  We investigate the flowing behavior of dense suspensions of non-colloidal
particles, by coupling macroscopic rheometric experiments and local velocity
and concentration measurements through MRI techniques. We find that the flow is
localized at low velocities, and that the material is inhomogeneous; the local
laws inferred from macroscopic rheometric observations must then be
reinterpreted in the light of these local observations. We show that the short
time response to a velocity step allows to characterize dense suspensions
locally: they have a purely viscous behavior, without any observable influence
of friction. In the jammed zone, there may be a contact network, whereas in the
sheared zone there are only hydrodynamic interactions: localization consists in
a change in configuration at the grain scale. From the concentration and
velocity profiles, we have provided for the first time local measurements of
the concentration dependence of viscosity; we find a Krieger-Dougherty law
$\eta(\phi)=\eta_0(1-\phi/0.605)^{-2}$. Shear induced migration is almost
instantaneous and seems inconsistent with most observations: it would imply
that the diffusion coefficients strongly depend on the concentration. We
finally propose a simple constitutive law for dense suspensions, based on a
purely viscous behavior, that accounts for all the macroscopic and local
observations.
