The motion of two spheres in a viscous fluid

Abstract

Abstract The problem of this paper is to determine the motion set up in a viscous fluid at rest at infinity by two solid spheres (equal or unequal) moving with equal small constant velocities parallel to their line of centres. The same analysis is immediately applicable to the corresponding problem in which the spheres are fixed and the fluid streams past them with constant velocity. The solution is based on the determination of Stokes’ stream-function for the motion of the fluid, and from this the forces necessary to maintain the motion of the spheres are calculated.