Translational drag coefficients of assemblies of spheres with higher‐order hydrodynamic interactions

Abstract

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)5, and (a/r)7 levels. Calculations were also made with the three‐ and 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)5 and (a/r)7, and between the three‐ and four‐body 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.