STEADY, VISCOUS, FREE-SURFACE FLOW ON A ROTATING CYLINDER

The commonly observed phenomenon of steady, viscous, free-surface flow on the outer surface of a rotating cylinder is investigated by means of an iterative, integral-equation formulation applied to the Stokes a pproximation of the Navier-Stokes equations. The method of solution pl aces no restriction on the thickness of the fluid layer residing on th e cylinder surface; indeed, results are presented for cases where the layer thickness is of the same order of magnitude as the cylinder radi us. Free-surface profiles and free-surface velocity distributions are presented for a range of flow parameters. Where appropriate, compariso ns are made with the results of thin-film theory; excellent agreement is observed. For all film thicknesses and surface tensions, results sh ow a high degree of symmetry about a horizontal axis even though the g ravity field is vertical. A proof is presented that, for vanishing sur face tension, this is a consequence of the Stokes approximation.