Rimming flow of liquid in a rotating cylinder

Abstract

Steady two-dimensional flow of Newtonian liquid in a layer around the inside of a rotating horizontal cylinder is analysed as a regular perturbation from rigid-body motion. The equations governing the first perturbation are solved in closed form. Parameter limits are taken in order to elucidate the flow structure and to provide simpler working formulae. The limiting cases are for small Reynolds numbers, which resembles viscous film flow down a curved wall; for large Reynolds numbers, which involves a periodic boundary layer; and for small ratios of average film thickness to cylinder radius. In every case the maximum film thickness occurs in the upper quadrant on the rising side of the cylinder and the minimum thickness is diametrically opposite.