Inertial migration of rigid spheres in two-dimensional unidirectional flows

TLDR

The Segré‑Silberberg effect describes inertia‑induced lateral migration of neutrally buoyant rigid spheres in Newtonian fluids. This study theoretically investigates that effect in simple shear flow and two‑dimensional Poiseuille flow. Particle trajectories were calculated for both flow types and compared with experimental data. The spheres attain a stable lateral equilibrium independent of release position, located midway between walls in simple shear flow and 0.6 of the channel half‑width from the centre‑line in Poiseuille flow, highlighting implications for measuring rheological properties of dilute suspensions.

Abstract

The familiar Segré-Silberberg effect of inertia-induced lateral migration of a neutrally buoyant rigid sphere in a Newtonian fluid is studied theoretically for simple shear flow and for two-dimensional Poiseuille flow. It is shown that the spheres reach a stable lateral equilibrium position independent of the initial position of release. For simple shear flow, this position is midway between the walls, whereas for Poiseuille flow, it is 0·6 of the channel half-width from the centre-line. Particle trajectories are calculated in both cases and compared with available experimental data. Implications for the measurement of the rheological properties of a dilute suspension of spheres are discussed.