Freezing process of ferrofluid droplets: Numerical and scaling analyses

In this study we present numerical and scaling analyses of deformation and freezing processes of ferrofluid droplets under magnetic field effects. A multiphase flow model coupled with an enthalpy-based lattice Boltzmann model is developed to directly simulate the deformation and subsequent freezing processes of a ferrofluid droplet with considerations of both volume expansion and magnetization effects. Meanwhile, analytical models and scaling analyses are derived to reveal how the morphology of the ferrofluid droplet responds to the magnetic field and how the morphology evolution affects the freezing time. We find that the magnetic force induced by magnetic field gradient is much larger than that induced by the magnetization effect, leading to the flattening or elongation of a ferrofluid droplet under magnetic squeeze or lift conditions. The height of the ferrofluid droplet almost linearly decreases (increases) in the low magnetic strength regime for magnetic squeeze (lift) cases, while it follows a nonlinear scaling law under high magnetic squeeze conditions. Besides, the propagation of the freezing front well obeys the scaling law h∼t0.5 for high magnetic squeeze cases, but deviates much from that at the final freezing stage for both magnetic absence and lift cases.