Inertial migration in pressure-driven channel flow: beyond the Segre-Silberberg pinch

Abstract

We examine theoretically the inertial migration of a neutrally buoyant rigid sphere in pressure-driven channel flow, accounting for its finite size relative to the channel width (the confinement ratio). For sufficiently large channel Reynolds numbers\,($Re_c$), a small but finite confinement ratio qualitatively alters the inertial lift velocity profiles obtained using a point-particle formulation. Finite size effects are shown to lead to new equilibria, in addition to the well known Segre-Silberberg pinch locations. Consequently, a sphere can migrate to either the near-wall Segre-Silberberg equilibria, or the new stable equilibria located closer to the channel centerline, depending on $Re_c$ and its initial position. Our findings are in accord with recent experiments and simulations, and have implications for passive sorting of particles based on size, shape and other physical characteristics, in microfluidic applications.