On the spin coating of viscoplastic fluids

The spin coating of a viscoplastic material is studied using a continuous viscosity function. Thus, the transient model requires the calculation of only velocity, pressure and the moving-free surface of the liquid film, but not the calculation of the yield surface within the liquid. A Finite Element/Newton-Raphson method is presented for solving this moving boundary problem after mapping the deforming domain onto a fixed one. Assuming axial symmetry, the effect of the Bingham, Reynolds, Capillary and gravitational Bond numbers is examined. The magnitude of the first two parameters affects significantly the flow field and the shape of the film as well as the required spinning time in order to produce a film of uniform thickness. Depending on their values, large departures from the corresponding Newtonian solution may be obtained. In these cases the film does not thin out uniformly, but a maximum in its profile is created at the center of the disk. Then, the magnitude of the Capillary number also affects the size of this maximum. The gravitational Bond number affects the film thickness and its profile to a lesser extent.Dedicated to the memory of Professor Tasos C. Papanastasiou