Slow Rotation of an Annular Disk in a Viscous Fluid

Abstract

Slow rotation of a thin circular annulus about an axis through the center of the annulus in an unbounded viscous fluid is investigated on the basis of the Stokes approximation. By using a general solution of the Stokes equations in cylindrical coordinates the problem is formulated as a set of triple integral equations which are reduced to a Fredholm integral equation of the second kind. It is shown that the annular disk is isotropic with respect to rotation about its center. By solving the Fredholm integral equation numerically, the couple on the annulus is given graphically as a function of the ratio of the inner to outer radius.