Shi Lingling, Pan Tsorng-Whay, Glowinski Roland
Department of Mathematics, University of Houston, Houston, Texas 77204, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 2):056308. doi: 10.1103/PhysRevE.86.056308. Epub 2012 Nov 13.
Lateral migration and equilibrium shape and position of a single red blood cell (RBC) in bounded two-dimensional Poiseuille flows are investigated by using an immersed boundary method. An elastic spring model is applied to simulate the skeleton structure of a RBC membrane. We focus on studying the properties of lateral migration of a single RBC in Poiseuille flows by varying the initial position, the initial angle, the swelling ratio (s), the membrane bending stiffness of RBC (k{b}), the maximum velocity of fluid flow (u{max}), and the degree of confinement. The combined effect of the deformability, the degree of confinement, and the shear gradient of the Poiseuille flow make the RBCs migrate toward a certain cross-sectional equilibrium position, which lies either on the center line of the channel or off center line. For s>0.8, the speed of the migration at the beginning decreases as one increases the swelling ratio s. But for s<0.8, the speed of the migration at the beginning is an increasing function of the swelling ratio s. Two motions of oscillation and vacillating breathing (swing) of RBCs are observed. The distance Y{d} between the cell mass center of the equilibrium position and the center line of the channel increases with increasing the Reynolds number Re and reaches a peak, then decreases with increasing Re. The peak of Re is a decreasing function of the swelling ratio (s<1.0). The cell membrane energy of the equilibrium position is an increasing function as Re increases. The slipper-shaped cell is more stable than the parachute-shaped one in the sense that the energy stored in the former is lower than that in the latter. For a given Re, the bigger the swelling ratio (s<1.0), the lower the cell membrane energy.
采用浸入边界法研究了单个红细胞（RBC）在有界二维泊肃叶流中的横向迁移以及平衡形状和位置。应用弹性弹簧模型来模拟红细胞膜的骨架结构。我们通过改变初始位置、初始角度、肿胀率（s）、红细胞的膜弯曲刚度（k{b}）、流体流动的最大速度（u{max}）和约束程度，着重研究单个红细胞在泊肃叶流中的横向迁移特性。泊肃叶流的可变形性、约束程度和剪切梯度的综合作用使红细胞向某个横截面平衡位置迁移，该位置要么位于通道的中心线上，要么偏离中心线。当s>0.8时，开始时迁移速度随肿胀率s的增加而降低。但当s<0.8时，开始时迁移速度是肿胀率s的增函数。观察到红细胞的两种振荡和摆动呼吸（摆动）运动。平衡位置的细胞质心与通道中心线之间的距离Y{d}随着雷诺数Re的增加而增加并达到峰值，然后随着Re的增加而减小。Re的峰值是肿胀率（s<1.0）的减函数。平衡位置的细胞膜能量随着Re的增加而增加。从前者储存的能量低于后者的意义上讲，拖鞋形细胞比降落伞形细胞更稳定。对于给定的Re，肿胀率（s<1.0）越大，细胞膜能量越低。
