Channel flow of rigid sphere suspensions: particle dynamics in the inertial regime

We consider suspensions of neutrally-buoyant finite-size rigid spherical particles in channel flow and investigate the relation between the particle dynamics and the mean bulk behavior of the mixture for Reynolds numbers $500 \le Re \le 5000$ and particle volume fraction $0\le \Phi \le 0.3$, via fully resolved numerical simulations. Analysis of the momentum balance reveals the existence of three different regimes: laminar, turbulent and inertial shear-thickening depending on which of the stress terms, viscous, Reynolds or particle stress, is the major responsible for the momentum transfer across the channel. We show that both Reynolds and particle stress dominated flows fall into the Bagnoldian inertial regime and that the Bagnold number can predict the bulk behavior although this is due to two distinct physical mechanisms. A turbulent flow is characterized by larger particle dispersion and a more uniform particle distribution, whereas the particulate-dominated flows is associated with a significant particle migration towards the channel center where the flow is smooth laminar-like and dispersion low.Interestingly, the collision kernel shows similar values in the different regimes, although the relative particle velocity and clustering clearly vary with inertia and particle concentration.