Asymptotic Theory for Directed Transport of Suspended Ferromagnetic Nanoparticles

TL;DR

This paper develops an asymptotic theoretical framework to analyze the directed transport of ferromagnetic nanoparticles under oscillating magnetic fields, providing analytical expressions for particle motion in dilute suspensions.

Contribution

It introduces a novel asymptotic analysis method for the translational and rotational dynamics of ferromagnetic nanoparticles in oscillating magnetic fields.

Findings

Derived analytical expressions for average particle velocity.

Identified conditions for directed transport in magnetic nanoparticle suspensions.

Provided asymptotic solutions for particle motion at different time scales.

Abstract

Using the rigid dipole model, we study the translational and rotational motions of single-domain fer-romagnetic nanoparticles in a dilute suspension induced by the harmonically oscillating gradient magnetic field in the presence of a time-independent uniform magnetic field. Our approach is based on a set of the first-order differential equations that describe the time dependencies of the particle coordinate and mag-netization angle. We find the asymptotic solutions of this set of equations at small and large times and, by applying the matched asymptotic expansions for discrete times, derive analytical expressions for the aver-age particle coordinate and velocity.