介電式液態透鏡中暫態流場之數值模擬

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姓名

詹謦聰(Qing-cong Zhan) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

介電式液態透鏡中暫態流場之數值模擬
(Numerical Simulation of the Transient Flow Field in Dielectric Liquid Lens)

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摘要(中)

液態透鏡有重量輕、體積小、易配置空間、可變焦、不怕破裂等優點，可以應用在許多需要成像的設備上，如手機、顯微鏡及相機等。液態透鏡是以改變透鏡形狀來達到可變焦之目的，有許多驅動機制可以選擇，其中以電驅動力調控較具發展潛力，這是以電壓來控制透鏡形狀。電驅動力調控有兩種方式，分別為電濕式與介電式，本研究以介電式液態透鏡作為研究之題目。
本研究使用有限元素法的套裝軟體COMSOL，模擬介電式液態透鏡的暫態行為與流場，數值方法使用層流兩相流-等位函數法(level set method)去追蹤介面，同時耦合流場的連續方程式、動量方程式及靜電場的帕松方程式。模擬結果得到電壓與接觸角的變化與實驗文獻趨勢相符，電場的分佈與電極圖案與介電常數有關，本研究中模擬採用同心圓電極，因此電場會沿著半徑方向r強弱交替，此外，在介電常數大的液體中其電場強度會相對較小，在介電常數小的液體中則有相對較大的電場。使用1000Hz交流電電壓，透鏡介面處可能會因為電壓來回震盪而產生振動，模擬結果高頻率電壓造成的相對偏差只在4%以下，這可能是實驗文獻中選擇高頻率電壓的原因。另外，交流電會造成介電力隨時間而變化，因此，流場會隨介電力不同而交替變化，由介電力與表面張力交互主導流場流動。峰值電壓時為介電力主導著流場，液體朝內流動產生渦旋擠壓著介面；零電壓時為表面張力主導著流場，液體會朝外流動有回復的趨勢，此外，低電壓及高電壓準穩態的暫態流場也有些差異。

摘要(英)

Liquid lens has many advantages such as light weight, small volume, variable focus, no fracture. Some imaging devices can apply with liquid lens, such as cell phone, microscope and camera. The lens shape can be adjusted to achieve the purpose of tunable focal length of the liquid lens. The electric force tuning has a higher potential development among the various mecha-nisms of liquid lens because it can adjust the voltage to conveniently control the lens shape. There are two methods for the electric force tuning which are electrowetting and dielectrophoresis respectively. This study is for dielectric liquid lens as the research topic.
The study uses the software of finite element method, COMSOL MUL-TIPHYSICS, to simulate the transient behavior and flow field of the dielectric liquid lens. The numerical simulations are carried out using laminar, two phase flow-level set method for tracking the deformation of the interface. At the same time, the continuity equation and momentum equation of flow field are coupled with Poisson’s equation of static electric field. The simulation results have showed a similar tendency of the contact angles varied with voltages with experimental results. The electric field distribution is related to the electrode pattern and dielectric constant of liquid. In this study, we use the concentric electrode. Therefore, it alternates the strong and weak electric field along r-axis. Moreover, the electric field is relatively weak in large dielectric constant liquid, and relatively strong in small dielectric constant liquid. Using 1000 Hz AC input, it may generate the vibration because of alternating voltage. The simulation results show that the high frequency voltage only causes the relative deviation under 4%. Maybe this is a reason why the experiments used the high frequency voltage. In addition, the dielectric force is varied with time because of AC voltage. Therefore, the flow field changes with different die-lectric force. The surface tension and dielectric force are dominated alter-nately in the flow field. First, the dielectric force is dominated in the flow field when the peak voltage is applied. Therefore, liquid flows inwardly that would generate a vortex in order to squeeze the interface. After that, the sur-face tension is dominated in the flow field when the zero voltage is applied. Liquid flows outwardly to recover the interface shape. In addition, there is some different transient flow field between the low voltage and the high volt-age.

關鍵字(中)

★ 介電式液態透鏡
★ 暫態流場
★ COMSOL數值模擬

關鍵字(英)

★ Dielectric liquid lens
★ Transient flow field
★ COMSOL numerical simulation

論文目次

摘要 i
Abstract ii
致謝 iv
目錄 v
圖目錄 vii
表目錄 x
符號說明 xi
第一章緒論 1
1-1 背景 1
1-2 表面張力、接觸角與滑移長度 2
1-2-1 表面張力 2
1-2-2 接觸角 2
1-2-3 滑移長度 3
1-3 液態透鏡的驅動方式 4
1-3-1 氣動調控 4
1-3-2 電動調控 5
1-3-3 刺激響應凝膠 5
1-3-4 流體動力調控 5
1-3-5 電驅動力調控 6
1-4 介電力理論 7
1-4-1 Kelvin Polarization Force Density 7
1-4-2 Korteweg-Helmholtz Force Density 9
1-4-3 Maxwell Stress Tensor 10
1-5 文獻回顧 11
1-5-1 同心圓電極 11
1-5-2 平板電極 12
1-5-3 徑向交指型電極 13
1-6 動機與目的 13
第二章研究方法 26
2-1 物理模型 26
2-2 數學模型 27
2-2-1 基本假設 27
2-2-2 統御方程式 27
2-2-3 初始條件與邊界條件 28
2-3 數學方法 29
2-3-1 連續表面張力法(CSF，continuum surface force method) 29
2-3-2 守恆等位函數法(Conservative level set method) 30
2-3-3 有限元素法(Finite element method) 31
2-4 無因次參數分析 31
2-5 數值解的流程 32
2-6 網格及收斂公差設定 33
第三章結果與討論 37
3-1 電場分佈 37
3-2 介面振動 38
3-3 接觸角與半徑隨電壓之變化 39
3-4 暫態流場 40
第四章結論與未來研究方向 58
4-1 結論 58
4-2 未來研究方向 59
參考文獻 60

參考文獻

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指導教授

陳志臣(Jyh-Chen Chen)

審核日期

2015-7-29

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