臺灣博碩士論文加值系統

雖然工業上使用潤滑油作為機具部件潤滑已有數個世紀之久，但工業用油對環境有很大的汙染，許多研究者嘗詴以水做為潤滑油的替代品。但水的黏度不高，在潤滑上較難建立起能有效承受負載的潤滑液膜。而電雙層的存在能夠對水溶液提供讓黏度提升的效果，因此本研究在許多前人有關電雙層以及液動潤滑的研究基礎上，期望導出相較於以往電雙層適用性更廣的電雙層模型，並將電雙層效應與非等向滑移加入雷諾方程式，並堆導出修正型雷諾方程式使之更貼近真實工作情況下，嘗詴以含電解質的水溶液做為潤滑油的取代品。
本研究主要目的為分析考慮到使用含電解質水溶液在電雙層效應與非等向滑移條件下的頸軸承液動潤滑性能。所以探討流道寬、離子濃度、電位高低對黏度的影響，在研究中發現流道寬、離子濃度與電位高低對黏度皆有不小的影響，三者大小需彼此配合才能找到較佳的電黏度效應，以提升較多的黏度。在本研究中頸軸承的工作間隙需在微奈米等級，才會對頸軸承負載能力有較好的貢獻，而對降低頸軸承的摩擦係數則有較明顯的效果。考慮到現今加工技術對奈米等級的加工精度，仍有些困難但水潤滑仍然是值得關注與研究的目標。

In this research, based on many previous studies on electric double layer and hydraulic lubrication, this study hopes to derive an electric double layer model that is more applicable than the previous electric double layer model. The electric double layer effect and the non-isotropic slip are added to the Reynolds equation, and the modified Reynolds equation is derived to make it closer to the real working condition. And considers the hydraulic lubrication performance of the journal bearing under the condition of electric double layer effect and non-isotropic slip.
As a result, it was found that the flow path width, the ion concentration and the potential level have a significant influence on the viscosity. The three conditions need to cooperate with each other to find a better electro-viscosity effect to enhance the viscosity. The electric viscosity has a significant effect on reducing the friction coefficient of the journal bearing. But in this study the working clearance of the journal bearing needs to be in the nanometer level, which will have a good contribution to the bearing capacity of the journal bearing.

目錄
中文摘要----------------------------------------------------------------------------------- i
Extend Abstract --------------------------------------------------------------------------ii
誌謝-------------------------------------------------------------------------------------- xii
目錄------------------------------------------------------------------------------------- xiii
表目錄-----------------------------------------------------------------------------------xvi
圖目錄----------------------------------------------------------------------------------xvii
符號表-----------------------------------------------------------------------------------xix
第一章 緒論 ----------------------------------------------------------------------------- 1
1.1 前言---------------------------------------------------------------------------- 1
1.2 文獻回顧----------------------------------------------------------------------- 2
1.2.1 電雙層效應理論發展----------------------------------------------- 2
1.2.2 潤滑理論的發展----------------------------------------------------- 5
1.2.3 潤滑邊界條件的進展----------------------------------------------- 5
1.2.4 電雙層效應對水潤滑的影響-------------------------------------- 6
1.3 研究動機---------------------------------------------------------------------- 7
1.4 研究目的---------------------------------------------------------------------- 8
1.5 本文架構----------------------------------------------------------------------- 9
第二章 研究理論--------------------------------------------------------------------- 11
2.1 電雙層模型----------------------------------------------------------------- 12
2.1.1 統御方程式--------------------------------------------------------- 13
2.1.2 離子孚恆定律------------------------------------------------------ 14
2.2 雷諾方程式----------------------------------------------------------------- 19
2.2.1 基本假設------------------------------------------------------------ 19
2.2.2 流體的質量孚恆方程式(微分連續方程式) ------------------- 20
2.2.3 流體的動量孚恆方程式------------------------------------------ 20
2.2.4 奈維爾-史托克方程式--------------------------------------------- 23
2.2.5 雷諾方程式--------------------------------------------------------- 24
2.3 非等向滑移邊界條件----------------------------------------------------- 26
2.4 含電雙層效應與非等向滑移之修正型雷諾方程式----------------- 28
2.5 空蝕效應-------------------------------------------------------------------- 36
2.6 軸承性能分析-------------------------------------------------------------- 37
2.6.1 基本膜厚方程式---------------------------------------------------- 38
2.6.2 負載性能------------------------------------------------------------ 40
2.6.3 摩擦力與摩擦係數------------------------------------------------ 41
第三章 數值方法--------------------------------------------------------------------- 43
3.1 有限元素法----------------------------------------------------------------- 43
3.1.1 Galerkin 法----------------------------------------------------------- 44
3.1.2 有限元素法離散化------------------------------------------------ 44
3.1.3 牛頓-拉弗森演算法----------------------------------------------- 45
3.1.4 補償函數法--------------------------------------------------------- 47
3.2 有限元素法物件化--------------------------------------------------------- 47
第四章 結果與討論------------------------------------------------------------------ 48
4.1 電雙層效應------------------------------------------------------------------ 48
4.1.1 電雙層網格測詴---------------------------------------------------- 48
4.1.2 電雙層模型驗證--------------------------------------------------- 50
4.1.3 邊界電位與電雙層------------------------------------------------ 51
4.1.4 電位對視黏度之影響--------------------------------------------- 54
4.1.5 在固定液膜厚度下不同電位差的電雙層視黏度變化------- 57
doi:10.6844/NCKU201902676
xv
4.1.6 離子濃度對視黏度之影響--------------------------------------- 58
4.2 含電雙層與非等向滑移之頸軸承參數分析-------------------------- 61
4.2.1 頸軸承模型網格測詴--------------------------------------------- 62
4.2.2 頸軸承分析結果驗證--------------------------------------------- 63
4.2.3 偏心比對含電雙層效應頸軸承負載之影響------------------ 65
4.3 含電雙層效應與非等向滑移之頸軸承性能分析-------------------- 70
4.3.1 含電雙層效應與非等向滑移之負載能力分析--------------- 70
4.3.2 含電雙層與非等向滑移之摩擦係數比之分析--------------- 74
第五章 結論 --------------------------------------------------------------------------- 81
5.1 結論-------------------------------------------------------------------------- 81
參考文獻-------------------------------------------------------------------------------- 83
附錄一 數值運算驗算--------------------------------------------------------------- 89
表目錄
表 4-1 電雙層網格測詴使用之參數---------------------------------------------- 49
表 4-2 電雙層模型網格加密測詴網格數目與電位差異---------------------- 49
表 4-3 與Qu and Li[8]驗證使用之參數表--------------------------------------- 50
表 4-5 頸軸承網格測詴使用之操作參數---------------------------------------- 62
表 4-6 含電雙層之頸軸承滑移模型加密測詴網格數目---------------------- 63
表 4-7 細長比對負載能力的影響表---------------------------------------------- 74
表 4-8 剪切應力zx  的項分部------------------------------------------------------- 76
圖目錄
圖 1-1 Helmholtz 模型示意圖-------------------------------------------------------------- 4
圖 1-2 Stern 模型示意圖-------------------------------------------------------------------- 4
圖 1-3 本研究架構流程-------------------------------------------------------------------10
圖 2-1 含電雙層之頸軸承示意圖-------------------------------------------------------12
圖 2-2 不對稱電位流道示意圖----------------------------------------------------------18
圖 2-3 連續方程式中單位體積內之各質量流率分量示意圖-----------------------22
圖 2-4 動量孚恆方程式中單位體積元素所受應力示意圖--------------------------22
圖 2-5 滑移與滑移長度示意圖-----------------------------------------------------------27
圖 2-6 非等向滑移示意圖-----------------------------------------------------------------27
圖 2-7 以軸承運轉為例，空蝕現象之示意圖-----------------------------------------37
圖 2-8 軸承偏心時之潤滑型態示意圖--------------------------------------------------39
圖 2-9 穩態負載說明圖--------------------------------------------------------------------41
圖 3-1 牛頓法疊代求解過程示意圖-----------------------------------------------------46
圖 3-2 有限元素法求解流程圖-----------------------------------------------------------46
圖 4-1 與Qu and Li[8]比較驗證電雙層模型------------------------------------------51
圖 4-2 在對稱電位下與Debye-Huckel 近似解比較---------------------------------53
圖 4-3 κh=5，不對稱表面電位的電位分佈比較--------------------------------------53
圖 4-4 在ζ1 = -75 mV, ζ2 電位不同下視黏度的變化---------------------------------55
圖 4-5 在 ζ1 = -90 mV, ζ2 電位不同下視黏度的變化---------------------------------55
圖 4-6 在ζ1 = -120 mV, ζ2 電位不同下視黏度的變化--------------------------------56
圖 4-7 在ζ1 = -160 mV, ζ2 電位不同下視黏度的變化--------------------------------56
圖 4-8 在 ζ1 固定以ζ1 與ζ2 電位差異觀察視黏度的變化--------------------------58
圖 4-9(a) 離子濃度不同下無因次視黏度對流道寬作圖----------------------------59
圖 4-9(b) 離子濃度不同下無因次視黏度對流道寬作圖----------------------------60
圖 4-10 與Jao 等人[35]比較驗證頸軸承模型----------------------------------------64
圖 4-11 短軸承在偏心比改變與負載能力變化---------------------------------------66
圖 4-12 短軸承在c = 1μm 下不同電位與偏心比負載能力比較------------------66
圖 4-13 短軸承在c = 0.1μm 下不同電位與偏心比負載能力比較----------------67
圖 4-14 方軸承在偏心比改變與負載能力變化---------------------------------------67
圖 4-15 方軸承在不同電位與偏心比負載能力比較---------------------------------68
圖 4-16 長軸承在c = 0.1μm 下偏心比改變與負載能力變化----------------------68
圖 4-17 長軸承在不同電位與偏心比負載能力比較---------------------------------69
圖 4-18(a) 短軸承在-75 mV 電位下不同滑移長度與滑移組合之負載----------71
圖 4-18(b) 短軸承在-75 mV 電位下不同滑移長度與滑移組合之負載----------71
圖 4-18(c) 短軸承在-75 mV 電位下不同滑移長度與滑移組合之負載----------72
圖 4-19(a) 長軸承在-75 mV 電位下不同滑移長度與滑移組合之負載----------72
圖 4-19(b) 長軸承在-75 mV 電位下不同滑移長度與滑移組合之負載----------73
圖 4-19(c) 長軸承-75 mV 電位下在不同滑移長度與滑移組合之負載----------73
圖 4-20 視黏度與初始黏度趨勢比較----------------------------------------------------77
圖 4-22 不同滑移長度下之剪應力(剪切速度項)圖----------------------------------77
圖 4-23(a) 短軸承在-75 mV 電位下不同滑移長度與滑移組合之COF----------78
圖 4-22(b) 短軸承在-75 mV 電位下不同滑移長度與滑移組合之COF----------78
圖 4-22(c) 短軸承在-75 mV 電位下不同滑移長度與滑移組合之COF----------79
圖 4-24(a) 長軸承在-75 mV 電位下不同滑移長度與滑移組合之COF----------79
圖 4-23(b) 長軸承在-75 mV 電位下不同滑移長度與滑移組合之COF----------80
圖 4-23(c) 長軸承在-75 mV 電位下不同滑移長度與滑移組合之COF----------80

參考文獻
[1] W. L. Li, “Effects of Electrodouble layer (EDL) and Surface Roughness
on Lubrication Theory, Tribology Letters, Vol. 20, pp. 53-61, 2005.
[2] D. Li, “Electro-viscous Effects on Pressure-driven Liquid Flow in
Microchannel, Colloids and Surfaces, Vol 195, pp. 35-57, 2001.
[3] D. Jing, Y. Pan, X. Wang, “The Non-monotonic Overlapping
EDL-induced Electroviscous Effect With Surface Charge-dependent Slip
and its Size Dependence, International Journal of Heat and Mass
Transfer, Vol. 113, pp. 32-39, 2017.
[4] H. Helmholtz, “Ueber einige Gesetze der Ver Vertheilung elektrischer
Ströme in körperlichen Leitern mit Anwendung auf die
thierisch-elektrischen Versuche, Annalen der Physik und Chemie, Vol.
165, pp. 211-233, 1853.
[5] M. Gouy, “Sur la constitution de la charge électrique à la surface d’un
electrolyte, Journal de Physique, Vol. 9, pp. 457-468, 1910.
[6] D. L. Chapman, “A Contribution to the Theory of Electrocapillarity,
The London, Edinburgh, and Dublin Philosophical Magazine and
Journal of Science, Vol. 25, pp. 475-48, 2010.
[7] O. Stern, “Zur theorie der elektrolytischen doppelschicht
Z. Elecktrochem., 30, 508-516, 1924.
[8] W. Qu, D. Li, “A Model for Overlapped EDL Fields, Journal of Colloid
and Interface Science, pp.397-407, 1999.
[9] C. L. Ren, D. Li, “Improved Understanding of the Effect of Electrical
Double Layer on Pressure-driven Flow in Microchannels, Analytica
Chimica Acta, Vol. 531, pp. 15-23, 2005.
[10] H. Ban, B. Lin and Z Song., “Effect of Electrical Double Layer on
Electric Conductivity and Pressure Drop in a Pressure-driven
Microchannel Flow, Biomicrofluidics 4, 014104, 2010.
[11] D. Dowson, History of tribology, Longman Group Limited, 1979.
[12] C. L. Navier, “Mémoire sur les lois du mouvement des fluides, Royale
Academie des Sciences, France 6, pp. 389-440, 1823.
[13] O. Reynolds, “On the Theory of Lubrication and its Application to Mr.
Beauchamp Tower’s Experiments, Including an Experimental
Determination of the Viscosity of Olive Oil, Royal Society of London,
3rd series, pp. 1-19, 1886.
[14] V. S. Craig, C. Neto, and D. R. Williams, “Shear-dependent Boundary
Slip in an Aqueous Newtonian Liquid, Phys Rev Lett, vol. 87, p.
054504, 2001.
[15] E. Bonaccurso, M. Kappl and H. J. Butt, “Hydrodynamic Force
Measurements: Boundary Slip of Water on Hydrophilic Surfaces and
Electrokinetic Effects, Physical Review Letters, Vol. 88, p. 076103,
2002.
[16] Y. Zhu and S. Granick, “Rate-dependent slip of Newtonian liquid at
smooth surfaces, Phys Rev Lett, vol. 87, pp. 096-105, 2001.
[17] S. Granick and Y. X. Zhu, “Apparent Slip of Newtonian Fluids Past
Adsorbed Polymer Layers, Macromolecules, vol. 35, pp. 4658-4663,
2002.
[18] Y. Zhu and S. Granick, “Limits of the Hydrodynamic No-slip Boundary
Condition, Phys Rev Lett, vol. 88, pp. 106-102, 2002.
[19] S. Granick and Y. X. Zhu, “The No Slip Boundary Condition Switches to
Partical Slip When Fluid Contains Surfactant, Langmuir, vol. 18, pp.
10058-10063, 2002.
[20] R.Pit,H. Hervet and L.Leger, “Direct Experimental Evidence of Slip in
Hexadecane Solid Interfaces, Phys Rev Lett, vol. 85, pp. 980-983, 2000.
[21] O. I. Vinogradova, “Slippage of Water Over Hydrophobic Surfaces,
International Journal of Mineral Processing, vol. 56, pp. 31-60, 1999.
[22] A.V. Belyaev and O. I. Vinogradova, “Effective Slip in Pressure-Driven
Flow Past Super-Hydrophobic Stripes, J. Fluid Mech, vol. 652, pp.
489-499, 2010.
[23] M. Z. Bazant and O. I. Vinogradova, “Tensorial Hydrodynamic Slip,
Journal of Fluid Mechanics, vol. 613, pp. 125-134, 2008.
[24] A. D. Stroock, S. K. Dertinger, G. M. Whitesides and A. Ajdari,
“Patterning Flows Using Grooved Surfaces, Analytical Chemistry, Vol.
74, pp. 5306-5312, 2002.
[25] N. Ishida, T. Inoue, M. Miyahara and K. Higashitani, “Nano Bubbles on
a Hydrophobic Surface in Water Observed by Tapping-Mode Atomic
Force Microscopy, Langmuir, Vol. 16, pp. 6377-6380, 2000.
[26] C. Cottin-Bizonne, S. Jurine, J. Baudry, J. Crassous, F. Restagno, and E.
Charlaix, “Nanorheology: An Investigation of the Boundary Condition at
Hydrophobic and Hydrophilic Interfaces, Eur Phys J E Soft Matter,
vol. 9, pp. 47-53, 2002.
[27] Y. Zheng, X. Gao and L. Jiang, “Directional Adhesion of 92
Superhydrophobic Butterfly Wings, Soft Matter, Vol. 3, pp. 178-182,
2007.
[28] David Quéré, “Non-sticking Drops, Reports on Progress in Physics,
Vol. 68, pp. 2495-2532, 2005.
[29] F. Chen, D. Zhang, Q. Yang, X. Wang, B. Dai, X. Li, X. Hao, Y. Ding, J.
Si and X. Hou, “Anisotropic Wetting on Microstrips Surface Fabricated
by Femtosecond Laser, Langmuir, Vol. 27, pp. 359-365, 2011.
[30] J. Ou and J. P. Rothstein, “Direct Velocity Measurements of the Flow
Past Dragreducing Ultrahydrophobic Surfaces, Physics of Fluids, Vol.
17, p. 103606, 2005.
[31] P. Joseph, C. Cottin-Bizonne, J.-M. Benoit, C. Ybert, C. Journet, P.
Tabeling and L. Bocquet, “Slippage of Water Past Superhydrophobic
Carbon Nanotube Forests in Microchannels, Physics Review Letters,
Vol. 97, p. 156104, 2006.
[32] C. H. Choi, U. Ulmanella, J Kim., C. M. Ho and C. J. Kim, “Effective
Slip and Friction Reduction in Nanograted Superhydrophobic
Microchannels, Physics of Fluids, Vol. 18, p. 087105, 2006.
[33] J. H. Choo, R. P. Glovnea, A. K. Forrest and H. A. Spikes, “A Low
Friction Bearing Based on Liquid Slip at the Wall, Journal of
Tribology, Vol. 129, pp. 611-620, 2007.
[34] C. Y. Chen, Q. D. Chen and W. L. Li, “Characteristics of Journal
Bearings with Anisotropic Slip, Tribology International, Vol. 61, pp.
144-156, 2013.
[35] H.C. Jao, K.M. Chang, L.M. Chu, and W.L. Li, “A Lubrication Theory
for Anisotropic Slips and Flow Rheology, Tribology Transactions, vol.
59, pp. 252-266, 2016.
[36] C. L. Rice, R. Whitehead, “Electrokinetic Flow in a Narrow Cylindrical
Capillary, The Journal of Physical Chemistry, pp.4017-4024, 1965.
[37] S. Levine, J. R. Marriott, G. Neale and N. Epstein, “Theory of
electrokinetic Flow in Fine Cylindrical Capillaries at High
Zeta-potential, Journal of Colloid and Interface Science, Vol. 52, pp.
136-149, 1975.
[38] D. Prieve and S. G. bike, “Electrokinetic Repulsion Between Two
Charged Bodies Undergoing Sliding Motion, Chemical Engineering
Communications, Vol 55, pp. 149-164, 1987.
[39] Z. Bo and N. Umehara, “Hydrodynamic Lubrication Theory Considering
Electric Double Layer for Very Thin Water Film Lubrication of
Ceramics, JSME International Journal Series C Mechanical Systems,
Machine Elements and Manufacturing, Vol. 4, pp. 285-290, 1998.
[40] W. L. Li and Z. Jin, “Effects of Electrokinetic Slip Flow on Lubrication
Theory, Journal of Engineering Tribology, Vol. 222, pp. 109-120,
2008.
[41] S. X. Bai, P. Huang, Y. G. Meng and S. Z Wen, “Modeling and Analysis
of Interfacial Electro-kinetic Effects on Thin Film Lubrication,
Tribology International, vol. 39, 1405-1412, 2002.
[42] P. L. Wong, Y. Meng and P. Huang, The Effect of the Electric Double
Layer on Very Thin water Lubricating Film, Tribology Letters, Vol. 14,
pp. 197-203, 2003.
[43] Q.Y. Zuo, T. M. Lai and P. Huang, “The Effect of the Electric Double
Layer on Very Thin Thermal Elastohydrodynamic Lubricating Film,
Tribology Letters, Vol. 45, pp. 455-463, 2012.
[44] Q. Y. Zuo, P. Huang and F. H. Su, “Theory Analysis of Asymmetrical
Electric Double Layer Effects on Thin Film Lubrication, School of
Mechanical and Automotive Engineering, Vol. 18, pp. 67-74, 2012.
[45] D. L. Jing, Y. Pan and X. M. Wang, “The Effect of the Electrical Double
Layer on Hydrodynamic Lubrication: a Non-monotonic Trend with
Increasing Zeta Potential , Beilstein J Nanotechnol, Vol. 8, pp.
1515-1522, 2017.
[46] G. R. Wiese and T. W. Healy, “Coagulation and Electrokinetic Behavior
of TiO2 and Al2O3 Colloidal Dispersions, Journal of Colloid and
Interface Science, Vol. 51, pp. 427-433, 1975.
[47] S. R. Wu, “A Penalty Formulation and Numerical Approximation of the
Reynolds-Hertz Problem of Elastohydrodynamic Lubrication,
International Journal of Engineering Science, Vol. 24, pp. 1001-1013,
1986.