Inertial migration of oblate spheroids in a plane channel

TL;DR

This study investigates how oblate spheroids migrate inertially in a plane channel flow, revealing their orientation behavior and how their equilibrium positions depend on their geometry, with implications for particle separation techniques.

Contribution

The paper introduces a detailed analysis of inertial migration of oblate spheroids, showing the lift force dependence on their geometric parameters and establishing the lift coefficient equivalence to spheres.

Findings

Spheroids orient with minor axis in vorticity direction (log-rolling).

Equilibrium positions depend only on equatorial radius for moderate aspect ratios.

Lift coefficient of oblate spheroids equals that of spheres of the same equatorial radius.

Abstract

We discuss an inertial migration of oblate spheroids in a plane channel, where steady laminar flow is generated by a pressure gradient. Our lattice Boltzmann simulations show that spheroids orient in the flow, so that their minor axis coincides with the vorticity direction (a log-rolling motion). Interestingly, for spheroids of moderate aspect ratios, the equilibrium positions relative to the channel walls depend only on their equatorial radius $a$. By analysing the inertial lift force we argue that this force is proportional to $a^3b$, where $b$ is the polar radius, and conclude that the dimensionless lift coefficient of the oblate spheroid does not depend on $b$, and is equal to that of the sphere of radius $a$.