Spin coating in the presence of a transverse magnetic field and non-uniform rotation: a numerical study

The development of a thin liquid film under non-uniform rotation and in the presence of transverse magnetic field has been studied numerically by usin g the finite-difference technique under the assumption of a planar interfac e. Similarity variables were used to transform the axisymmetric Navier-Stok es equations into a set of coupled, nonlinear, unsteady, partial differenti al equations. The time-dependent free surface was mapped into a finite fixe d computational domain. It is shown that the rate of him thinning slowed do wn by increasing either the Hartmann or Eckman number. It is also observed that a small change in the Eckman number has a stronger effect in film thin ning than that for the Hartmann number. Furthermore, it is found that a fas ter rate of thinning can be obtain if the spinner starts impulsively and th en increases its spinning rate continuously.