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| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 許文翰 | |
| dc.contributor.author | Sheng-Feng Wang | en |
| dc.contributor.author | 王聖鋒 | zh_TW |
| dc.date.accessioned | 2021-06-16T13:33:26Z | - |
| dc.date.available | 2013-07-19 | |
| dc.date.copyright | 2013-07-19 | |
| dc.date.issued | 2013 | |
| dc.date.submitted | 2013-07-19 | |
| dc.identifier.citation | [1] Prashanta Dutta and Ali Beskok,
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, 國立台灣大學博士論文, 2005. [15] Christopher K. W. Tam, Jay C. Webb, Dispersion-ralation-preserving finite difference schemes for computational acoustics, Journal of Computational Physics., Vol. 194, pp. 194-214, 1993. [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] 袁聖宗,在曲線座標下求解非線性EHD方程, 國立台灣大學碩士論文, 2013. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/62200 | - |
| dc.description.abstract | 本論文在有限差分的架構下發展一數值方法
以求解二維之對流-擴散方程。 首先發展兩個具有無條件單調性之五點離散格式， 再引入權重係數將兩離散格式做一線性之疊加， 使其具有色散關係保持的九點離散格式。 利用此一數值方法求解電液動(EHD)之非線性動力系統方程， 此系統包含了描述外加電場之Laplace方程、描述壁面所施加之電位分佈以及離子濃度分佈的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Poisson-Nernst-Planck方程組，以描述電滲流模型，以觀察流速對離子分佈的影響， 以及描述受zeta電位所產生之電雙層，及描繪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 the numerical scheme for solving the unsteady
convection-diffusion scalar equation is developed in a domain of two dimensions. Two newly developed unconditionally monotonic five-point schemes, which have one common nodal point, are linearly combined through a weighting coefficient to yield the proposed nine-point conditionally monotonic scheme. Our main objective is to get a dispersively more accurate result from the nine-point stencil conditionally monotonic scheme. We also apply the nine-point stencil scheme to simulate Eelectroosmotic flow.The electroosmotic flow details in plannar and channels are revealed through this study with the emphasis placed 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 2021-06-16T13:33:26Z (GMT). No. of bitstreams: 1 ntu-102-R00525059-1.pdf: 11002549 bytes, checksum: 5465aef5f4acd2447c283c62ab2cd53e (MD5) Previous issue date: 2013 | en |
| dc.description.tableofcontents | 誌謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
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 8 2.1 電雙層之內涵. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 電泳(Electrophoresis)現象 . . . . . . . . . . . . . . . . . . . . . . . . 12 第三章 物理模型16 3.1 基本假設. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2 統御方程式. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2.1 描述外加電場電位勢之Laplace方程式. . . . . . . . . . . . . 17 3.2.2 描述壁面電位勢之Poisson方程式 . . . . . . . . . . . . . . . . 17 3.2.3 描述正負離子分佈之Nernst-Planck方程式. . . . . . . . . . . 18 3.2.4 不可壓縮黏性流之Navier-Stokes方程式[2] . . . . . . . . . . 18 3.3 二維無因次化Electrohydrodynamics方程組. . . . . . . . . . . . . . 20 3.4 將無因次方程組從卡式座標轉換到曲線座標系統. . . . . . . . . . . 22 第四章 數值方法之建構25 4.1 有限差分離散方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.2 時間之離散格式.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.3 空間之離散格式... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.3.1 二維CDR精確之差分格式.. . . . . . . . . . . . . . . . . . . . 27 4.3.2 二維角點CDR精確之差分格式.. . . . . . . . . . . . . . . . . . 28 4.3.3 二維九點CDR-DRP精確之差分格式.. . . . . . . . . . . . . . . 30 4.3.4 基本分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.4 求解不可壓縮流之無散度補償方法之推導.. . . . . . . . . . . . . . 48 4.5 壓力之離散格式.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.6 具面積比保持特性之緊緻格式.. . . . . . . . . . . . . . . . . . . . . . . 50 4.7 計算程序. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 第五章 程式驗證 56 5.1 流體、電方程組之驗證. . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.1.1 二維Navier-Stokes方程之實解驗證. . . . . . . . . . . . . . . 56 5.1.2 方腔拉穴流問題之測試. . . . . . . . . . . . . . . . . . . . . . 57 5.1.3 二維Poisson-Nernst-Planck (PNP)方程組之實解驗證. . . . 59 5.2 電滲流方程組解析解之驗證. . . . . . . . . . . . . . . . . . . . . . . . 60 5.2.1 電滲直流管解析解I . . . . . . . . . . . . . . . . . . . . . . . . 60 5.2.2 電滲直流管解析解II . . . . . . . . . . . . . . . . . . . . . . . . 62 5.2.3 電滲直流管解析解III . . . . . . . . . . . . . . . . . . . . . . . 63 5.3 數值驗證之結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 第六章 電滲流之數值模擬78 6.1 問題之描述. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.1.1 參數設定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.2 二維電滲流之流場分析. . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.2.1 計算模型之初始與邊界條件.. . . . . . . . . . . . . . . . . . . . 78 6.2.2 結果討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 第七章 結論 118 7.1 研究成果與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 7.2 未來工作與展望. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 附錄A 經簡化後之Poisson-Nernst-Planck方程組推導 120 A.1 基本假設. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 A.2 Poisson-Nernst-Planck方程組轉換到Poisson-Boltzmann方程之推導121 A.3 電滲流直管解析解I方程組之推導. . . . . . . . . . . . . . . . . . . 122 A.4 電滲流直管解析解II方程組之推導. . . . . . . . . . . . . . . . . . . 123 A.5 電滲流直管解析解III方程組之推導. . . . . . . . . . . . . . . . . . 124 參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 | |
| dc.language.iso | zh-TW | |
| dc.subject | 色散關係保持 | zh_TW |
| dc.subject | Navier-Stokes 方程組 | zh_TW |
| dc.subject | 波浪狀流道 | zh_TW |
| dc.subject | 庫倫力 | zh_TW |
| dc.subject | 無條件單調性 | zh_TW |
| dc.subject | Poisson-Nernst-Planck 方程組 | zh_TW |
| dc.subject | Coulomb force | en |
| dc.subject | PNP | en |
| dc.subject | NS | en |
| dc.subject | unconditionably monotonic | en |
| dc.subject | nine-point stencil | en |
| dc.subject | wavy | en |
| dc.title | 發展求解NS與PNP耦合方程之方法 | zh_TW |
| dc.title | Development of a numerical method for solving the coupled NS and PNP equations | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 101-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 李佳翰,王安邦,林太家 | |
| dc.subject.keyword | 無條件單調性,色散關係保持,Poisson-Nernst-Planck 方程組,Navier-Stokes 方程組,波浪狀流道,庫倫力, | zh_TW |
| dc.subject.keyword | PNP,NS,unconditionably monotonic,nine-point stencil,wavy,Coulomb force, | en |
| dc.relation.page | 127 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2013-07-19 | |
| 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 |
| Appears in Collections: | 工程科學及海洋工程學系 | |
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| ntu-102-1.pdf Restricted Access | 10.74 MB | Adobe PDF |
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