A droplet in a ferrofluid droplet under a rotating magnetic field

Two-dimensional (2-D) direct numerical simulations of a compound droplet (a non-magnetizable droplet wrapped in a ferrofluid droplet) suspended in a non-magnetizable ambient fluid under a rotating uniform magnetic field are carried out. The motion and deformation of the compound droplet are studied. The numerical results show that there are two stable states (the concentric and the eccentric states) for the compound droplet at the stable stage, dependent on the frequency of the rotating magnetic field and the magnetic Bond number. The feature of the concentric state for the compound droplet at the stable stage is studied in detail. We find that the inner and outer parts of the compound droplet rotate with the magnetic field, while there is hysteresis between the inner (or outer) droplet and the external magnetic field. The hysteresis effect for the inner droplet is weaker than that of the outer droplet, mainly due to the viscous sweeping effect of the outer droplet on the inner droplet. Increasing the frequency of the external magnetic field, both the phase angle between the inner and outer droplets and the time required for the compound droplet to shift from the stable eccentric state to the stable concentric one will increase. For the eccentric state at the stable stage, the eccentricity decreases with the frequency of the rotating magnetic field increasing, but has a peak with the magnetic Bond number increasing. It is hoped that this paper would lay a solid foundation for some potential applications in magnetic biodevices.