Inertial migration regimes of a neutrally buoyant sphere in pipe Poiseuille flow

The inertial migration of a neutrally buoyant sphere in pipe Poiseuille flow is examined using numerical simulations. Three migration regimes are observed with increasing Reynolds number ( ${\textit{Re}}$ ): monotonic convergence to the equilibrium position, overshooting convergence and damped oscillations. The critical Reynolds numbers separating these regimes decrease with the sphere-to-pipe diameter ratio, $d/D$ . The axial entry length, $L_{p}$ , required for the sphere to reach equilibrium decreases with both ${\textit{Re}}$ and $d/D$ in the monotonic regime, but increases in the oscillatory regime. These results elucidate the dynamics of inertial migration and inform strategies for manipulating particles in confined, particle-laden flows.