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.

• Received 16 July 2012

DOI:https://doi.org/10.1103/PhysRevE.86.056308