Motion of a single red blood cell in plane shear flow

Abstract

To study the rotation and shearing deformation of a single red blood cell (RBC) in simple shear flow, a two-dimensional hydrodynamic calculation in the creeping flow approximation is made.

The model particle is assumed to have a fixed shape resembling the actual cross section of an RBC. In plane polar coordinates (r,ψ) the cross section of the particle is described by $\mathit{r}=\mathit{a}\mathrm{(}1+\mathit{p}cos2\mathit{\psi }$ ). The model cell is assumed to be bounded by an infinitesimally thin. inextensible, and completely flexible membrane and to contain a Newtonian fluid of viscosity μ _i, inside. The cell is suspended in another Newtonian fluid of viscosity μ _o. The only allowed motion of the membrane is along the perimeter of the cell such that the shape of cell is not changed.

In the Stokes approximation a biharmonic expansion of the stream function is obtained both in the interior and the exterior.

For the deformable cell, the period of rotation and the amplitude of the displacement of the membrane are found to rise sharply with an increase in the ratio μ _o/μ _i. At a certain ratio, depending on the parameter p, the motion ceases to be periodic, and the cell settles at a stationary orientation with its major axis inclined at an angle less than 45° to the direction of now, while the membrane remains in continuous motion around the interior.

The existence of two modes of motion is in agreement with experimental observations.