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/ε. 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 ε, the system can be effectively described by a multiscale model.
@article{arxiv.2501.12918,
title = {Derivation of a Multiscale Ferrofluid Model: Superparamagnetic Behavior due to Fast Spin Flip},
author = {Alexandre Girodoux-Lavigne and Richard M. Höfer},
journal= {arXiv preprint arXiv:2501.12918},
year = {2026}
}