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研究生： 黃勝騰
Huang, Sheng-Teng
論文名稱： 非對稱電雙層分析與純擠壓水潤滑理論
Analysis of Asymmetric Electric Double Layer and Water Lubrication Theory on Pure Squeeze
指導教授： 李旺龍
Li, Wang-Long
學位類別： 碩士
Master
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： 2019
畢業學年度： 107
語文別： 中文
論文頁數： 197
中文關鍵詞： 電雙層 、電雙層效應 、雷諾方程式 、純擠壓潤滑理論 、水 、電解質
外文關鍵詞： electric double layer, effect of electric double layer, reynolds equation, Lubrication Theory on Pure Squeeze, Water, Electrolyte
相關次數： 點閱：87  下載：4 
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    • 近年來，隨著各種3C產品或是機械元件的輕量化，體積減少方便攜帶，在機件與機件之間的間隙，也隨著加工技術的進步，而逐漸減少，因此在探究微流道下機具部件下之間的潤滑，防止金屬與水之間的氧化作用在現今也已經做的很好，同時水的比熱容較需多液體大，可以同時帶走小型零件的熱量達到散熱的目的。
    水溶液本身黏度不高，但電解質水溶液會因為自身離子受到流道壁面性質而產生吸附現象，進而使流道邊界攜上帶電離子形成電雙層，而電雙層的存在會對整體水溶液提供一定黏度的提升。傳統的電雙層具有許多限制，無法討論非對稱邊界條件的電雙層或是無法適用於較高電位，隨著應用範圍不斷的擴大，這些條件逐漸束縛住新的研究。因此，本篇研究的主要目的為探討流道寬、電位和濃度對黏度的影響，找出最佳黏度和適用範圍，考慮到電效應並對傳統雷諾方程式執行進一步的修正，推導出非對稱修正型雷諾方程式。
    在研究中發現，電位的增加會增加電效應黏度，但是需配合在特定的德拜長度與流道寬才能有較佳的電效應黏度，也可以藉由改變黏度來控制流體流動。但在接觸區域的視黏度主要是由壓力黏度控制，因此水溶液的黏度表現有大幅提升的現象。但即使考慮到電黏度的貢獻，液膜厚度之尺度在奈米等級，而目前工業加工精度仍在微米等級，擠壓至奈米等級會使物體表面磨損，產生裂縫及破壞。以目前的生產技術及防鏽技術，水流體仍不適合作為工業潤滑用油的替代品。但微小流道內電效應仍然是為來關注的目標。
    本研究的貢獻在於脫離非線性帕松-波茲曼方程式(non linear Poisson-Boltzmann equation)及德拜-休克耳近似(Debye-Huckel approximation)的假設條件，利用數值方法迭代求出離子濃度分布，並考慮到水分子再解離，而且適用於非對稱邊界條件，能夠在不同環境條件下進行電位分布模擬。

    Debye Huckel and nonlinear Poisson-Boltzmann solution is classical solution derived by semi-infinite space boundary conditiom. In this research, Our electric double layer model want to deviate from the topic of classic assumption, and developed a numerical solution for electrical double layer with asymmetric boundary condition instead of symmetric boundary condition.
    　　In past study, the electric conductivity in classic Reynold is constant, In our new modified Reynold equation, the electric conductivity varies with temperatue and ionic coconcentration, at the same time, our new modified Reynold equation is derived with asymmetric boundary condition and ionic conservation rule.

    目錄 摘要 i 致謝 v 表目錄 xiv 圖目錄 xv 符號表 xvii 第一章 研究動機、目的及文獻回顧 1 1.1前言及文獻回顧 2 1.1.1傳統電雙層理論 5 1.1.2重疊電雙層理論 7 1.1.3非對稱電雙層理論 8 1.1.4電雙層離子流動情形 8 1.1.5電雙層應用 11 1.1.6考慮電雙層純擠壓接觸模型部分 12 1.1.7電雙層對水潤滑膜的影響 13 1.3純擠壓潤滑理論 14 1.4考慮電雙層效應之潤滑理論 16 1.5研究目的 16 1.5.1研究動機 17 1.5.2論文架構 17 第二章 研究理論 19 2.1研究理論 19 2.2電雙層模型 20 2.2.1統御方程式 20 2.2.2離子守恆定律 21 2.2.3數值方法求解 27 2.3含電雙層之純擠壓分析 28 2.3.1流體的基本假設 28 2.3.2純擠壓雷諾方程式 28 2.3 純擠壓潤滑理論 35 2.4參數等效方程式 35 2.5液膜厚度方程式 36 2.6壓力與流體黏度之關係式 37 2.7壓力與流體密度之關係式 38 2.8彈性變形方程式 38 2.9負載平衡方程式 39 第三章 研究方法 42 3.1 蓋勒肯(Galerkin)法 42 3.1.1求解有限元素方法 42 3.1.2離散公式 43 3.1.3運算法則 44 3.2有限元素法物件化 45 第四章 結果與討論 47 4.1電雙層現象 47 4.1.1電雙層網格測試 47 4.1.2電雙層模型驗證 48 4.1.3電雙層和邊界電位的關係 48 4.1.4流道寬度與電雙層之間的關係 51 4.1.5溶液濃度對電雙層的影響 53 4.1.6本研究之電雙層模型與文獻[41]比較 54 4.2純擠壓網格測試 63 4.3非對稱電雙層黏度性能比較與分析 68 4.3.1 含電雙層黏度性能與其他文獻之比較分析 68 4.3.2本研究與其他文獻電雙層黏度表示式比較分析 73 4.3.3在固定流道寬度下不同電位差的電雙層黏度性能分析 77 4.3.4在固定電位差下不同流道寬度的電雙層黏度性能分析 78 4.3.4不同電解質濃度下流道寬度對電雙層黏度性能分析 78 4.4含電雙層之模型驗證與純擠壓分析 88 4.4.1 利用電位變化在純擠壓中分析電黏度性能 88 4.4.2 不同材料及負載對膜厚變化 89 4.4.3 不同材料及負載對壓力變化 89 第五章 結論 99 5.1結論 99 5.1.1 電雙層之數值模擬方法討論 99 5.1.2 含電雙層之黏度表示式比較與分析 100 5.1.3 含電雙層之純擠壓分析 101 文獻 p.1 附錄一：電雙層資料庫 p.9 附錄二：文獻[23]推導過程 p.58 附錄三：文獻[49]推導過程 p.62 附錄四：文獻[60]推導過程 p.65 附錄五：電雙層演進分類 p.69 附錄六：離子吸附例子 p.70   表目錄 表1-1 電雙層文獻適用範圍 4 表4-1 電雙層網格測試參數 55 表4-2 電雙層網格加密模型測試組參數 A1~A5 56 表4-3 電雙層網格加密模型測試電位誤差比較 56 表4-4 與參考文獻[26]驗證電雙層模型之參數設定表 57 表4-5 純擠壓網格加密參數表 64 表4-6 純擠壓網格加密測試組E1~E6 64 表4-7 純擠壓網格加密測試組0.6 ms時的膜厚誤差 65 表4-8 純擠壓網格加密測試組0.6 ms時的壓力誤差 65 表4-9 純擠壓網格加密測試組0.6 ms時的視黏度誤差 66 表4-10 文獻[23]、[49]及[60] 71 表4-11 文獻[23]、[49]及[60]黏度表示式分項 72 表4-12與Chu等人[27]進行驗證使用參數 90   圖目錄 圖1-1 Helmholtz提出的平板電雙層模型 7 圖1-2 Gouy-Chapman引入擴散層的概念 7 圖1-3 同性離子和反性離子分布 10 圖1-4壓力驅動電解質溶液流動以及傳導電流提供的電黏度 10 圖1-5剛球壓平板 14 圖1-6剛球壓流體液模與平板 15 圖2-7 不對稱流道示意圖 27 圖2-8 純擠壓模型示意圖 41 圖3-1 數值方法求解電雙層模型流程示意圖 46 圖4-1 電雙層網格加密模型示意圖 55 圖4-2 與參考文獻[26]比較電雙層模型驗證 57 圖4-3 在對稱邊界電位下本研究電雙層模型與德拜-休克耳近似解做比較 58 圖4-4 在不對稱邊界電位下本研究電雙層模型與德拜-休克耳近似解做比較 58 圖4-5 在對稱邊界電位下本研究電雙層模型與非線性帕松-波茲曼解做比較 59 圖4-6 在不對稱邊界電位且高電位下本研究電雙層模型在不同流道寬之表現 59 圖4-7 kh=10不對稱邊界電位對離子濃度的影響比較 60 圖4-8 kh=4不對稱邊界電位對電位的影響比較 60 圖4-9 kh=4不對稱邊界電位對離子濃度的影響比較 61 圖4-10 kh=0.5 本研究與文獻[41]之比較 61 圖4-11 kh=1 本研究與文獻[41]之比較 62 圖4-12 kh=2 本研究與文獻[41]之比較 62 圖4-13 純擠壓網格加密示意圖 63 圖4-14 純擠壓網格測試-中心膜厚隨時間變化 66 圖4-15 純擠壓網格測試-中心壓力隨時間變化 67 圖4-16 純擠壓網格測試-中心視黏度隨時間變化 67 圖4-17 濃度10-3M黏度隨流道寬與德拜長度比值在不同邊界電位下的變化 80 圖4-18 濃度10-5M黏度隨流道寬與德拜長度比值在不同邊界電位下的變化 80 圖4-19 濃度10-1M黏度隨流道寬與德拜長度比值在不同邊界電位下的變化 81 圖4-20 本研究A2與文獻[23]的分布項B2進行比較 81 圖4-21 本研究A1與文獻[23]的電效應項B1進行比較 82 圖4-22 本研究A2與文獻[49]的分布項D2進行比較 82 圖4-23 本研究A1與文獻[49]的電效應項D1進行比較 83 圖4-24 本研究A2與文獻[60]的分布項G2進行比較 83 圖4-25 本研究A1與文獻[60]的電效應項G1進行比較 84 圖4-26 本研究與文獻[23]、[49]及[60]的黏度進行比較 84 圖4-27 相同流道寬下視黏度對電位差作圖 85 圖4-28 相同電位差下視黏度對流道寬和德拜長度的比值作圖 85 圖4-29 濃度不同下視黏度對流道寬作圖 86 圖4-30 濃度不同下固定邊界電位其視黏度對流道寬作圖觀察適用範圍 86 圖4-31 左右邊界電位相反對黏度的影響 87 圖4-32 本研究之擠壓模型與Chu等人[27]進行驗證 91 圖4-33 非對稱邊界電位下視黏度擠壓在擠壓過程中的變化 91 圖4-34 非對稱邊界電位下視黏度擠壓在擠壓過程中的變化 92 圖4-35 非對稱邊界電位下膜厚在擠壓過程中的變化 92 圖4-36 不同電位下擠壓區黏度變化 93 圖4-37 不同負載下擠壓區膜厚變化 94 圖4-38 不同材料下擠壓區膜厚變化 95 圖4-39 不同材料及負載下擠壓區壓力變化 96 圖4-40 不同負載下擠壓區壓力變化 97 圖4-41 不同材料下擠壓區壓力隨負載的變化 98

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