On the Motion of Spheres in a Fluid at Low Reynolds Numbers (Two Equal-Sized Spheres Moving Along Their Center Lines)

抄録

The velocities and drag forces experienced by two equal-sized spheres freely falling along their center lines are measured using the "falling-spheres" technique at low Reynolds numbers. The width of the test tank, which has a square cross section, is 100 times the diameter of the spheres used. The measurements, with an estimated uncertainty of ±1.2%, show that the lower sphere experiences the Oseen drag and that the upper sphere experiences the Stokes drag, which was predicted by Stimson and Jeffery. Flow visualization using a naturally occurring phenomenon in glycerol illustrates the difference in the hydrodynamic drag force between the lower sphere and the upper sphere. The numerical calculations of Stimson-Jeffery's solution reveal in detail the occurrence of vortex flows within a closed separating region between the two spheres.