A novel energy-based phase field model for ferrodroplet deformation and breakup in a uniform magnetic field

In this paper, we propose a novel, thermodynamically consistent phase field model to simulate the deformation and breakup of a ferrodroplet that is immersed in a viscous medium and subject to an applied uniform magnetic field. Instead of using the magnetic body force in the traditional Rosensweig model, the key idea of this model is to propose a new magnetic energy that enables direct effects of the magnetic field on the interface evolution. The model can thereby be derived from the variational principle via minimizing the free energy of the total system. This energy based modeling idea can be easily extended to include more external fields in a convenient and consistent way for more complicated applications involving multiple external fields. We validate the model by performing a series of numerical simulations, including the comparison with analytic solutions, the investigation of the effect of different types of magnetic fields, the dynamical behaviors of the ferrodroplet breakup under the strong magnetic field, magnetic/velocity/pressure field distributions, the magnetic energy density, and the inertial phenomenon, etc.