Mathematical modeling and computer simulation for spin coating of ferrofluid

Abstract

In the investigation of fluid flow in spin coating a thin film of ferrofluid mixture, the major considerations arc the effects of: (1) centrifugation of heavier ferromagnetic particles in lighter binder fluid; (2) ferromagnetism, when an external magnetic field is imposed in the process; and (3) evaporation of the binder fluid from the free surface. 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 nov: 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 now until the ferromagnetic particle concentration reaches the “saturation conentration” whereat the fluid becomes effectively rigid, resulting in coating formation. In the absence of applied magnetic field, we have established a computer simulation model for the flow. It is implemented on the computer by the application of IBM program offering DSL. The program is flexible enough to allow inputs of experimentally determined material properties, as well as time dependent operating conditions. © 1988 IEEE