Derivation of a multiscale ferrofluid model: superparamagnetic behavior due to fast spin flip

We consider a microscopic model of N magnetic nanoparticles in a Stokes flow. We assume that the temperature is above the critical Néel 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.