Mathematical modeling and computer simulation spin coating of ferrofluid

An investigation of fluid flow in spin coating a thin film of ferrofluid mixture is reported. The composition of the mixture is determined by the mass concentration of ferromagnetic particles in the ferrofluid. The enrichment of ferromagnetic particle concentration due to evaporation loss of binder fluid affects the material properties of the ferrofluid, resulting in drastic change of flow characteristics. Regarding the inhomogeneous ferrofluid mixture as a continuum, the hydrodynamic equations consist of the continuity and the momentum equations of the ferrofluid. An additional equation of continuity of the concentration of ferromagnetic particles is derived subject to the combined effects of evaporation, diffusion, the centrifugal potential, and the externally applied field. The ferrofluid mixture continues to flow until the ferromagnetic particle concentration reached the saturation concentration, where the fluid becomes effectively rigid, resulting in coating formation. In the absence of applied magnetic field, a computer simulation model for the flow has been established