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 $1\mathrm{/}\epsilon$. 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 $\epsilon$, the system can be effectively described by a multiscale model.