Numerical Analysis of Equation of Motion for a Cluster of Spheres in Fluid at Low Reynolds Numbers.

Abstract

The equation of motion for a cluster of spheres moving in fluid at low Reynolds numbers is developed under the consideration of hydrodynamic interaction among the spheres. The hydrodynamic forces of the spheres in the equation of motion are estimated using their relative velocities. The relative velocities are derived by applying the conventional reflection method for the Stokes flow field to the newly developed reflection method for the Oseen flow field. In order to discuss the effectiveness of this method, experiments on two equal-sized spheres with equal densities falling freely in quiescent glycerol are carried out. The width of the test tank with a square cross section is 100 times the sphere diameter. The positions of the spheres with time lapse are measured using a stroboscope-camera system. The numerical results show good agreement with the experimental results.