A numerical study of rupture of a ferrofluid interlayer in a sandwiched fluid system

Surface rupture in ferrofluid layers is a special case of the well-known Rosensweig instability, which can be triggered by applying a strong magnetic field. This study investigates the rupture dynamics in a ferrofluid interlayer sandwiched between two non-magnetic fluids, influenced by a non-homogenous vertical magnetic field. Simulations are performed using a generalized conservative phase-field lattice Boltzmann method for the flow field and interface with a coupled solution of Maxwell's equations for the evolution of magnetic field. The numerical results demonstrate the complete rupture process of ferrofluid layers. In most cases, the ferrofluid layer ruptures into two parts, while under certain conditions, such as a thinner interlayer or high magnetic field intensity, daughter droplets appear at the meniscus. A parametric analysis involving Weber number (We) and dimensionless magnetic parameter (N_m) elucidates the connection between different rupture conditions, such as a deformed interlayer without rupture, rupture with two semi-spindle shaped domains, and rupture with droplets. Additionally, a phase diagram illustrating the various rupture regions is also provided.