Translational drag coefficients of assemblies of spheres with higher-order hydrodynamic interactionsa)

Calculations were made of the anisotropic translation drag coefficients of rigid assemblies of spheres in a variety of arrays, including lines, circular equilateral polygons, disks (polygons with a central sphere), and stacked squares. The objective was to compare results obtained using polynomial expansions for the two-body hydrodynamic interaction tensor truncated at the (a/r) 1 , (a/r)3, (a/r)S, and (a/r)71evels. Calculations were also made with the threeand four-body hydrodynamic interaction tensors recently obtained by Mazur and van Saarlos, thereby examining the relative importance of two-, three-, and four-body interactions. There are substantial cancellations between terms of order (a/r)s and (a/r)7, and between the threeand fourbody hydrodynamic interactions. For the arrays studied here the Rotne-Prager [two-body, (a/r)3] hydrodynamic interaction tensor gives results which are at least as satisfactory as the results obtained from the full Mazur-van Saarlos [four-body, (a/r)7] interaction tensors.