Self-mobility correction from a distant force-free sphere

For two equal spheres of radius $a$ separated by $\mathbf{R}$, let the first have applied force $\mathbf{F}$ and let the second be force-free and torque-free. With ${\mathbf{U}}_0=\mathbf{F}/(6\pi \mu a)$, the leading reflected stresslet changes the first velocity byThe distant sphere's freely translating and rotating rigid motions remove its monopole force and torque fields; its incident rate-of-strain tensor produces the first self-mobility correction.