Numerical approach to the motion of a red blood cell in Couette flow

The motion of a red blood cell in a plane Couette flow is studied theoretically, introducing a two-dimensional microcapsule model for the cell. It is assumed that the microcapsule is deformed into an elliptical shape with a constant area and that its membrane moves like a tank-tread around the interior. The flow fields both inside and outside the microcapsule are analyzed using the finite element method in the Stokes equations and the obtained viscous forces on the membrane are used to determine its deformation and tank-treading motion. It is shown that a decrease in viscosity ratio of internal to external fluids causes the microcapsule to be more elongated, with its inclination angle increasing, whereas the microcapsule becomes more elongated at a smaller inclination angle with a longer tank-treading period as the elastic compliance of the membrane or the shear rate of the Couette flow increases. The force acting on the wall is also examined in relation to the abnormal viscosity of blood.