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

## TL;DR

This paper theoretically investigates how slender prolate and thin oblate spheroids migrate laterally in plane Poiseuille flow at low particle Reynolds numbers, revealing shape-dependent equilibrium positions and rotation behaviors.

## Contribution

It provides a novel theoretical analysis of inertial migration for spheroids with different aspect ratios, including shape-dependent equilibrium positions and rotation arrest phenomena.

## Key findings

- Spheroids rapidly reach tumbling orbits driven by inertia.
- Equilibrium positions depend on particle shape and flow Reynolds number.
- Disks and rods exhibit rotation arrest near walls at high Re_c.

## Abstract

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 ($Re_p$) and small confinement ratio ($\lambda$), with channel Reynolds number $Re_c = Re_p/\lambda^2$ arbitrary. For $\lambda \ll 1$, inertia rapidly drives the spheroid to the tumbling orbit ($C = \infty$), 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 $Re_c$, both rods and disks can undergo rotation arrest near walls, with these arrested regions expanding toward the centerline as $Re_c$ increases. Unlike spheres, the resulting equilibrium positions shift inward with increasing $Re_c$; for disks, these positions themselves become arrested beyond a threshold $Re_c$. The $\kappa$-dependence of equilibrium locations suggests passive shape-sorting strategies in microfluidic devices.