Two regimes of liquid film flow on a rotating cylinder

A steady flow of a thin film of a viscous incompressible liquid on a rotating cylinder (the cylinder axis is perpendicular to the direction of the force of gravity) is considered. Capillary effects are taken into account on the free surface. Thin-layer equations derived by Pukhnachov, which depend on the Galileo number and capillary number, are solved. If the first parameter equals zero, the force of gravity also equals zero. If the second parameter equals zero, the surface-tension coefficient also equals zero. The values of these parameters that ensure the solution existence and the number of solutions are determined by the method of collocations. One more solution corresponding to the drop-shaped free surface is found numerically. Variations of flow parameters caused by variations of the Galileo number and capillary number are considered. Branching of the solutions is examined numerically.