A continuum model for the transport of red blood cells (RBC) inside arteries and capillaries of small diameters is proposed. The pressure and velocity fields are solved using the Navier-Stokes equations while the distribution of the RBC volume fraction, namely, hematocrit is obtained by solving the particle transport equation arising from the diffusive flux model. The momentum and hematocrit transport equations are coupled through a hematocrit-dependent blood viscosity model. The coupled equations are numerically solved using a 3D unstructured finite volume method. The proposed model predicts the shear induced diffusion of RBCs where RBCs migrate from the wall to the center of the blood vessel leading to a cell free layer (CFL) near the wall. Three geometries with sizes of the order of 40 µm have been considered for the present work. For flow inside a tube, results in terms of the concentration distribution and cell-free layer from the present continuum model show a good match with experiments and DPD simulations. For flow inside a tube with a constriction it is found that hematocrit depletion is greater downstream of the neck of the constriction. In addition, the effect of hematocrit loading on its distribution is correctly predicted. Finally, for a flow inside a tube with a bifurcation the average hematocrit concentration is found to be higher for the branch with the higher flow rate, thereby complying with the well-known bifurcation law.

提出了一种用于小直径动脉和毛细血管内红细胞（RBC）运输的连续模型。使用Navier-Stokes方程求解压力和速度场，而RBC体积分数（即血细胞比容）的分布是通过求解由扩散通量模型产生的颗粒传输方程获得的。动量和血细胞比容传输方程通过与血细胞比容有关的血液粘度模型耦合。使用3D非结构化有限体积法对耦合方程进行数值求解。所提出的模型预测了红细胞的剪切诱导扩散，其中红细胞从壁向血管中心迁移，导致壁附近的无细胞层（CFL）。目前的工作已经考虑了三种尺寸为40 µm的几何形状。对于管内的流动，从当前连续模型得出的浓度分布和无细胞层的结果与实验和DPD模拟非常吻合。对于在具有收缩部的管内流动而言，发现在收缩部颈部的下游血细胞比容消耗更大。另外，正确预测了血细胞比容负荷对其分布的影响。最后，对于具有分叉的管内的流动，发现具有较高流速的分支的平均血细胞比容浓度更高，从而符合众所周知的分叉定律。对于在具有收缩部的管内流动而言，发现在收缩部颈部的下游血细胞比容消耗更大。另外，正确预测了血细胞比容负荷对其分布的影响。最后，对于具有分叉的管内的流动，发现具有较高流速的分支的平均血细胞比容浓度更高，从而符合众所周知的分叉定律。对于具有狭窄的管内流动，发现在狭窄的颈部下游血细胞比容耗竭更大。另外，正确预测了血细胞比容负荷对其分布的影响。最后，对于具有分叉的管内的流动，发现具有较高流速的分支的平均血细胞比容浓度更高，从而符合众所周知的分叉定律。