Numerical investigation on falling ferrofluid droplet under uniform magnetic field

In this study, ferrofluid droplet behavior in nonmagnetic viscous fluid under the uniform magnetic field is studied numerically by developing a robust two-dimensional hybrid lattice-Boltzmann/Finite-volume method. The lattice Boltzmann equation (LBE) with the magnetic force term is solved to update the flow field while the magnetic induction equation is solved using the finite volume method to calculate the magnetic field. To validate the flow field solution two test cases have been considered:  the falling droplet and Laplace law. In order to validate the magnetic field, deformation of static drop under magnetic field is checked. The comparison of results between present study and previous researches shows a good agreement. The effects of the magnetic Bond number, susceptibility and magnetic field direction on deformation of the falling droplet are also investigated. The results show that the horizontal magnetic field accelerates the falling process of ferrofluid droplet while the vertical magnetic field slows down it by increasing the magnetic Bond number and susceptibility. Also, the increase in the magnetic Bond number and susceptibility enhances the magnitudes of magnetic force along the magnetic field.