Spin-coating of a viscoplastic material

The flow of a thin film of a yield-stress material on a rotating disc is considered. For the constitutive relation we use the biviscosity model, of which the usual Bingham model is a limiting case. We show that this limiting process conflicts with the usual thin film approximation, so that care is needed to avoid contradictions. It is found that the flow consists of three regions: (1) an inner region centered on the axis of rotation which is unyielded, (2) a shear flow region adjacent to the disc which is bounded above by the yield surface and (3) a region near to the free surface which is unyielded and has the yield surface as lower boundary. It is in the third region that difficulties occur in the straightforward ‘‘Bingham limit.’’ For on the one hand the material is rigid, and on the other it is supposed to move outwards radially. This conflict can be removed by using the biviscosity model and a suitable limiting process.