  We study the shearing rheology of dense suspensions of elastic capsules,
taking aggregation-free red blood cells as a physiologically relevant example.
Particles are non-Brownian and interact only via hydrodynamics and short-range
repulsive forces. An analysis of the different stress mechanisms in the
suspension shows that the viscosity is governed by the shear elasticity of the
capsules, whereas the repulsive forces are subdominant. Evidence for a dynamic
yield stress above a critical volume fraction is provided and related to the
elastic properties of the capsules. The shear stress is found to follow a
critical jamming scenario and is rather insensitive to the
tumbling-to-tank-treading transition. The particle pressure and normal stress
differences display some sensitivity to the dynamical state of the cells and
exhibit a characteristic scaling, following the behavior of a single particle,
in the tank-treading regime. The behavior of the viscosity in the fluid phase
is rationalized in terms of effective medium models. Furthermore, the role of
confinement effects, which increase the overall magnitude and enhance the
shear-thinning of the viscosity, is discussed.

Soft Condensed Matter;Fluid Dynamics;Medical Physics