THEORETICAL AND EXPERIMENTAL ANALYSES OF THE MAXIMUM-SUPPOTABLE FLUID LOAD ON A ROTATING CYLINDER

Thin-film theory is used to derive an implicit criterion for the existence of a viscous, free-surface flow on the outer surface of a rotating circular cylinder. We estimate both the maximum fluid load supportable at a given Stokes number, and the maximum Stokes number permitting the support of a prescribed fluid load. The results of our theory are in excellent agreement with those obtained from an independent, numerical solution of the full Stokes equations; the comparison reveals that our thin-film theory works well beyond its expected range of validity. Explicit existence criteria, in the form of small-parameter expansions, are presented for the extreme cases of small fluxes and large Stokes numbers. We derive an expression for the minimum angular velocity which will support a given load; our results show qualitative agreement with those of basic experiments.