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  • 學位論文

小血管分層血液模型之微連續體理論與數值分析

Micromorphic Modeling of Two-Layer blood flow through small arteries

指導教授 : 葉超雄
共同指導教授 : 陳國慶(Kuo-Ching Chen)

摘要


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。

並列摘要


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.

參考文獻


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