The fluid profile during spin-coating over a small sinusoidal topography

We consider spin-coating over a small sinusoidal topography modelling the physical problem of the coating of a television screen. This involves depositing a phosphor layer on a substrate with a precoating consisting of small parallel striations. Despite the fact that the basic flow is radial, we show that the final liquid coating does not have radial variation; rather, it varies according to the underlying topography. We use a thin film model resulting in an evolution equation for the fluid thickness and sketch several techniques for obtaining approximate solutions in appropriate limiting situations.