Modelling of a free-surface ferrofluid flow

The Cauchy's stress tensor of a ferrofluid exposed to an external magnetic field is subject to additional magnetic terms. For a linearly magnetizable medium, the terms result in interfacial magnetic force acting on the ferrofluid boundaries. This force changes the characteristics of many free-surface ferrofluid phenomena. The aim of this work is to implement this force into the incompressible Navier-Stokes equations and propose a numerical method to solve them. The interface of ferrofluid is tracked with the use of the characteristic level-set method and additional reinitialization step assures conservation of its volume. Incompressible Navier-Stokes equations are formulated for a divergence-free velocity fields while discrete interfacial forces are treated with continuous surface force model. Velocity-pressure coupling is implemented via the projection method. To predict the magnetic force effect quantitatively, Maxwell's equations for magnetostatics are solved in each time step. Finite element method is utilized for the spatial discretization. At the end of the work, equilibrium droplet shape are compared to known experimental results.