Far-field theory for trajectories of magnetic ellipsoids in rectangular and circular channels

TL;DR

This paper develops a far-field theoretical framework to predict and control the trajectories of magnetic ellipsoids in rectangular and circular channels, enabling particle focusing and segregation in microfluidic devices.

Contribution

It introduces a far-field theory based on Blake's image tensor to accurately predict magnetic ellipsoid trajectories in channels, validated by numerical simulations.

Findings

Particles can be directed to focusing regions or channel walls by adjusting magnetic field orientation.

The theory accurately predicts particle motion in rectangular channels.

Particles can be focused to a single line in circular channels.

Abstract

We report a method to control the positions of ellipsoidal magnets in flowing channels of rectangular or circular cross section at low Reynolds number.A static uniform magnetic field is used to pin the particle orientation, and the particles move with translational drift velocities resulting from hydrodynamic interactions with the channel walls which can be described using Blake's image tensor.Building on his insights, we are able to present a far-field theory predicting the particle motion in rectangular channels, and validate the accuracy of the theory by comparing to numerical solutions using the boundary element method.We find that, by changing the direction of the applied magnetic field, the motion can be controlled so that particles move either to a curved focusing region or to the channel walls.We also use simulations to show that the particles are focused to a single line in a circular channel.Our results suggest ways to focus and segregate magnetic particles in lab-on-a-chip devices.