The motion of a sphere in a cylinder filled with a viscous liquid and with a diameter slightly larger than the sphere diameter

The flow around a sphere, moving under the influence of gravity in a long cylinder filled with a viscous liquid, is investigated, for the case where the inside diameter of the tube is only slightly larger than the diameter of the sphere. For low Reynolds numbers, an extension of the Christopherson and Dowson (1) theory is obtained in the form of a first order Reynolds number correction. It is shown that the fluid exerts a first order inertial force on the ball, tending to increase the eccentricity ratio. The sideways motion of the ball due to this force has been calculated approximately. For very high Reynolds numbers, a potential flow solution has been found in the form of a Fourier series. This solution also yields a force tending to increase the eccentricity ratio. Experiments have been done for intermediate Reynolds numbers. The motion of the ball appears to be unstable when the Reynolds number exceeds a critical value (about 10)