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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 許文翰 | |
| dc.contributor.author | Sheng-Tzung Yuan | en |
| dc.contributor.author | 袁聖宗 | zh_TW |
| dc.date.accessioned | 2021-06-16T16:18:23Z | - |
| dc.date.available | 2015-02-16 | |
| dc.date.copyright | 2013-02-16 | |
| dc.date.issued | 2013 | |
| dc.date.submitted | 2013-02-04 | |
| dc.identifier.citation | [1] Prashanta Dutta and Ali Breskok, Analytical solution of
combined electroosmotic/pressure driven flows in two- dimensional straight channels:Finite Debye layer effects, Anal. Chem., Vol 73, pp. 1979-7986, 2001 [2] Zhang Yao, Wu Jiankang. and Chen Bo, A coordinate transformation method for numerical solutions of the electric double layer and electroosmotic flows in a microchannel Int. J. for Numerical Methods in Fluids, Vol 68, pp. 671-685, 2012 [3] Grahame, D.C., The Electrical Double layer and the Theory of Electrocapillary, Chem. Rev., Vol. 44, pp. 441-501, 1947 [4] Neelesh A. Patankar, Howard H. Hu, Numerical Simulation of Electroosmotic Flow, Anal. Chem., Vol. 70, pp. 1870- 1881, 1998 [5] Shizhi Qian, Haim H. Bau, Theoretical investigation of electro-osmotic flows and chaotic stirring in rectangular cavities, Applied Mathematical Modelling, Vol. 29, pp. 726-753, 2005 [6] R.-J. Yang, L.-M. Fu, and C.-C. Hwang, Electroosmotic Entry Fwlow in a Microchannel, Journal of Colloid and Interface Science, Vol 244, pp. 173-179, 2001 [7] W.B. Russel, D.A. Saville, and W.R. Schowalter, Colloidal dispersions, cambridge monographs on mechanics and applied mathematics Cambridge University Press, cambridge, 1989. [8] S. V. Ptankar, Numerical Heat Transfer and Fuild Flow, Hemisphere, New York, 1980. [9] Chun Yang, Dongqing Li, , Jacob H. Masliyah, Modeling forced liquid convection in rectangularmicrochannels with electrokinetic effects, Int. J. Heat and Mass Transfer, Vol. 41, pp. 4229-4249, 1998 [10] Jahrul Alam, John C. Bowman, Energy-Conserving Simulation of Incompressible Electro-Osmotic and Pressure-Driven Flow, Theoretical and computational Fluid Dynamics, pp. 1-17, 2002. [11] U. Ghia, K. N. Ghia, High Re Solutions for incompressible Flow Using the Navier-Stokes Equation and a Multigrid Method, J. Comp. Physics, Vol. 48, pp. 387-411, 1982 [12] Tony W. H. Sheu and P. H. Chiu, A divergence-free-condition compensated method for incompressible Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, Vol. 196, pp. 4479-4494, 2007. [13] Tony W. H. Sheu and R. K. Lin, An incompressible Navier-Stokes model implemented on non-staggered grids, Numer. Heat Transf., B Fundam. Vol. 44(3), pp. 277-294, 2003. [14] 林瑞國, 不可壓縮黏性熱磁流之科學計算方法, 博士論文, 2005. [15] P. H. Chiu, Tony W. H. Sheu, On the development of a dispersion-relation-preserving dual-compact upwind scheme for convection-diffusion equation, Journal of Computational Physics., Vol. 228, pp. 3640-3655, 2009. [16] Richard D. Handy, A Frank von der Kammer, A Jamie R. Lead A, Martin Hassellov, A Richard Owen, A Mark Crane, The ecotoxicology and chemistry of manufactured nanoparticles, Ecotoxicology, Vol. 17, pp. 287-314, 2008. [17] Peter C. Chu, Chenwu Fan, A three-point combined compact difference scheme, J. Comput. Phys., Vol. 140, pp. 370-399, 1998. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/63004 | - |
| dc.description.abstract | 本論文發展一有限差分方法並在非正交曲線座標下求解電液動之非線性動力系統方程，這包含了描述外加電場之Laplace方程、描述壁面所施加之電位分布以及離子濃度分布的Poisson-Nernst-Planck方程組及由庫倫力所驅動的不可壓縮Navier-Stokes方程組。
論文之內容主要是使用離子守恆方程式Poisson-Nernst-Planck方程組，以描述電滲流模型，以觀察流速對離子分布的影響，及是否能描述受zeta電位所產生之電雙層，及描繪出靠近壁面之速度邊界層、電荷擴散層等物理行為。 | zh_TW |
| dc.description.abstract | In this study we aim to develop a high order scheme for approximating the spatial derivative terms shown in the Poisson-Nernst-Planck(PNP) as well as in the
incompressible Navier-Stokes(NS) equations. To resolve sharp solution profiles near the wall, within the three-point stencil the combined compact difference scheme in applied to yield sixth-order accuracy for the second-order derivative terms while fifth-order accuracy for the first-order derivative terms, the differential set of PNP-NS equations has been transformed to the nonlinear coordinates so as to be able to know how the channel curvature can affect the electroosmotic flow motion in a wavy channel. In this study the scheme in developed in detail and is analyzed rigorously though the modified equation analysis. In addition, the developed method has been computationally verified through three problems available to exact solutions. The electroosmotic flow details in plannar and channels have been revealed through this study with the emphasis an the formation of Coulomb force. The competition among the pressure gradient, diffusion and Coulomb forces leadings to the convective electroosmotic flow motion is also investigated in detail. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T16:18:23Z (GMT). No. of bitstreams: 1 ntu-102-R99525055-1.pdf: 11795822 bytes, checksum: f4693b1ee082f2512c6ce5637710d9ee (MD5) Previous issue date: 2013 | en |
| dc.description.tableofcontents | 摘要..................................................i
abstract............................................ii 第一章 序論 1.1 前言............................................2 1.2 研究動機.........................................3 1.3 文獻回顧.........................................4 1.4 論文大綱.........................................5 第二章 理論背景 2.1 電雙層..........................................8 2.2 電泳(Electrophoresis)現象.......................12 第三章 物理模型 3.1 基本假設........................................16 3.2 統御方程式.......................................16 3.2.1 電方程式...................................17 3.2.2 不可壓縮流之Navier-Stokes方程式[2]...........18 3.3 二維無因次化Electrohydrodynamics方程組............20 3.4 將無因次化方程組從卡式座標轉換到曲線座標..............22 第四章 數值方法 4.1 有限差分法......................................25 4.2 時間之離散格式...................................26 4.3 空間之離散格式 - Combined Compact difference方法..26 4.3.1 二階偏導數項的緊緻格式........................27 4.3.1 一階偏導數項的波數關係保持緊緻格式..............27 4.4 無散度補償方法之推導..............................31 4.5 壓力之離散格式...................................32 4.6 具面積保持特性之緊緻格式...........................33 4.7 計算程序........................................35 第五章 程式驗證 5.1 流體、電方程組之驗證..............................39 5.1.1 二維Navier-Stokes方程組之實解驗證............39 5.1.2 方腔拉穴流問題..............................40 5.1.3 二維Poisson-Nernst-Planck方程組之實解驗證....42 5.2 電滲流方程組解析解之驗證...........................44 5.2.1 電滲流直管解析解I............................44 5.2.2 電滲流直管解析解II...........................46 5.2.3 電滲流直管解析解III..........................47 5.3 數值驗證之結果....................................48 第六章 電滲流之數值模擬 6.1 問題之描述.......................................62 6.1.1 參數設定....................................62 6.2 二維電滲流之流場分析...............................62 6.2.1 計算模型之初始與邊界條件.......................62 6.2.2 討論.......................................66 第七章 結論 7.1 研究成果與討論....................................79 7.2 未來工作與展望....................................80 附錄A 簡化之Poisson-Nernst-Planck方程組 A.1 基本假設.........................................81 A.2 PNP方程組轉換到PB方程組............................82 A.3 電滲流直管解析解I方程組簡化..........................83 A.4 電滲流直管解析解II方程組簡化.........................84 A.5 電滲流直管解析解III方程組簡化........................85 參考文獻................................................86 | |
| dc.language.iso | zh-TW | |
| dc.subject | Poisson-Nernst-Planck 方程組 | zh_TW |
| dc.subject | 庫倫力 | zh_TW |
| dc.subject | 波浪狀流道 | zh_TW |
| dc.subject | 緊緻格式 | zh_TW |
| dc.subject | Navier-Stokes方程組 | zh_TW |
| dc.subject | Coulomb force | en |
| dc.subject | NS | en |
| dc.subject | three-point stencil | en |
| dc.subject | combined compact difference | en |
| dc.subject | wavy | en |
| dc.subject | PNP | en |
| dc.title | 在曲線座標下求解EHD方程 | zh_TW |
| dc.title | Calculation of the coupled system of PNP and NS equations in curvilinear coordinates | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 101-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 李佳翰,Yogesh G. Bhumkar | |
| dc.subject.keyword | Poisson-Nernst-Planck 方程組,Navier-Stokes方程組,緊緻格式,波浪狀流道,庫倫力, | zh_TW |
| dc.subject.keyword | PNP,NS,three-point stencil,combined compact difference,wavy,Coulomb force, | en |
| dc.relation.page | 87 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2013-02-04 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 工程科學及海洋工程學研究所 | zh_TW |
| 顯示於系所單位： | 工程科學及海洋工程學系 | |
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|---|---|---|---|
| ntu-102-1.pdf 未授權公開取用 | 11.52 MB | Adobe PDF |
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