Motion of a Sphere in a Viscous Fluid

Abstract

This problem was originally attacked by Stokes, and the formula obtained by Stokes for the case of steady motion (given at the end of § 1 below) is now generally used in experimental work. However, this formula throws no light on the way in which the velocity of the sphere approaches its steady value: and the only known discussion of this problem was given by Boggio (his results will be found in § 2 below). Unfortunately, when the specific gravity of the sphere exceeds ⅝ (or the constant σ, defined later, is less than 4) the solution so obtained cannot be converted into numerical results, because the constants α, β become complex numbers; and even when α, β are real, the formula is not very convenient for large values of t (as the velocity approaches the steady value).