Derivation of a Multiscale Ferrofluid Model: Superparamagnetic Behavior due to Fast Spin Flip

TL;DR

This paper derives a multiscale ferrofluid model capturing superparamagnetic behavior by analyzing a microscopic stochastic system of magnetic nanoparticles with rapid spin flips, applicable in the large particle limit.

Contribution

It introduces a novel multiscale model for ferrofluids based on microscopic stochastic dynamics of nanoparticles with fast spin flips.

Findings

Effective multiscale description derived for large N and small particle volume.

Model captures superparamagnetic behavior due to rapid spin flips.

Framework applicable to ferrofluid systems with high particle counts.

Abstract

We consider a microscopic model of $N$ magnetic nanoparticles in a Stokes flow. We assume that the temperature is above the critical N\'eel temperature such that the particles' magnetizations undergo random flip with rate $1/\varepsilon$. The microscopic system is the modeled through a piecewise deterministic Markov jump process. We show that for large $N$, small particle volume fraction and small $\varepsilon$, the system can be effectively described by a multiscale model.