Steady-state coating flows inside a rotating horizontal cylinder

Abstract

Thin coating flows inside a rotating circular cylinder are investigated when the axis of rotation is perpendicular to the direction of gravity. Attention is restricted to flows of power-law fluids having negligible inertia. Four distinct steady-state liquid-film profiles are found to be possible. Two of the cases correspond to a continuous coating, i.e. films that cover the entire inner surface of the cylinder. The other two cases involve partial films covering a limited portion of the cylinder surface. Of the two continuous films, one is the expected configuration involving a coating that gradually changes in thickness as one moves around the cylinder, the film being thicker on the ascending portion of the cylinder and thinner on the descending portion. The second continuous-film configuration has regions on the rising side of cylinder where a rapid change in depth is possible. This case also has the potential to have recirculating zones where a portion of the fluid is trapped in either one or two eddies at fixed locations on the rising side of the cylinder. Of the two partial films, one corresponds to a weakly deformed puddle at the bottom of the cylinder and is the appropriate solution at small rotation rates. The second partial film is a film which coats a portion of the ascending side of the cylinder, the extent of which depends on the film volume.