STOKES DRAG ON A CIRCULAR ANNULUS

Abstract

Slow translation of a thin circular annulus in an unbounded viscous fluid is investigated on the basis of the Stokes approximation. Using a general solution for the Stokes flow, the problem is reduced to that of finding harmonic functions which satisfy three-part mixed boundary conditions. The formal expression for the flow is obtained by solving a set of triple integral equations. The solution is found after reducing the triple integral equations to integral equations which are amenable to treatment by well-tried numerical procedures. The drag exerted on the annulus is determined for various ratios of the inner to outer radius. Asymptotic expressions for the drag are obtained for a slender annulus.