面追蹤的數值處理	                37
3-5-1 自由表面之建立/重建	          37
3-5-2 自由表面之傳遞	                    42
3-5-3 流體體積的重新分佈	                  44
3-6 邊界條件的設定	                    46
3-6-1 自由表面之邊界條件	                  47
3-6-2 固體邊牆之邊界條件	                  49
3-7 穩定度的要求	                     50
3-8 解析的方法、步驟與流程圖	       51

第四章	實驗方法與步驟	                 70
4-1 實驗設備	                       70
4-2 實驗條件的設定	                    71
4-3 液滴體積、飛行距離與飛行速度的決定	  72

第五章	結果與討論	                   78
5-1 液滴噴射之模擬結果與實驗驗證	     78
5-2 液滴撞擊至標的之模擬結果	       80
5-3 製程參數對液滴噴射行為之影響分析	   81
5-3-1 表面張力與黏滯性的影響	        81
5-3-2 壓力波型態的影響	                   82
5-3-3 噴墨頭長度的影響	                   84
5-4 製程參數對液滴噴射行為影響之實驗研究	 86
5-4-1 操作頻率的影響	                    86
5-4-2 脈衝時間的影響	                    88
5-4-3 電壓大小的影響	                    89

第六章	結論	                      133
第七章	未來研究方向	                  135
參考文獻	                               137 
附錄A 動量方程式之詳細差分式	              144
附錄B 壓力與速度修正之推導	               153
附錄C 界面法向量之差分式	                161
附錄D 曲率之差分式	                   163
附錄E 前向問題及逆向問題	                167
附錄F 自由表面之應力平衡條件               170

                                    

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校外：2004-06-08公開

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