Hydromechanics of low-Reynolds-number flow. Part 6. Rotation of oblate bodies
Journal
Journal of Engineering Mathematics
Journal Volume
20
Journal Issue
4
Pages
307-322
Date Issued
1986
Author(s)
Abstract
Uniform ring distributions of fundamental singularities for Stokes flows, Stokeslets and rotlets, are applied to obtain exact solutions for rotating oblate bodies in an unbounded viscous fluid. The technique used in the present investigation is the inverse-problem approach. Instead of determining the types of singularities and their spatial distributions for a given body geometry, the body shape is determined for a given distribution of singularities. The rotating axis of a body is perpendicular to the plane containing the ring and it passes through the center of the circular ring. The direction of rotlets is parallel to the rotating axis, while the Stokeslets are tangent to the ring and lie in its plane. By changing the radius of the ring and/or changing the strengths of Stokeslets and rotlets, we obtain a family of rotating oblate bodies including simply-connected and doubly-connected bodies. Two special cases involving a slightly deformed sphere and a spinning slender torus are also discussed. © 1986 Martinus Nijhoff Publishers.
Type
journal article