THE DYNAMICS OF RED BLOOD CELL UNDER THE EFFECT OF SHAPE MEMORY

An one-dimensional elastic spring model is proposed to study the effect of shape memory on the motion of a red blood cell in two-dimensional flows. In simple shear flow, the shape memory effect also plays a role for having two well known motions: tumbling and swinging. The intermittent behavior of the cell with a nonuniform natural state has been obtained in a narrow range of the capillary number and has been studied thoroughly. The critical value of the swelling ratio for having the intermittent behavior has been estimated. In plane Poiseuille flow, the cell with the shape memory has an equilibrium shape as a slipper or parachute depending on capillary number. To ensure the tank-treading motion while in slippery shape, the upper bound of the shape memory coefficient has been suggested. Then our 1D model has been extended to 2D, which has been validated by several benchmarking tests. In three-dimensional shear flow, the critical shear rate for the cell motion transition from tumbling to swinging is consistent with the experiments. And in tube Poiseuille flow with rectangular cross section, the cell without shape memory always has a symmetric equilibrium shape while the one with shape memory can obtain a slippery shape at low flow rate. When the cell with shape memory passes through a very narrow channel, it becomes a cup-shape first and then recovers its biconcave shape with a rotation of its orientation. Such rotation is due to the tank-treading motion of the membrane caused by the shape memory.