Solidification and downstream meniscus prediction in the planar-flow spin casting process

A mathematical model describing the fluid flow, heat transfer and solidification in planar-flow spin casting is introduced. Asymptotic solutions are derived, including expressions for key physical quantities such as the solid/liquid and liquid/gas interfaces. The time-dependent fluid flow in the turning and nearly rectilinear regions is investigated numerically. A recirculation region, in which vorticity accumulates over time, is shown to form immediately downstream of the nozzle. A significant part of this region is periodically washed downstream. As its vorticity diffuses, it eventually fills a large portion of the available gap. This large recirculation region, which restricts the mass flow by almost entirely blocking the gap, is proposed as the physical mechanism for the detachment of the downstream meniscus.