Periodic Motions of a Viscous Fluid past a Sphere in a Cylindrical Tube

概要

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Slow periodic motions of a viscous incompressible fluid past a sphere in an infinitely long circular cylinder are considered. The basic equations are the Navier-Stokes equations of motion linearized by omitting convection terms. The primary parameters involved are a/R_0, b/R_0, a^2ω/v and R^2_0ω/v, where a and R_0 are the radii of the sphere and cylinder respectively, b is the distance of the particle from the cylinder axis, and ω/v is the angular frequency divided by the kinematic viscosity. The drag and couple acting on the sphere and the translational and angular velocities of the sphere floating in the stream are finally given in the forms of power series with respect to these parameters.
1966-10-05