Sedimentation of a dilute suspension

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Abstract
Two methods, based upon the idea of multiple scattering, are used to calculate the sedimentation velocity of a dilute suspension of identical rigid spheres. One method is valid when the correlation length l of the distribution of spheres is large compared to the sphere radius a. For dilute simple cubic arrays it yields Hasimoto’s [J. Fluid Mech. 5, 317 (1959)] result. The second method applies for all values of l/a. For a dilute uniform homogeneous distribution it yields Batchelor’s [J. Fluid Mech. 5 2, 245 (1972)] result. Both methods apply to other distributions and to other flows of dilute suspensions.