Phase Diagram and Breathing Dynamics of Red Blood Cell Motion in Shear Flow

We present phase diagrams of red blood cell dynamics in shear flow using three-dimensional numerical simulations. By considering a wide range of shear rate and interior-to-exterior fluid viscosity ratio, it is shown that the cell dynamics is often more complex than the well-known tank-treading, tumbling and swinging motion, and is characterized by an extreme variation of the cell shape. We identify such complex shape dynamics as `breathing' dynamics. During the breathing motion, the cell either completely aligns with the flow direction and the membrane folds inward forming two cusps, or, it undergoes large swinging motion while deep, crater-like dimples periodically emerge and disappear. At lower bending rigidity, the breathing motion occurs over a wider range of shear rates, and is often characterized by the emergence of a quad-concave shape. The effect of the breathing dynamics on the tank-treading-to-tumbling transition is illustrated by detailed phase diagrams which appear to be more complex and richer than those of vesicles. In a remarkable departure from classical theory of nondeformable cells, we find that there exists a critical viscosity ratio below which the transition is dependent on shear rate only.