Dynamics of three ferrofluid droplets in a rotating magnetic field

Two-dimensional (2D) direct numerical simulations on the dynamics of three identical ferrofluid droplets suspended in a non-magnetic ambient fluid under a rotating uniform magnetic field are conducted, and the motion and deformation of the three ferrofluid droplets are studied in this paper. Results show that there are four modes (i.e., the three droplets' direct coalescence (TC), the coalescence of two droplets and the subsequent planetary motion with the third droplet (CAP), the three droplets' planetary motion (TP), and the independent spin (IS)) for the three ferrofluid droplets, dependent on the magnetic Bond number (Bom) and the initial distance (d0) between two of the droplets. It is found that the decrease in d0 and the increase in Bom can make the droplets' mode change from the IS to the planetary motion, and then turn to the CAP. Furthermore, reducing Bom or d0 is helpful for the droplets to become merged.