  Two motions of oscillation and vacillating breathing (swing) of a red blood
cell have been observed in bounded Poiseuille flows (Phys. Rev. E 85, 16307
(2012)). To understand such motions, we have studied the oscillating motion of
a neutrally buoyant rigid particle of the same shape in Poiseuille flow in a
narrow channel and obtained that the crucial point is to have the particle
interacting with Poiseuille flow with its mass center moving up and down in the
channel central region. Since the mass center of the cell migrates toward the
channel central region, its oscillating motion of the inclination angle is
similar to the aforementioned motion as long as the cell keeps the shape of
long body. But as the up-and-down oscillation of the cell mass center damps
out, the oscillating motion of the inclination angle also damps out and the
cell inclination angle approaches to a fixed angle.
