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We characterise the flow regimes of suspensions of finite-size rigid particles in a viscous fluid. We explore the system behavior as a function of the particle volume fraction and the Reynolds number. 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 of a relatively dense suspension to a fully turbulent regime at arbitrary high speed of the flow. We then focus on the turbulent regime and examine the effect of particle density, shape and size. Simulations are first performed for particles heavier than the fluid, yet without gravity, to untangle the effect of particle and fluid inertia. Interestingly, we observe that the turbulence is determined by the excluded volume rather than by the particle inertia. As next step, the channel flow of disc-like oblate particles is compared to the results for spherical particles. Finally, by examining smaller particles, we propose an universal scaling for the mean turbulent velocity profile. |