Numerical investigation of falling ferrofluid droplets under magnetic fields

A methodical analysis on the dynamic interaction behavior between a pair of uneven sized ferrofluid droplets freely falling under gravity and uniform magnetic fields is presented in this article. Here, a conservative level set method (LSM) is adopted to precisely calculate the free interface curvature of the droplet, which again couples both magnetic and flow fields. The results indicate that at a unity viscosity ratio (i.e., lambda = 1) and a fixed Galilei number (i.e., Ga = 1600), in the absence of any external forces except gravity, a critical initial vertical separation distance between the droplets prevails (Delta Y-cr*>= 6), which prohibits them from undergoing coalescence phenomenon before hitting the bottom wall of the computational domain. However, enacting a magnetic field along alpha = 0 degrees hinders coalescence, while it is expedited by the implementation of the magnetic field along alpha = 90 degrees . Contrarily, at alpha = 45 degrees, the droplets exhibit downward lateral migration along the secondary diagonal of the domain, leading to a larger separation between them at higher magnetic Bond numbers Bo(m) (i.e., Bo(m) = 8). Additionally, the investigation on the effects of surface tension suggests an increase in the vertical separation between droplets at higher Eotvos numbers (i.e., Eo = 9.48). Moreover, a magnetic field along alpha = 0 degrees results in the formation of round-bottom hull shaped droplets, whereas they transform into teardrop shaped droplets before coalescence at alpha = 90 degrees. Furthermore, the magnetic field along alpha = 45 degrees greatly impedes the coalescence phenomenon, which eventually leads to migration of droplets along divergent lateral directions. Finally, if the droplets are dispersed in air, they do not exhibit any coalescence event before the impact under gravity or gravity and magnetic fields.