Motion and deformation of a red blood cell in a shear flow: a two-dimensional simulation of the wall effect

The motion and deformation of a single red blood cell in a simple shear flow between two parallel walls is studied theoretically. A two-dimensional deformable microcapsule is adopted as a model for the cell, which has a thin moving membrane, like a tank-tread, around the interior and is deformed into an elliptical shape with a constant area. Applying the finite element method to the Stokes equations, the tank-tread motion and deformation is determined in a stationary motion, under fluid dynamic interaction between the cell and the walls. It is shown that the motion and deformation of the microcapsule crucially depends on the channel width between the two walls. As the width decreases, the microcapsule is more elongated and the frequency of tank-tread motion decreases at a constant shear rate. In addition, the angle of inclination decreases at the low range of the viscosity ratio of internal to external fluids and increases at the high range. The results obtained are compared with experimental observations and applied to the behavior of cells under mutual interaction.