Chow J C
Bull Math Biol. 1975 Oct;37(5):471-88. doi: 10.1007/BF02459515.
A study is made of blood flow by assuming that the blood constitutes a suspension of cells in plasma instead of a simple homogeneous fluid. A macroscopic theory governing the motion of plasma in a plasma-cell system is derived from the local volume averaging method for a system without mass transfer between the phases, and its characteristic length is much larger than the size of the cells. The equations governing the motion of the local averaged fluid quantities include one additional term in the equation of motion and two additional terms in the energy equation. These terms represent, respectively, the force exerted upon the fluid by the particles, and the rate of heat transfer and work kone upon the fluid by the particles. The theory is applied to obtain the effective viscosity as the explicit function of the volume concentration of the cells by assuming that the cells behave like rigid spherical particles with slip-collision, and the plasma is an compressible Newtonian fluid. Comparison with existing experimental results shows a good agreement. The theory is also used to obtain the effects of cell distribution upon the overall effective viscosity in a circular tube. The quantitative result shows that there is a decrease in overall effective viscosity as the concentration of cells increases toward the center of the tube, and the overall effective viscosity is smaller than the flow with evenly distributed cells.
通过假设血液是细胞在血浆中的悬浮液而非简单的均匀流体来对血流进行研究。一个支配血浆 - 细胞系统中血浆运动的宏观理论是从无相际传质系统的局部体积平均法推导出来的，其特征长度远大于细胞大小。支配局部平均流体量运动的方程在运动方程中包含一个附加项，在能量方程中包含两个附加项。这些项分别表示颗粒对流体施加的力，以及颗粒对流体的热传递速率和做功。通过假设细胞表现为具有滑移碰撞的刚性球形颗粒且血浆是可压缩牛顿流体，该理论被用于得出有效黏度作为细胞体积浓度的显式函数。与现有实验结果的比较显示出良好的一致性。该理论还被用于得出细胞分布对圆管中整体有效黏度的影响。定量结果表明，随着细胞浓度向管中心增加，整体有效黏度会降低，且整体有效黏度小于细胞均匀分布时的流动情况。
