= 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 by
$$
\delta\mathbf U=-\frac{15a^4}{4R^6}(\mathbf U_0\cdot\mathbf R)\mathbf R.
$$
The 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.
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