# Inertial migration of spherical and oblate particles in straight ducts

## TL;DR

This study numerically investigates the inertial migration behaviors of spherical and oblate particles in straight ducts, revealing differences in focusing positions, tumbling motions, and migration lengths relevant for microfluidic device design.

## Contribution

It provides detailed analysis of how oblate particles migrate and focus compared to spheres, including chaotic behaviors and tumbling effects at high Reynolds numbers.

## Key findings

- Oblate particles can focus near duct corners if large enough.
- Oblate tumbling causes less uniform lateral motion and longer focusing in square ducts.
- Migration behaviors differ significantly between square and rectangular ducts.

## Abstract

We study numerically the inertial migration of a single rigid sphere and an oblate spheroid in straight square and rectangular ducts. A highly accurate interface-resolved numerical algorithm is employed to analyse the entire migration dynamics of the oblate particle and compare it with that of the sphere. Similarly to the inertial focusing of spheres, the oblate particle reaches one of the four face-centred equilibrium positions, however they are vertically aligned with the axis of symmetry in the spanwise direction. In addition, the lateral trajectories of spheres and oblates collapse into an equilibrium manifold before ending at the equilibrium positions, with the equilibrium manifold tangential to lines of constant background shear for both sphere and oblate particles. The differences between the migration of the oblate and sphere are also presented, in particular the oblate may focus on the diagonal symmetry line of the duct cross-section, close to one of the corners, if its diameter is larger than a certain threshold. Moreover, we show that the final orientation and rotation of the oblate exhibit a chaotic behaviour for Reynolds numbers beyond a critical value. Finally, we document that the lateral motion of the oblate particle is less uniform than that of the spherical particle due to its evident tumbling motion throughout the migration. In a square duct, the strong tumbling motion of the oblate in the first stage of the migration results in a lower lateral velocity and consequently longer focusing length with respect to that of the spherical particle. The opposite is true in a rectangular duct where the higher lateral velocity of the oblate in the second stage of the migration, with negligible tumbling, gives rise to shorter focusing lengths. These results can help the design of microfluidic systems for bio-applications.