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The fluid profile during spin-coating over a small sinusoidal topography. (English) Zbl 1155.76329

Summary: 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.

MSC:

76D45 Capillarity (surface tension) for incompressible viscous fluids
76D08 Lubrication theory
76A20 Thin fluid films
34E10 Perturbations, asymptotics of solutions to ordinary differential equations
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