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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 葉超雄(Chau-Shioung Yeh) | |
| dc.contributor.author | Meng-Chien Wu | en |
| dc.contributor.author | 吳孟謙 | zh_TW |
| dc.date.accessioned | 2021-06-15T02:53:48Z | - |
| dc.date.available | 2009-08-06 | |
| dc.date.copyright | 2009-08-06 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-08-04 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/44372 | - |
| dc.description.abstract | 本研究主要探討小尺度的血液流動問題(直徑尺寸介於40μm~500μm)，考慮分層現象、紅血球的濃度分佈與紅血球顆粒之微觀平均旋轉與變形量。以雙層流體模型進行理論分析，雙層模型的外層為牛頓流體，內層為微形流體，我們解得旋轉場、速度場、體積流率與管壁上之無因次應力場理論解。理論之模擬結果符合F效應與F-L效應。最後將理論延伸應用於：(1)解析狹窄血管模型的阻力與管壁應力問題，(2)提出以微形流體為架構的穆瑞定律。
對於分層現象與紅血球的濃度分佈問題，本研究建立了小尺度血管濃度-管徑-分層位置之理論式，將分層厚度視為相依變數，使獨立變數因而降低，提高了雙層流體模型之微形流體各場量理論解的應用性。 數值模擬方面，提出邊界上旋轉場的修正參數β1，並以數值方法逼近速度場實驗結果反算求得最佳修正參數β1，建議值為0.3。實際問題中，計算了冠狀動脈狹窄管在各種濃度下對應之無因次阻力與壁面無因次剪力，將模擬結果與各種血液病症之實驗結果相互對照；最後，我們提出微形流體理論對穆瑞定律之修正。 本論文為微形流體數值計算過程中高度不定自由度解析過程提供了一套化簡的方法，理論解推廣的問題皆有數值模擬結果與實驗數據相互比較。 | zh_TW |
| dc.description.abstract | This study focused on the blood flow in small-scale problems (diameter between 40μm ~ 500μm), consider the stratification, the red blood cells (RBCs) distribution and the deformability of RBCs. Two-layer fluid model to the theoretical analysis of the peripheral layer for the Newtonian fluid, the inner layer for the micromorphic fluid. We derive the velocity field, microrotate field, the volume flow rate and the wall shear stress. Simulation results in line with the effect of the F effects and the F-L effects. Finally, an extension of the theory applies to: (1) Analysis of the problem with the stenosis blood vessels (2) The modification of Murray's law.
For the problem of stratification thickness, this study established the theorical relation between RBCs concentration distribution and the location of interface, which is between the peripheral layer and the core region. We reducing the number of independent variables in this theory by considering the thickness of peripheral layer is a dependent variable, thereby increasing the possibility of application of this theory. In the numerical simulation, we will use seven micromorphic fluid’s viscosity coefficients given by Ligia et al. [2006]. By inverse methods to obtain the optimal parameter β1. In further applications：First, we not only calculated the stenosis of coronary vascular resistance and wall shear stress, but also compared the results of simulation to the blood disease experimental data, the second, we reformulate the Murray’s law by micromorphic blood fluid. The theoretical solution of the issue both have numerical simulation and experimental data cross-referencing. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T02:53:48Z (GMT). No. of bitstreams: 1 ntu-98-R96543016-1.pdf: 2485895 bytes, checksum: 80a6276b6e888aef9c017b1d672bce07 (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | 誌謝 i
摘要 ii Abstract iii 目錄 v 圖目錄 ix 表目錄 xi 符號表 xii 第 一 章 緒論 1 1.1前言 1 1.2文獻回顧 3 1.3研究動機 10 1.4論文架構 12 第 二 章 血液的性質與流變現象 13 2.1血液的組成 13 2.2血液的流變特性 16 2.2.1簡介血液黏滯性 16 2.2.2溫度對血液黏度的影響 18 2.2.3剪應變率對血液黏度的影響 19 2.2.4濃度對血液黏度的影響 20 2.2.5管徑尺寸對血液黏度的影響 21 2.3血液的小尺度效應與現象 22 2.3.1分層現象 22 2.3.2 F效應 23 2.3.3 F-L效應 25 第 三 章 微連續體力學基本原理 26 3.1微連續體簡介 26 3.2宏觀自由度與微觀自由度 28 3.3運動與變形 30 3.3.1宏觀元素與微觀元素的位置向量 30 3.3.2速度與加速度 32 3.3.3變形梯度與速度梯度 33 3.4微觀場之區域平均 36 3.4.1應用張量積的廣義轉動物理量 36 3.4.2微觀場量的平均 37 3.5微連續體之平衡方程式 41 3.5.1宏觀質量守恆 41 3.5.2微觀質量守恆 41 3.5.3微慣性矩守恆 42 3.5.4線動量守恆 43 3.5.5角動量守恆 44 3.5.6能量守恆 47 3.6基本守恆方程式總整理 52 3.7組成律 53 第 四 章 小動脈數學模型與理論解 59 4.1微形流體之矩形渠道問題 60 4.1.1基本假設 60 4.1.2邊界條件 61 4.1.3統御方程式 61 4.2微形流體之圓形管問題 65 4.2.1濃度分布與分層位置 65 4.2.2雙層流體模型 67 4.2.2基本假設 68 4.2.3邊界條件 69 4.2.4統御方程式 71 4.3理論解 73 4.4管壁的剪力與阻力 76 第 五 章 數值模擬與分析 79 5.1數值模擬流程 80 5.2數值分析[階段一]：計算濃度分布參數n 81 5.3數值分析[階段二]：計算黏滯性係數 85 5.3.1外層黏滯係數 86 5.3.2內層黏滯係數 90 5.4數值分析[階段三]：計算最佳參數β1 92 5.5數值結果與討論 94 第 六 章 理論之應用 99 6.1理論之應用[一]：穆瑞定律與最佳分岔角度分析 99 6.1.1耗能函數 99 6.1.2分岔系統 101 6.1.3 分岔應用之數值分析 108 6.2理論之應用[二]：阻塞分析 110 6.2.1阻塞模型 110 6.2.2阻力與管壁剪應力 111 6.2.3 阻塞應用之模擬結果與討論 113 第 七 章 結論與建議 116 7.1結論 116 7.2未來展望 118 參考文獻 119 附錄A 詳細推導過程I 126 A.1.1不可壓縮微形連續體線動量守恆之化簡過程: 126 A.1.2不可壓縮微形連續體角動量式化簡過程: 128 附錄B 詳細推導過程II 138 B.1.1體積流率關係式之計算過程 138 B.1.2體積流率之進一步化簡過程 141 B.1.3穆瑞定律耗能函數微分求極值之過程 143 附錄C 圓柱座標與卡氏座標的轉換 148 附錄D 微形流體黏滯係數 150 | |
| dc.language.iso | zh-TW | |
| dc.subject | 雙層流體模型 | zh_TW |
| dc.subject | 穆瑞定律 | zh_TW |
| dc.subject | 血管阻塞 | zh_TW |
| dc.subject | 微形連續體力學 | zh_TW |
| dc.subject | 微形流體 | zh_TW |
| dc.subject | 血液動力學 | zh_TW |
| dc.subject | 血液流變性 | zh_TW |
| dc.subject | Two layered fluid model | en |
| dc.subject | Blood rheology | en |
| dc.subject | Hemodynamics | en |
| dc.subject | Micromorphic fluid | en |
| dc.subject | Microcontinnum theory | en |
| dc.subject | Murray’s law. | en |
| dc.subject | Stenosis | en |
| dc.title | 小血管分層血液模型之微連續體理論與數值分析 | zh_TW |
| dc.title | Micromorphic Modeling of Two-Layer blood flow through small arteries | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.coadvisor | 陳國慶(Kuo-Ching Chen) | |
| dc.contributor.oralexamcommittee | 陳東陽(Tungyang chen),鄧崇任 | |
| dc.subject.keyword | 微形連續體力學,微形流體,血液動力學,血液流變性,雙層流體模型,血管阻塞,穆瑞定律, | zh_TW |
| dc.subject.keyword | Microcontinnum theory,Micromorphic fluid,Hemodynamics,Blood rheology,Two layered fluid model,Stenosis,Murray’s law., | en |
| dc.relation.page | 153 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2009-08-04 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 應用力學研究所 | zh_TW |
| 顯示於系所單位： | 應用力學研究所 | |
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| ntu-98-1.pdf 未授權公開取用 | 2.43 MB | Adobe PDF |
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