Slow Rotation of a Disk in a Fluid-Filled Circular Cylinder

Abstract

Steady symmetric rotation of a disk in an infinitely long circular cylinder is considered on the basis of the Stokes approximation. A series expression in powers of the disk-cylinder radius ratio is obtained for the torque necessary to maintain the rotation. As the ratio approaches to unity, the torque increases logarithmically and the estimate from the series expression is shown to agree well with that from an exact asymptotic theory.