Change to unsymmetrical motion of two particles with respect to the axis settling inside a vertical tube

The motion of two rigid spheres settling in a viscous fluid inside a circular cylinder is investigated both theoretically and experimentally. The ratio of the particle radius to the cylinder radius, and the particle Reynolds number are small. The cylinder Reynolds number based on the cylinder radius is finite. At the cylinder Reynolds number 6.74,two settling spheres change the motion to unsymmetrical one from the symmetrical motion with respect to the cylinder axis. As cylinder Reynolds number become large, two spheres are forced towards the equilibrium positions. Method of matched asymptotic expansions was used.