  The aim of this Letter is to characterize the flow regimes of suspensions of
finite-size rigid particles in a viscous fluid at finite inertia. We explore
the system behavior as function of the particle volume fraction and the
Reynolds number (the ratio of flow and particle inertia to viscous forces).
Unlike single phase flows where a clear distinction exists between the laminar
and the turbulent states, three different regimes can be identified in the
presence of a particulate phase, with smooth transitions between them. At low
volume fractions, the flow becomes turbulent when increasing the Reynolds
number, transitioning from the laminar regime dominated by viscous forces to
the turbulent regime characterized by enhanced momentum transport by turbulent
eddies. At larger volume fractions, we identify a new regime characterized by
an even larger increase of the wall friction. The wall friction increases with
the Reynolds number (inertial effects) while the turbulent transport is weakly
affected, as in a state of intense inertial shear-thickening. This state may
prevent the transition to a fully turbulent regime at arbitrary high speed of
the flow.
