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

Abstract

Paper presented at the 7th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Turkey, 19-21 July, 2010.This paper investigates the stability of a thin electrically conductive fluid under the applied uniform magnetic filed during spin coating. A generalized nonlinear kinematic model is derived by the long-wave perturbation method to represent the physical system. After linearizing the nonlinear evolution equation, the method of normal mode is applied the linear stability. The weakly nonlinear dynamics of a film flow are studied by the multiple scales method. The Ginzburg-Landau equation is determined to discuss the necessary conditions of the various states of the critical flow states, namely sub-critical stability, sub-critical instability, supercritical stability and supercritical explosion. The study reveals that the rotation number and the radius of the rotating circular disk generate similar destabilizing effects but Hartman number gives a stabilizing effect. Moreover, the optimum conditions can be found to alter stability of the film flow by controlling the applied magnetic field.