Weakly nonlinear stability analysis of a thin magnetic fluid during spin coating (Q1958917)

The study of MHD (magnetohydrodynamic) effects is important inter alia in thin film materials technology, namely, in the stabilization of the film flow by applying a magnetic field is advantageous since neither electrical nor mechanical contacts wiht the fluid are necessary and the active control of the technological process is simple. That is why the spin coating process is fundamental in chip manufactoring process of integrated circuits (wafer, manufactoring, photolithography and sputtering deposition). Here a weakly nonlinear stability analysis of a thin electrically conductive fluid under an applied uniform magnetic field on a rotating disc (spin coating) is presented. Since during spin coating the magnetic induced field can. be neglected, the magnetic Reynolds number is much smaller than unity. The disc radius is much larger than the film thickness, the peripheral effects are negligible in comparison to the total film area. The stability is revealed in the region near the rotating axis due to centrifugal force and MHD-effects. The influence of the rotational motion, disk size and Hartmann number on the equilibrium finite amplitude is studied and characterized. Several numerical examples are presented to show the effectivity of the modeling approach.