Ferrofilm in a magnetic field

A vertically draining thin ferrofilm under the influence of gravity and a nonuniform magnetic field is considered. It is observed experimentally that the presence of the magnetic field greatly alters the drainage of the film. A mathematical model is developed to describe the behavior. Experiments are conducted for multiple magnetic field configurations. The model is solved for two different sets of boundary conditions and results are compared to experiments. It is shown that the magnetic field structure, the concentration of magnetite in the solution, and the boundary conditions all have noticeable affects on the evolution of the thinning film. Good qualitative agreement between the model and the experiments is observed.