  An exhaustive description of the dynamics under shear flow of a large number
of red blood cells in dilute regime is proposed, which highlights and takes
into account the dispersion in cell properties within a given blood sample.
Physiological suspending fluid viscosity is considered, a configuration
surprisingly seldom considered in experimental studies, as well as a more
viscous fluid that is a reference in the literature. Stable and unstable
flipping motions well described by Jeffery orbits or modified Jeffery orbits
are identified, as well as transitions to and from tank-treading motion in the
more viscous suspending fluid case. Hysteresis loops upon shear rate increase
or decrease are highlighted for the transitions between unstable and stable
orbits as well as for the transition between flipping and tank-treading. We
identify which of the characteristic parameters of motion and of the transition
thresholds depend on flow stress only or also on suspending fluid viscosity.
