Gravitational Sedimentation of Several Spheres

By the reflection method, some relations between the drag force F and the sedimentation velocity U averaged with respect to various orientations of particles of equal radius in space were obtained in [179]. It was assumed that the maximum distance l between the sphere centers is much larger than their radius a. In all considered cases, the drag force is described by formula (2.9.1), where A is the correction coefficient depending on the configuration of the system of particles. In what follows, we write out the correction coefficient for some typical configurations of particles. 

For a system of four spheres arranged in vertices of a square, one has 

Flow past periodic arrays of spheres was studied in [87, 517], 

External boundary shape Particle center position Motion direction k 

---