In my work investigating suspensions in viscoelastic fluids using Stokesian dynamics, I found that there were a number of small errors in the important paper
Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow.
Journal of Fluid Mechanics 139, 261–290.
A partial list of errata has been published by Kengo Ichiki, and some of these errors appear to have been noticed by authors using this paper in their extensions. Here I present a full list of errata and a comprehensive description of how to fully generate, from scratch, the corrected near-field asymptotic forms of scalar resistance functions,
$$X^A_{11}, X^A_{12}, Y^A_{11}, Y^A_{12}, Y^B_{11}, Y^B_{12}, X^C_{11}, X^C_{12}, Y^C_{11}, Y^C_{12},$$
$$X^G_{11}, X^G_{12}, Y^G_{11}, Y^G_{12}, Y^H_{11}, Y^H_{12}, X^M_{11}, X^M_{12}, Y^M_{11}, Y^M_{12}, Z^M_{11}, Z^M_{12}.$$
Originally posted on the arXiv in 2018, correspondence from teams using the work has led to improvements and it was published in Physics of Fluids in December 2023.
In the work, I use two later, useful papers:
The calculation of the low Reynolds number resistance functions for two unequal spheres.
Physics of Fluids A: Fluid Dynamics (1989–1993) 4(1), 16–29.
Resistance functions for two unequal spheres in linear flow at low Reynolds number with the Navier slip boundary condition.
arXiv:1302.0461 [cond-mat, physics:physics].
Equations in these papers will be referenced as:
| Jeffrey & Onishi (1984) | (JO 1.1) |
| Jeffrey (1992) | (J 1) |
| Ichiki et al. (2013) | (I 1) |
The full expressions can be downloaded below as an open-access PDF: