  The axisymmetric flow of a thin liquid film is considered for the problem of
a vertically rotating disk that is partially immersed in a liquid bath. A model
for the fully three-dimensional free-boundary problem of the rotating disk,
that drags a thin film out of the bath is set up. From this, a
dimension-reduced extended lubrication approximation that includes the meniscus
region is derived. This problem constitutes a generalization of the classic
drag-out and drag-in problem to the case of axisymmetric flow. The resulting
nonlinear fourth-order partial differential equation for the film profile is
solved numerically using a finite element scheme. For a range of parameters
steady states are found and compared to asymptotic solutions. Patterns of the
film profile, as a function of immersion depth and angular velocity are
discussed.
