On the Slow Motion of a Sphere in a Viscous Fluid

抄録

The flow around a spinning sphere moving in a viscous fluid is considered, on the basis of the Navier-Stokes equations, using the method of matched asymptotic expansions for small values of the Reynolds number. With this solution the force and torque on the sphere are computed. It is found that, in addition to the drag force, the sphere experiences a force orthogonal to its direction of motion, and that the drag is increased in proportion to the square of the spin velocity. It is also shown that the retarding torque is so exerted that the axis of rotation with any initial direction eventually settles down to be perpendicular to the direction of motion.