Thin liquid droplet on top of a rotating non-isothermal liquid layer

Wafers are usually coated by using spin-coating, where centrifugal forces are used to spread a droplet on the rotating wafer. This flow is unstable to the fingering instability, where several segments of the wetting front spread faster than the average, resulting in several fingers. The liquid flows via the existing fingers while the area in between does not get coated. A precise experimental investigation is problematic, as the droplet has to be placed quite exactly in the center of the rotation. Replacing the wafer by a second liquid should lead to a parabolic-shaped free interface and the droplet should center itself due to gravity. Here, we derive a model for the free interfaces of a thin droplet on top of a rotating liquid by taking gravity, centrifugal forces, friction, (thermo-)capillary and line forces into account. Additionally, this setup is the simplest example of multiple coating, where several free interfaces and contact lines influence each other. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)