The effect of air shear on the flow of a thin liquid film over a rough rotating disk

The depletion of thin liquid films due to the combined effect of centrifugation, surface roughness, and air shear is addressed. As a liquid film flows on a horizontal rotating solid surface, it is thinned by both inertial forces as well as by shearing forces at the liquid-air interface. The equations describing the flow of a thin viscous film over a rough rotating disk are solved by numerical techniques. Depletion histories of the thin film are given for several cases involving both deterministic and random surface asperities. It is noted that surface roughness of a rotating disk markedly enhances the retention of the thin liquid film. The thinner the liquid layer, the more significant is the effect of surface roughness. On the other hand, shearing forces between the free liquid surface and ambient air increase the depletion of the liquid film at a rate that is dependent on the speed of rotation. In general, inertial forces play a secondary role in the depletion of very thin films; the asymptotic limits of liquid retention are strongly influenced by the topographic structures of the surface roughness and the air shear.