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

Laminar, turbulent and inertial shear-thickening regimes in channel flow of neutrally buoyant particle suspensions