Inertial migration of finite-size filaments in Poiseuille flow

We investigate the inertial migration of slender, axisymmetric, neutrally buoyant filaments in planar Poiseuille flow over a wide range of channel Reynolds numbers ( ${\textit{Re}}_c \in [0.5, 2000]$ ). Filaments exhibit complex oscillatory trajectories during tumbling, with the lateral migration velocity strongly coupled to their orientation. Using a singular perturbation approach, we derive a quasi-analytical expression for the migration velocity that captures both instantaneous and period-averaged behaviour. Finite-size effects are incorporated through solid-phase inertia and the influence of fluid inertia on the orientation dynamics. To validate the theory, we develop a fully resolved numerical framework based on the lattice Boltzmann and immersed boundary methods. The theoretical predictions show good agreement with simulation results over a wide range of Reynolds numbers and confinement ratios. Our model outperforms previous theories by providing improved agreement in predicting equilibrium positions across the investigated range of ${\textit{Re}}_c$ , particularly at high values. Notably, it captures the inward migration trend toward the channel centreline at high ${\textit{Re}}_c$ and reveals a new dynamics, including the cessation and resumption of tumbling under strong inertial effects. These findings provide a robust foundation for understanding filament migration and guiding inertial microfluidic design.