Inertial focusing of a dilute suspension in pipe flow

The dynamics of rigid particle suspensions in a wall-bounded laminar flow present several non-trivial and intriguing features, including particle ordering, lateral transport, and the appearance of stable, preferential locations like the Segr\'e-Silberberg annulus. The formation of more than one annulus is a particularly puzzling phenomenon that is still not fully explained. Here, we present numerical simulation results of a dilute suspension of particles in (periodic) pipe flow based on the lattice Boltzmann and the discrete element methods (DEM). Our simulations provide access to the full radial position history of the particles while traveling downstream. This allows to accurately quantify the transient and steady states. We observe the formation of the secondary, inner annulus and show that its position invariably shifts toward the Segr\'e-Silberberg one if the channel is sufficiently long, proving that it is, in fact, a transient feature for Reynolds numbers (Re) up to 600. We quantify the variation of the channel focusing length ($L_s/2R$) with Re. Interestingly and unlike the theoretical prediction for a point-like particle, we observe that $L_s/2R$ increases with Re for both the single particle and the suspension.