Friction coefficient of rod-like chains of spheres at very low Reynolds numbers. II. Numerical simulations

(Received 30 November 1993, received in final form 11 February 1994, accepted 18 February 1994)

Abstract
Experiments on the sedimentation of chains of spherical particles in a viscous fluid are presented in the preceding paper [1]. In this paper, we compare the predictions of numerical simulations based on Stokesian dynamics to the experimental results reported in reference [1], and to analytical expressions available for this problem. For unbounded fluids, the experimental measured velocity and the numerical results are compared to slender body theory. This comparison shows a correct agreement for a ratio of the length of the chain to its diameter as small as 5. When the fluid is limited by a wall, we use the expression given by Brenner [3] for the friction coefficient of particles in a bounded fluid. We find that this relation holds even for distances that are smaller than the length of the chain. The good agreement between the numerical and the experimental results shows the reliability of the Stokesian dynamics for simulating the hydrodynamical interactions between all the particles and the wall.