Numerical simulation of falling droplet under uniform magnetic field, using a hybrid lattice-Boltzmann and finite-volume method

In this study, falling ferrofluid droplet behavior in nonmagnetic viscous fluid under the uniform magnetic field in two-phase flow is studied numerically. To this approach, a hybrid lattice-Boltzmann base shan-chen model and finite-volume method is used. The lattice Boltzmann equation 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 tests have been considered: the free bubble rising and Laplace law. In order to validate the magnetic field, permeable circle and deformation of static drop under magnetic field is simulated. The comparison of results between present study and previous researches shows that there is a good agreement between the results. The effects of the magnetic Bond number, susceptibility and magnetic field direction on deformation of the falling droplet are investigated. The results show that increase in the magnetic Bond number or susceptibility leads to a larger deformation of the droplet. Also in horizontal magnetic field, the falling process takes more time in compared to the vertical magnetic field.