Swinging and Synchronized Rotations of Red Blood Cells in Simple Shear Flow

The dynamics of red blood cells (RBCs) in simple shear flow was studied using a theoretical approach based on three variables: a shape parameter, the inclination angle $\theta$, and phase angle $\varphi$ of the membrane rotation. At high shear rate and low viscosity contrast of internal fluid, RBCs exhibit tank-treading motion, where $\varphi$ rotates with swinging oscillation of shape and $\theta$. At low shear rate, tumbling motion occurs and $\theta$ rotates. In the middle region between these two phases, it is found that synchronized rotation of $\varphi$ and $\theta$ with integer ratios of the frequencies occurs in addition to intermittent rotation. These dynamics are robust to the modification of the potential of the RBC shape and membrane rotation. Our results agree well with recent experiments.