Axisymmetric motion of a file of red blood cells through capillaries

Abstract

The axisymmetric, pressure-driven motion of red blood cells through cylindrical capillaries is investigated by numerical simulation. The mathematical formulation takes into consideration the nearly incompressible and elastic properties of the cell membrane with respect to shearing and bending deformation from the unstressed shape of the biconcave disk. In the theoretical model, the cells are arranged in a periodic file that is coaxial with the capillaries, and the evolution from the equilibrium to a highly deformed steady shape is computed using a boundary-integral method for axisymmetric Stokes flow. The results illustrate the significance of the capillary radius and cell spacing on the discharge hematocrit and apparent viscosity of the one-dimensional suspension, and validate the assumptions of approximate solutions based on the lubrication approximation for tightly fitting cells developed by previous authors.