Lateral Velocity of a Small Sphere Sedimenting in a Viscous Fluid between Two Concentric Cylinders

Abstract

A theoretical study has been made of the lateral velocity of a small sphere sedimenting with a velocity U in a viscous fluid between two concentric circular cylinders. The ratio e of the particle radius a to the distance L between two concentric cylinders, and the particle Reynolds number R e (= U a /ν) are assumed small. The cylinder Reynolds number R L (= U L /ν= R e / e ), however, is assumed finite. Lateral velocity of first-order in R e is obtained using the method of matched asymptotic expansions. Even if its radius is much smaller than the outer cylinder radius, the effect of the inner cylinder cannot be neglected. When a cylinder, whose radius is 0.01 times the radius of the outer cylinder is placed at the axis of the cylinder the lateral equillibrium position of the sphere is at a distance of about 0.3 times the outer cylinder radius from the axis.