微循環是指心血管系統的終端血管網路的血液循環，其中血管尺寸可小至幾微米。血液和組織細胞之間的物質交換，例如氧氣、二氧化碳和營養物質皆發生在微循環中。此外，微流體裝置以被顯示具有按照細胞大小或硬度對細胞進行分類的潛力。因此，更好地了解微米流中的血液流動實屬重要。此論文使用一個離散描述來模擬紅血球，結合晶格波茲曼法與沈浸邊界法來研究微流通道中的血流。

本論文研究翻滾或皮划艇似的紅血球在剪切流的影響下在侷限微流道中的組態重組。在小雷諾數 (Re = 0.1) 和小毛細管數 (Ca) 的條件下，考慮流體與懸浮 粒子的流體力學耦合但不額外引進紅血球間的黏附作用，這項研究揭示了盤狀 似的紅血球之間的流體動力學交互作用促使紅血球排列成行，並且行與行、細胞與細胞之間的間隔規律，此外細胞行列間可見同步旋轉的紅血球配對，在此 稱為華爾滋配對。此剪切誘發的紅血球組態重組並未明顯地改變這個可形變粒子懸浮夜的剪切稀化特性。然而，特性黏度對微觀結構重組特別敏感。特性黏 度對細胞體積分率 𝜙 和Ca 的關聯性與紅血球配對體積分率相關。經由與一個雙細胞系統的比較，其中細胞的體積分率經由改變模擬場域體積來控制，此稀薄紅血球懸浮液中的血球集體運動進一步獲得驗證。

本論文也檢視在微流通道中的可黏聚性紅血球懸浮液的紅血球細胞空乏層厚度。數個因素會影響懸浮液黏度、紅細胞空乏層厚度和在微流道中的細胞分 佈，其中包括紅血球細胞比容、血管大小、紅細胞硬度、黏聚交互作用和剪切 速率。特別是，剪切速率對紅細胞空乏層厚度的影響尚有分歧。本論文研究發現，在低剪切速率的極限下，隨著剪切速率的增加，可黏聚性紅血球懸浮液的 相對粘度首先增加，接著降低。只要剪切速率足夠強，相對粘度就會隨著剪切 速率的進一步增加而減小。紅血球細胞空乏層厚度可以闡明此相對黏度對剪切 速率非單調的相依性。

Microcirculation is the blood circulation in the terminal vascular network of the cardiovascular system where the vessel size can be down to a few micrometers. The exchange of substances, such as oxygen, carbon dioxide, and nutrients, between the blood and tissue cells takes place in the microcirculation. Additionally, microfluidic devices have shown the potential to sort cells by size or by stiffness. Therefore, it is vital to have a better understanding of blood perfusion in microflows. Herein, a discrete model for the red blood cell (RBC) and the lattice Boltzmann method coupled with the immersed boundary method are applied to investigate blood flow in microchannels.

This thesis examines the shear-induced reorganization of tumbling/kayaking red blood cells (RBCs) in confined shear flow. For small Reynolds (Re = 0.1) and capillary numbers (Ca), with fully coupled hydrodynamic interaction and without intercellular adhesion, this study reveals that hydrodynamic interaction between disk-like RBCs prompts the formation of well-spaced RBC files and synchronized rotating RBC pairs, referred as "waltzing doublets". This shear-induced reorganization of RBCs does not significantly change the shear-thinning nature of this deformable particle suspension. Nevertheless, the intrinsic viscosity is particularly sensitive to microstructural rearrangements. The dependence of the intrinsic viscosity on the cell volume fraction 𝜙 and Ca is correlated with the change in the RBC doublet fraction. The shear-induced collective motion of RBCs in this dilute suspension is verified by comparison with a two-cell system where 𝜙 is controlled by varying the domain volume.

The cell-free layer thickness δ of an aggregating RBC suspension in microchannels is also investigated. Several factors affect the suspension viscosity, δ, and cell distribution in the microchannel, including the hematocrit, vessel size, red cell stiffness, aggregation interaction, and shear rate. In particular, the shear rate effect on δ is controversial. This study indicates that as the shear rate increases, the relative viscosity η of the aggregating RBC suspension first increases followed by a decrease in the low shear rate regime. As long as the shear rate is strong enough, η decreases as the shear rate further increases. This non-monotonic dependence of η on the shear rate can be elucidated by δ of this aggregating RBC suspension.

Abstract (Chinese) I
Abstract II
Acknowledgments IV
Contents V
List of Figures VIII
List of Tables XVI

1 General Introduction 1
1.1 Research Objectives........................... 1
1.2 Thesis Outline.............................. 2
1.3 Human Blood.............................. 2
1.4 Cardiovascular System ......................... 6
1.5 Microcirculation............................. 6
1.6 Blood Flow in Microcirculation .................... 7
1.7 Cell-Free Layer Formation ....................... 9
1.8 Red Blood Cell Aggregation ...................... 10
1.8.1 Bridging Model ......................... 11
1.8.2 Depletion Model ........................ 12
1.8.3 Recent Progress......................... 13

2 Red Blood Cell Modeling 14
2.1 Red Blood Cell Structure........................ 14
2.2 Modeling Approaches.......................... 15
2.3 Discrete Spring Network Model .................... 17
2.3.1 Discretization of the RBC Surface. . . . . . . . . . . . . . . 17
2.3.2 In-plane Elasticity ....................... 18
2.3.3 Bending Resistance....................... 19
2.3.4 Area and Volume Constraints ................. 19
2.3.5 Macroscopic Quantities..................... 20
2.3.6 Scaling of Model and Physical Units . . . . . . . . . . . . . 21

3 Fluid Solver 23
3.1 Lattice Boltzmann Method in a Nutshell . . . . . . . . . . . . . . . 23
3.2 Boundary and Initial Conditions.................... 26
3.2.1 Periodic Boundary Condition ................. 27
3.2.2 Solid Boundary ......................... 28
3.2.3 Immersed Boundary Method.................. 29
3.2.4 Initial Condition ........................ 32
3.2.5 Multi-relaxation-time Collision Operator . . . . . . . . . . . 32
3.2.6 External Forces......................... 39
3.3 Choice of Parameter Values ...................... 41

4 Waltzing Red Blood Cells Induced by Confined Shear Flow 43
4.1 Introduction............................... 43
4.2 Methods and Parameters........................ 45
4.3 Results and Discussion ......................... 48
4.3.1 Waltzing Red Blood Cells ................... 48
4.3.2 Dynamics Analysis ....................... 52
4.3.3 State Diagram.......................... 55
4.3.4 Suspension Viscosity ...................... 56
4.4 Summary ................................ 59

5 Cell-Free Layer of RBCs in a Microchannel 62
5.1 Introduction............................... 62
5.2 Methods and Parameters........................ 65
5.3 Results and Discussion ......................... 68
5.3.1 RBC Aggregate Structure under Shear . . . . . . . . . . . . 68
5.3.2 Cell Aggregation Effects on Viscosity and CFL . . . . . . . . 70
5.3.3 Boundary Condition Effects .................. 72
5.3.4 Volume Fraction Dependence ................. 74
5.4 Summary ................................ 78

6 Summary and Outlook 79
6.1 Summary ................................ 79
6.2 Outlook ................................. 80

A Details of the Red Blood Cell Model 82
Publications 86

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