Numerical Analysis of Equation of Motion for a Cluster of Spheres in Fluid at Low Reynolds Numbers by Superposing Oseen's Flow Field.

Abstract

The equation of motion for a cluster of solid spheres moving in fluid at low Reynolds numbers is developed taking into 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 assumed to be represented by superposing Oseen's flow field around each sphere. When the inertia term is negligible in the equation of motion for the spheres, it is shown that the analytical solutions are easily obtained for free-fall motions of solid spheres in fluid. In order to discuss the effectiveness of the above-described method, experiments for two equal spheres falling freely in quiescent glycerol are carried out. The numerical results show good agreement with the experimental results.