Blood flow in micro capillaries of diameter approximately 15–500 μm is accompanied with a lower tube hematocrit level and lower apparent viscosity as the diameter decreases. These effects are termed the Fåhraeus and Fåhraeus–Lindqvist effects, respectively. Both effects are linked to axial accumulation of red blood cells. In the present investigation, we extend previous works using a shear-induced model for the migration of red blood cells and adopt a model for blood viscosity that accounts for the suspending medium viscosity and local hematocrit level. For fully developed hematocrit profiles (i.e., independent of axial location), the diffusion fluxes due to particle collision frequency and viscosity gradients are of equal magnitude and opposite directions. The ratio of the diffusion coefficients for the two fluxes affects both the Fåhraeus and Fåhraeus–Lindqvist effects and is found related to the capillary diameter and discharge hematocrit using a well-known data-fit correlation for apparent blood viscosity. The velocity and hematocrit profiles were determined numerically as functions of radial coordinate, tube diameter, and discharge hematocrit. The velocity profile determined numerically is consistent with the derived analytical expression and the results are in good agreement with published numerical results and experimental data for hematocrit ratio and hematocrit and velocity profiles.

中文翻译：

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血流动力学：使用剪切诱导的红细胞迁移模型对 Fåhraeus 和 Fåhraeus-Lindqvist 效应进行建模

直径约为 15-500 μm 的微毛细血管中的血流伴随着较低的管血细胞比容水平和随着直径的减小而降低的表观粘度。这些效应分别称为 Fåhraeus 和 Fåhraeus-Lindqvist 效应。这两种效应都与红细胞的轴向积累有关。在本研究中，我们使用剪切诱导的红细胞迁移模型扩展了以前的工作，并采用了血液粘度模型，该模型考虑了悬浮介质粘度和局部血细胞比容水平。对于完全发展的血细胞比容曲线（即，与轴向位置无关），由于粒子碰撞频率和粘度梯度引起的扩散通量大小相等，方向相反。两种通量的扩散系数之比影响 Fåhraeus 和 Fåhraeus-Lindqvist 效应，并且发现与毛细血管直径和排出血细胞比容相关，使用众所周知的表观血液粘度数据拟合相关性。速度和血细胞比容曲线作为径向坐标、管直径和排出血细胞比容的函数在数值上确定。数值确定的速度分布与导出的分析表达式一致，结果与已发表的数值结果和血细胞比容比以及血细胞比容和速度分布的实验数据非常一致。速度和血细胞比容曲线作为径向坐标、管直径和排出血细胞比容的函数在数值上确定。数值确定的速度分布与导出的分析表达式一致，结果与已发表的数值结果和血细胞比容比以及血细胞比容和速度分布的实验数据非常一致。速度和血细胞比容曲线作为径向坐标、管直径和排出血细胞比容的函数在数值上确定。数值确定的速度分布与导出的分析表达式一致，结果与已发表的数值结果和血细胞比容比以及血细胞比容和速度分布的实验数据非常一致。