On the hydrodynamics of pairs of spheres falling along their line of centres in a viscous medium
Journal of Fluid Mechanics, 34 (4):
809--819 (1968)DOI: 10.1017/s0022112068002259
Abstract
The velocities, accelerations and drag forces experienced by two equal spheres falling along their line of centres in a viscous fluid were determined for three groups of Reynolds numbers R in the range where it is commonly assumed that Stokes's approximation applies. For all groups, with R ranging between 0·060 and 0·216, both spheres continually acclerated as they fell, and the upper sphere fell faster and accelerated more than the lower one. In contrast to Stimson & Jeffery's (1926) theory, which is based on the Stokes approximation, and to most earlier experimenters, the drag-force coefficients of the upper sphere computed from the experiments were significantly smaller than those for the lower sphere. Oseen's theory for this case agreed with the experiments in some respects, but contrary to it the drag-force coefficient varied with R for the upper sphere as well as the lower sphere.