Rotational Dynamics of the Magnetic Particles in Ferrofluids

TL;DR

This paper develops a comprehensive 3D theoretical model for the rotational dynamics of magnetic particles in ferrofluids, incorporating inertial effects, Brownian motion, and magnetic interactions, providing insights into their dynamic susceptibility.

Contribution

It introduces a first-principles 3D approach to ferrofluid particle dynamics, including inertial and Brownian effects, filling a gap left by previous phenomenological models.

Findings

Numerical analysis of the blocked magnetic moment limit.

Explicit calculation of particle trajectories under magnetic fields.

Derivation of response functions and susceptibility matrices.

Abstract

A new theory for the dynamics of the magnetic particles and their magnetic moments in ferrofluids is developed. Based on a generalized Lagrangian formulation for the equations of motion of the colloidal particle, we introduce its interaction with the solvent fluid via dissipative and random noise torques, as well as the interactions between the particle and its magnetic moment, treated as an independent physical entity and characterized by three generalized coordinates, its two polar angles and its modulus. It has been recognized recently that inertial effects, as well as the particle's rotational Brownian motion, may play important roles on the dynamic susceptibility of a class of magnetic fluids. No satisfactory theory existed, up to now, that takes this effects into account. The theory presented here is a first-principles 3-dimensional approach, in contrast to some phenomenological 2-dimensional approaches that can be found in the recent literature. It is appropriate for superparamagnetic, non-superparamagnetic and mixed magnetic fluids. As a simple application, the blocked limit (magnetic moment fixed in the particle) is treated numerically. The rotational trajectory of the particles in presence of a magnetic field, as well as the response functions and dynamic susceptibility matrices are explicitly calculated for some values of the parameters