Inertial migration of slender prolate and thin oblate spheroids in plane Poiseuille flow

We theoretically examine the inertial migration of a neutrally buoyant spheroid of aspect ratio $\kappa$ in wall-bounded plane Poiseuille flow at small particle Reynolds number ($R{e}_p$) and small confinement ratio ($\lambda$), with channel Reynolds number $R{e}_c=R{e}_p\mathrm{/}{\lambda }^2$ arbitrary. For $\lambda \ll 1$, inertia rapidly drives the spheroid to the tumbling orbit ($C=\mathrm{\infty }$), with migration governed by the time-averaged lift over orientations sampled in this orbit. Spheroids with $\kappa =O(1)$ follow Jeffery rotation closely, while deviations for slender rods and thin disks yield equilibrium positions distinct from the classical Segre-Silberberg result. Above a threshold $R{e}_c$, both rods and disks can undergo rotation arrest near walls, with these arrested regions expanding toward the centerline as $R{e}_c$ increases. Unlike spheres, the resulting equilibrium positions shift inward with increasing $R{e}_c$; for disks, these positions themselves become arrested beyond a threshold $R{e}_c$. The $\kappa$-dependence of equilibrium locations suggests passive shape-sorting strategies in microfluidic devices.