The run-off condition for coating and rimming flows

A layer of liquid can be supported on the inside or outside of a horizontal rotating cylinder if the viscous forces pulling the liquid around with the cylinder are large enough to overcome the force of gravity. If there are places on the cylinder where the thickness of the layer is larger than a critical value, the excess fluid will run off. For a given maximum thickness the critical condition may be expressed as the minimum speed at which the given layer can be maintained. An approximation of the critical condition using lubrication theory was given by Wallis (1969) and by Deiber & Cerro (1976) for rimming flow and by Moffatt (1977) for coating and rimming flow. Here we address the question of the axial variations of the free surface on the coating layers, and show that they are dominated by the same type of balance between capillarity and centripetal acceleration which determines the shape of rotating drops and bubbles in the absence of gravity. The main results of this paper are the experiments which establish the validity of approximations used to describe the underlying fluid mechanics involved in rimming and coating flows.