  We present an experimental study of the rheology and structure of a confined
suspension of deformable particles flowing in a quasi-two-dimensional
Poiseuille flow. Thanks to a precise microfluidic viscosimetry technique
combined with measurements of concentration profiles, our study provides the
first experimental confirmation {with three-dimensional particles} of a strong
relationship between structuring effects and rheology, previously only reported
in numerical simulations of purely two-dimensional systems. In conditions where
strong structuring effects take place due to confinement, the evolution of the
effective viscosity with particle concentration (here, red blood cells) shows a
remarkable succession of ranges of rapid growth and plateaus that are
associated to qualitative transitions in the structure of the suspension.
