Lateral migration and equilibrium shape and position of a single red blood cell in bounded Poiseuille flows

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.