Numerical Analysis of the Nanoparticle Dynamics in a Viscous Liquid: Deterministic Approach

TL;DR

This study models the deterministic rotational and translational behavior of ferromagnetic nanoparticles in a viscous liquid under combined magnetic fields, revealing how the uniform field components influence periodicity and drift motion.

Contribution

It introduces a numerical analysis of nanoparticle dynamics considering both gradient and uniform magnetic fields, highlighting the impact of the parallel component on particle drift.

Findings

Perpendicular uniform magnetic field induces non-periodic, drift motion.

Parallel component reduces particle displacement and drift velocity.

Nanoparticle motion transitions from periodic to drift with the presence of the uniform field.

Abstract

We study the deterministic dynamics of single-domain ferromagnetic nanoparticles in a viscous liquid induced by the joint action of the gradient and uniform magnetic fields. It is assumed that the gradient field depends on time harmonically and the uniform field has two components, perpendicular and parallel to the gradient one. We also assume that the anisotropy magnetic field is so strong that the nanoparticle magnetization lies along the anisotropy axis, i.e., the magnetization vector is "frozen" into the particle body. With these assumptions and neglecting inertial effects we derive the torque and force balance equations that describe the rotational and translational motions of particles. We reduce these equations to a set of two coupled equations for the magnetization angle and particle coordinate, solve them numerically in a wide range of the system parameters and analyze the role of the parallel component of the uniform magnetic field. It is shown, in particular, that nanoparticles perform only periodic rotational and translational motions if the perpendicular component of the uniform magnetic field is absent. In contrast, the nanoparticle dynamics in the presence of this component becomes non-periodic, resulting in the drift motion (directed transport) of nanoparticles. By analyzing the short and long-time dependencies of the magnetization angle and particle coordinate we show that the increase in the parallel component of the uniform magnetic field decreases both the particle displacement for a fixed time and its average drift velocity on each period of the gradient magnetic field.