Film flow thickness along the outer surface of rotating cones

A thin liquid film flow goes fully upward along the outer surface of a rotating cone, when the cone is immersed in the liquid, turned upside down and rotated. We derive equations for the velocities and the film thickness of the rising film flow by using the boundary layer theory, and solve them analytically and numerically. The film thickness is obtained analytically in the centrifugal zone, while it is numerically in the Coriolis zone where two different branches with a turning point are found. It is proven that the upper branch is unstable for normalized film thickness δ+>3 from Rayleigh's criterion.